## CryptoDB

### Papers from ASIACRYPT 2024

**Year**

**Venue**

**Title**

2024

ASIACRYPT

A new security evaluation method based on resultant for arithmetic-oriented algorithms
Abstract

The rapid development of advanced cryptographic applications like multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge (ZK) proofs have motivated the designs of the so-called arithmetic-oriented (AO) primitives. Efficient AO primitives typically build over large fields and use large S-boxes. Such design philosophy brings difficulties in the cryptanalysis of these primitives as classical cryptanalysis methods do not apply well. The generally recognized attacks against these primitives are algebraic attacks, especially Gr\"obner basis attacks. Thus, the numbers of security rounds are usually derived through the complexity of solving the system of algebraic equations using Gr\"obner bases.
In this paper, we propose a novel framework for algebraic attacks against AO primitives. Instead of using Gr\"obner basis, we use {\it resultants} to solve a system of multivariate equations that can better exploit the algebraic structures of AO primitives. We employ several techniques to redu

2024

ASIACRYPT

A Tight Security Proof for SPHINCS+, Formally Verified
Abstract

SPHINCS+ is a post-quantum signature scheme that, at the
time of writing, is being standardized as SLH-DSA. It is the most conser-
vative option for post-quantum signatures, but the original tight proofs
of security were flawed — as reported by Kudinov, Kiktenko and Fe-
dorov in 2020. In this work, we formally prove a tight security bound
for SPHINCS+ using the EasyCrypt proof assistant, establishing greater
confidence in the general security of the scheme and that of the param-
eter sets considered for standardization. To this end, we reconstruct the
tight security proof presented by Hülsing and Kudinov (in 2022) in a
modular way. A small but important part of this effort involves a com-
plex argument relating four different games at once, of a form not yet
formalized in EasyCrypt (to the best of our knowledge). We describe
our approach to overcoming this major challenge, and develop a general
formal verification technique aimed at this type of reasoning.
Enhancing the set of reusable EasyCrypt artifacts previously produced
in the formal verification of stateful hash-based cryptographic construc-
tions, we (1) improve and extend the existing libraries for hash func-
tions and (2) develop new libraries for fundamental concepts related to
hash-based cryptographic constructions, including Merkle trees. These
enhancements, along with the formal verification technique we develop,
further ease future formal verification endeavors in EasyCrypt, especially
those concerning hash-based cryptographic constructions.

2024

ASIACRYPT

Actively Secure Polynomial Evaluation from Shared Polynomial Encodings
Abstract

Many of the currently best actively secure Multi-Party Computation (MPC) protocols like SPDZ (Damgård et al., CRYPTO 2012) and improvements thereof use correlated randomness to speed up the time-critical online phase. Although many of these protocols still rely on classical Beaver triples, recent results show that more complex correlations like matrix or convolution triples lead to more efficient evaluations of the corresponding operations, i.e. matrix multiplications or tensor convolutions. In this paper, we address the evaluation of multivariate polynomials with a new form of randomness: polytuples. We use the polytuples to construct a new family of randomized encodings which then allow us to evaluate the given multivariate polynomial. Our approach can be fine-tuned in various ways to the constraints of applications at hand, in terms of round complexity, bandwidth, and tuple size. We show that for many real-world setups, a polytuples-based online phase outperforms state-of-the-art protocols based on Beaver triples.

2024

ASIACRYPT

Adaptive Hardcore Bit and Quantum Key Leasing over Classical Channel from LWE with Polynomial Modulus
Abstract

Quantum key leasing, also known as public key encryption with secure key leasing (PKE-SKL), allows a user to lease a (quantum) secret key to a server for decryption purpose, with the capability of revoking the key afterwards. In the pioneering work by Chardouvelis et al (arXiv:2310.14328), a PKE-SKL scheme utilizing classical channels was successfully built upon the noisy trapdoor claw-free (NTCF) family. This approach, however, relies on the superpolynomial hardness of learning with errors (LWE) problem, which could affect both efficiency and security of the scheme.
In our work, we demonstrate that the reliance on superpolynomial hardness is unnecessary, and that LWE with polynomial-size modulus is sufficient to achieve the same goal. Our approach enhances both efficiency and security, thereby improving the practical feasibility of the scheme on near-term quantum devices. To accomplish this, we first construct a noticeable NTCF (NNTCF) family with the adaptive hardcore bit property, based on LWE with polynomial-size modulus. To the best of our knowledge, this is the first demonstration of the adaptive hardcore bit property based on LWE with polynomial-size modulus, which may be of independent interest. Building on this foundation, we address additional challenges in prior work to construct the first PKE-SKL scheme satisfying the following properties: (i) the entire protocol utilizes only classical communication, and can also be lifted to support homomorphism. (ii) the security is solely based on LWE assumption with polynomial-size modulus.
As a demonstration of the versatility of our noticeable NTCF, we show that an efficient proof of quantumness protocol can be built upon it. Specifically, our protocol enables a classical verifier to test the quantumness while relying exclusively on the LWE assumption with polynomial-size modulus.

2024

ASIACRYPT

Adaptor Signatures: New Security Definition and A Generic Construction for NP Relations
Abstract

An adaptor signatures (AS) scheme is an extension of digital signatures that allows the signer to generate a pre-signature for an instance of a hard relation. This pre-signature can later be adapted to a full signature with a corresponding witness. Meanwhile, the signer can extract a witness from both the pre-signature and the signature. AS have recently garnered more attention due to its scalability and interoperability. Dai et al. [INDOCRYPT 2022] proved that AS can be constructed for any NP relation using a generic construction. However, their construction has a shortcoming: the associated witness is exposed by the adapted signature. This flaw poses limits the applications of AS, even in its motivating setting, i.e., blockchain, where the adapted signature is typically uploaded to the blockchain and is public to everyone.
To address this issue, in this work we augment the security definition of AS by a natural property which we call witness hiding. We then prove the existence of AS for any NP relation, assuming the existence of one-way functions. Concretely, we propose a generic construction of witness-hiding AS from signatures and a weak variant of trapdoor commitments, which we term trapdoor commitments with a specific adaptable message. We instantiate the latter based on the Hamiltonian cycle problem. Since the Hamiltonian cycle problem is NP-complete, we can obtain witness hiding adaptor signatures for any NP relation.

2024

ASIACRYPT

An Algorithmic Approach to $(2,2)$-isogenies in the Theta Model and Applications to Isogeny-based Cryptography
Abstract

In this paper, we describe an algorithm to compute chains of $(2,2)$-isogenies between products of elliptic curves in the theta model. The description of the algorithm is split into various subroutines to allow for a precise field operation counting.
We present a constant time implementation of our algorithm in Rust and an alternative implementation in SageMath. Our work in SageMath runs ten times faster than a comparable implementation of an isogeny chain using the Richelot correspondence. The Rust implementation runs up to forty times faster than the equivalent isogeny in SageMath and has been designed to be portable for future research in higher-dimensional isogeny-based cryptography.

2024

ASIACRYPT

Analysis on Sliced Garbling via Algebraic Approach
Abstract

Recent improvements to garbled circuits are mainly focused on reducing their size.
The state-of-the-art construction of Rosulek and Roy~(Crypto~2021) requires $1.5\kappa$ bits for garbling AND gates in the free-XOR setting.
This is below the previously proven lower bound $2\kappa$ in the linear garbling model of Zahur, Rosulek, and Evans~(Eurocrypt~2015).
Recently, Ashur, Hazay, and Satish~(eprint 2024/389) proposed a scheme that requires $4/3\kappa + O(1)$ bits for garbling AND gates.
Precisely they extended the idea of \emph{slicing} introduced by Rosulek and Roy to garble 3-input gates of the form $g(u,v,w) := u(v+w)$.
By setting $w = 0$, it can be used to garble AND gates with the improved communication costs.
However, in this paper, we observe that the scheme proposed by Ashur, Hazy, and Satish leaks information on the permute bits,
thereby allowing the evaluator to reveal information on the private inputs.
To be precise, we show that in their garbling scheme, the evaluator can compute the bits $\alpha$ and $\beta + \gamma$,
where $\alpha$, $\beta$, and $\gamma$ are the private permute bits of the input labels $A$, $B$, and $C$, respectively.

2024

ASIACRYPT

Anamorphic Authenticated Key Exchange: Double Key Distribution under Surveillance
Abstract

Anamorphic encryptions and anamorphic signatures assume a double key pre-shared between two parties so as to enable the transmission of covert messages. How to securely and efficiently distribute a double key under the dictator's surveillance is a central problem for anamorphic cryptography, especially when the users are forced to surrender their long-term secret keys or even the randomness used in the algorithms to the dictator.
In this paper, we propose Anamorphic Authentication Key Exchange (AM-AKE) to solve the problem. Similar to anamorphic encryption, AM-AKE contains a set of anamorphic algorithms besides the normal algorithms. With the help of the anamorphic algorithms in AM-AKE, the initiator and the responder are able to exchange not only a session key but also a double key. We define robustness and security notions for AM-AKE, and also prove some impossibility results on plain AM-AKE whose anamorphic key generation algorithm only outputs a key-pair. To bypass the impossibility results, we work on two sides.
-- On the one side, for plain AM-AKE, the securities have to be relaxed to resist only passive attacks from the dictator. Under this setting, we propose a generic construction of two-pass plain AM-AKE from a two-pass AKE with partially randomness-recoverable algorithms.
-- On the other side, we consider (non-plain) AM-AKE whose key generation algorithm also outputs an auxiliary trapdoor besides the key-pairs. We ask new properties from AKE: its key generation algorithm has secret extractability and other algorithms have separability. Based on such a two-pass AKE, we propose a generic construction of two-pass (non-plain) AM-AKE. The resulting AM-AKE enjoys not only robustness but also the strong security against any dictator knowing both users' secret keys and even the internal randomness of the AKE algorithms and implementing active attacks.
Finally, we present concrete AM-AKE schemes from the popular SIG+KEM paradigm and three-KEM paradigm for constructing AKE.

2024

ASIACRYPT

Attacking ECDSA with Nonce Leakage by Lattice Sieving: Bridging the Gap with Fourier Analysis-based Attacks
Abstract

The Hidden Number Problem (HNP) has found extensive applications in side-channel attacks against cryptographic schemes, such as ECDSA and Diffie-Hellman. There are two primary algorithmic approaches to solving the HNP: lattice-based attacks and Fourier analysis-based attacks. Lattice-based attacks exhibit better efficiency and require fewer samples when sufficiently long substrings of the nonces are known. However, they face significant challenges when only a small fraction of the nonce is leaked, such as 1-bit leakage, and their performance degrades in the presence of errors.
In this paper, we address an open question by introducing an algorithmic tradeoff that significantly bridges the gap between these two approaches. By introducing a parameter $x$ to modify Albrecht and Heninger's lattice, the lattice dimension is reduced by approximately $(\log_2{x})/ l$, where $l$ represents the number of leaked bits. We present a series of new methods, including the interval reduction algorithm, several predicates, and the pre-screening technique. Furthermore, we extend our algorithms to solve the HNP with erroneous input. Our attack outperforms existing state-of-the-art lattice-based attacks against ECDSA. We obtain several records including 1-bit and less than 1-bit leakage on a 160-bit curve, while the best previous lattice-based attack for 1-bit leakage was conducted only on a 112-bit curve.

2024

ASIACRYPT

Bootstrapping Small Integers With CKKS
Abstract

The native plaintexts of the Cheon-Kim-Kim-Song (CKKS) fully homomorphic encryption scheme are vectors of approximations to complex numbers. Drucker \emph{et al} [J. Cryptol.'24] have showed how to use CKKS to efficiently perform computations on bits and small bit-length integers, by relying on their canonical embeddings into the complex plane. For small bit-length integers, Chung \emph{et al} [IACR eprint'24] recently suggested to rather rely on an embedding into complex roots of unity, to gain numerical stability and efficiency. Both works use CKKS in a black-box manner.
Inspired by the design by Bae \emph{et al} [Eurocrypt'24] of a dedicated bootstrapping algorithm for ciphertexts encoding bits, we propose a CKKS bootstrapping algorithm, $\style{SI\mbox{-}BTS}$ (small-integer bootstrapping), for ciphertexts encoding small bit-length integers. For this purpose, we build upon the DM/CGGI-to-CKKS conversion algorithm from Boura \emph{et al} [J.~Math. Cryptol.'20], to bootstrap canonically embedded integers to integers embedded as roots of unity. $\style{SI\mbox{-}BTS}$ allows functional bootstrapping: it can evaluate an arbitrary function of its input while bootstrapping. It may also be used to batch-(functional-)bootstrap multiple DM/CGGI ciphertexts. For example, its amortized cost for evaluating an 8-bit look-up table on~$2^{12}$ DM/CGGI ciphertexts is~3.75ms (single-thread CPU, 128-bit security).
We adapt $\style{SI\mbox{-}BTS}$ to simultaneously bootstrap multiple CKKS ciphertexts for bits. The resulting $\style{BB\mbox{-}BTS}$ algorithm (batch-bits bootstrapping) allows to decrease the amortized cost of a binary gate evaluation. Compared to Bae \emph{et al}, it gives a 2.4x speed-up.

2024

ASIACRYPT

Bounded Collusion-Resistant Registered Functional Encryption for Circuits
Abstract

As an emerging primitive, Registered Functional Encryption (RFE) eliminates the key-escrow issue that threatens numerous works for functional encryption, by replacing the trusted authority with a transparent key curator and allowing each user to sample their decryption keys locally. In this work, we present a new black-box approach to construct RFE for all polynomial-sized circuits. It considers adaptive simulation-based security in the bounded collusion model (Gorbunov et al. - CRYPTO'12), where the security can be ensured only if there are no more than Q >= 1 corrupted users and Q is fixed at the setup phase. Unlike earlier works, we do not employ unpractical Indistinguishability Obfuscation (iO). Conversely, it can be extended to support unbounded users, which is previously only known from iO.
Technically, our general compiler exploits garbled circuits and a novel variant of slotted Registered Broadcast Encryption (RBE), namely global slotted RBE. This primitive is similar to slotted RBE, but needs optimally compact public parameters and ciphertext, so as to satisfy the efficiency requirement of the resulting RFE. Then we present two concrete global slotted RBE from pairings and lattices, respectively. With proposed compiler, we hence obtain two bounded collusion-resistant RFE schemes. Here, the first scheme relies on k-Lin assumption, while the second one supports unbounded users under LWE and evasive LWE assumptions.

2024

ASIACRYPT

C'est très CHIC: A compact password-authenticated key exchange from lattice-based KEM
Abstract

Driven by the NIST's post-quantum standardization efforts and the selection of Kyber as a lattice-based Key-Encapsulation Mechanism (KEM), several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a KEM to create an efficient, easy-to-implement and secure PAKE. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic compilers that transform KEM into PAKE, relying on an Ideal Cipher (IC) defined over a group. However, although IC on a group is often used in cryptographic protocols, special care must be taken to instantiate such objects in practice, especially when a low-entropy key is used. To address this concern, Dos Santos et al. (EUROCRYPT 2023) proposed a relaxation of the IC model under the Universal Composability (UC) framework called Half-Ideal Cipher (HIC). They demonstrate how to construct a UC-secure PAKE protocol, EKE-KEM, from a KEM and a modified 2-round Feistel construction called m2F. Remarkably, the m2F sidesteps the use of an IC over a group, and instead employs an IC defined over a fixed-length bitstring domain, which is easier to instantiate.
In this paper, we introduce a novel PAKE protocol called CHIC that improves the communication and computation efficiency of EKE-KEM, by avoiding the HIC abstraction. Instead, we split the KEM public key in two parts and use the m2F directly, without further randomization. We provide a detailed proof of the security of CHIC and establish precise security requirements for the underlying KEM, including one-wayness and anonymity of ciphertexts, and uniformity of public keys. Our findings extend to general KEM-based EKE-style protocols and show that a passively secure KEM is not sufficient. In this respect, our results align with those of Pan and Zeng (ASIACRYPT 2023), but contradict the analyses of KEM-to-PAKE compilers by Beguinet et al. (ACNS 2023) and Dos Santos et al. (EUROCRYPT 2023).
Finally, we provide an implementation of CHIC, highlighting its minimal overhead compared to the underlying KEM -- Kyber. An interesting aspect of the implementation is that we reuse the rejection sampling procedure in Kyber reference code to address the challenge of hashing onto the public key space. As of now, to the best of our knowledge, CHIC stands as the most efficient PAKE protocol from black-box KEM that offers rigorously proven UC security.

2024

ASIACRYPT

Code-Based Zero-Knowledge from VOLE-in-the-Head and Their Applications: Simpler, Faster, and Smaller
Abstract

Zero-Knowledge (ZK) protocols allow a prover to demonstrate the truth of a statement without disclosing additional information about the underlying witness. Code-based cryptography has a long history but did suffer from periods of slow development. Recently, a prominent line of research have been contributing to designing efficient code-based ZK from MPC-in-the-head (Ishai et al., STOC 2007) and VOLE-in-the head (VOLEitH) (Baum et al., Crypto 2023) paradigms, resulting in quite efficient standard signatures. However, none of them could be directly used to construct privacy-preserving cryptographic primitives. Therefore, Stern's protocols remain to be the major technical stepping stones for developing advanced code-based privacy-preserving systems.
This work proposes new code-based ZK protocols from VOLEitH paradigm for various relations and designs several code-based privacy-preserving systems that considerably advance the state-of-the-art in code-based cryptography. Our first contribution is a new ZK protocol for proving the correctness of a regular (non-linear) encoding process, which is utilized in many advanced privacy-preserving systems. Our second contribution are new ZK protocols for concrete code-based relations. In particular, we provide a ZK of accumulated values with optimal witness size for the accumulator (Nguyen et al., Asiacrypt 2019). Our protocols thus open the door for constructing more efficient privacy-preserving systems. Moreover, our ZK protocols have the advantage of being simpler, faster, and smaller compared to Stern-like protocols. To illustrate the effectiveness of our new ZK protocols, we develop ring signature scheme, group signature scheme, fully dynamic attribute-based signature scheme from our new ZK. The signature sizes of the resulting schemes are two to three orders of magnitude smaller than those based on Stern-like protocols in various parameter settings. Finally, our first ZK protocol yields a standard signature scheme, achieving ``signature size + public key size'' as small as $3.05$ KB, which is slightly smaller than the state-of-the-art signature scheme (Cui et al., PKC 2024) based on the regular syndrome decoding problems.

2024

ASIACRYPT

Compute, but Verify: Efficient Multiparty Computation over Authenticated Inputs
Abstract

Traditional notions of secure multiparty computation (MPC) allow mutually distrusting parties to jointly compute a function over their private inputs, but typically do not specify how these inputs are chosen. Motivated by real-world applications where corrupt inputs could adversely impact privacy and operational legitimacy, we consider a notion of authenticated MPC where the inputs are authenticated (for instance, signed using a digital signature) by some certification authority. We propose a generic and efficient compiler that transforms any linear secret sharing based honest-majority MPC protocol into one with input authentication.
Our compiler achieves an ideal notion of authenticated MPC equipped with stronger and more desirable security guarantees than those considered in prior works, while incurring significantly lower computational costs and competitive communication overheads when compared to existing solutions. In particular, we entirely avoid the (potentially expensive) protocol-specific techniques and pre-processing requirements that are inherent to these solutions. For certain corruption thresholds, our compiler additionally preserves the stronger identifiable abort security of the underlying MPC protocol. No existing solution for authenticated MPC achieves this regardless of the corruption threshold.
Along the way, we make several technical contributions that are of independent interest. This includes the notion of distributed proofs of knowledge and concrete realizations of the same for several relations of interest, such as proving knowledge of many popularly used digital signature schemes, and proving knowledge of opening of a Pedersen commitment.

2024

ASIACRYPT

Concurrent Encrypted Multimaps
Abstract

Encrypted data structures have received a lot of attention due to their use as building blocks in the design of fast encrypted search algorithms and encrypted databases. An important design aspect that, as far as we know, has not been considered is that modern server architectures are concurrent in the sense that they support the execution of multiple operations simultaneously. In this work, we initiate the study of concurrent encrypted data structures. We identify new definitional and technical challenges posed by concurrency in the setting of encrypted search. In order to formalize the security of these schemes, we extend the standard framework of structured encryption to capture, among other things, fine-grained leakage which occurs at the instruction level as well as schedule-dependent leakage which changes as a function of the order in which instructions are executed. The latter is particularly challenging to handle when the scheduler is adversarial and adaptive. We provide security definitions in the ideal/real-world model which allows us to capture both security and consistency together.
We combine techniques from structured encryption and concurrent data structures to design the first concurrent encrypted multi-map. We show that it is not only secure and efficient, but also satisfies a strong consistency guarantee called linearizability while supporting lock-free append operations and requiring no inter-client communication.

2024

ASIACRYPT

Constrained Pseudorandom Functions for Inner-Product Predicates from Weaker Assumptions
Abstract

In this paper, we build a framework for constructing Constrained Pseudorandom Functions (CPRFs) with inner-product constraint predicates, using ideas from subtractive secret sharing and related-key-attack security.
Our framework can be instantiated using a random oracle or any suitable Related-Key-Attack (RKA) secure pseudorandom function. We provide three instantiations of our framework:
1. an adaptively-secure construction in the random oracle model;
2. a selectively-secure construction under the DDH assumption; and
3. a selectively-secure construction with a polynomial domain under the assumption that one-way functions exist.
All three instantiations are constraint-hiding and support inner-product predicates, leading to the first constructions of such expressive CPRFs under each corresponding assumption. Moreover, while the OWF-based construction is primarily of theoretical interest, the random oracle and DDH-based constructions are concretely efficient, which we show via an implementation.

2024

ASIACRYPT

Count Corruptions, Not Users: Improved Tightness for Signatures, Encryption and Authenticated Key Exchange
Abstract

In the multi-user with corruptions (muc) setting there are $n\geq 1$ users, and the goal is to prove that, even in the face of an adversary that adaptively corrupts users to expose their keys, un-corrupted users retain security. This can be considered for many primitives including signatures and encryption. Proofs of muc security, while possible, generally suffer a factor $n$ loss in tightness, which can be large. This paper gives new proofs where this factor is reduced to the number $c$ of corruptions, which in practice is much smaller than $n$. We refer to this as corruption-parametrized muc (cp-muc) security. We give a general result showing it for a class of games that we call local. We apply this to get cp-muc security for signature schemes (including ones in standards and in TLS 1.3) and some forms of public-key and symmetric encryption. Then we give dedicated cp-muc security proofs for some important schemes whose underlying games are not local, including the Hashed ElGamal and Fujisaki-Okamoto KEMs and authenticated key exchange. Finally, we give negative results to show optimality of our bounds.

2024

ASIACRYPT

CPA-secure KEMs are also sufficient for Post-Quantum TLS 1.3
Abstract

In the post-quantum migration of TLS 1.3, an ephemeral Diffie-Hellman must be replaced with a post-quantum key encapsulation mechanism (KEM). At EUROCRYPT 2022, Huguenin-Dumittan and Vaudenay [HV22] demonstrated that KEMs with standard CPA security are sufficient for the security of the TLS1.3 handshake. However, their result is only proven in the random oracle model (ROM), and as the authors comment, their reduction is very much non-tight and not sufficient to
guarantee security in practice due to the $O(q^6)$-loss, where $q$ is the number of adversary’s queries to random oracles. Moreover, in order to analyze the post-quantum security of TLS 1.3 handshake with a KEM, it is necessary to consider the security in the quantum ROM (QROM). Therefore, they leave the tightness improvement of their ROM proof and the QROM proof of such a result as an interesting open question.
In this paper, we resolve this problem. We improve the ROM proof in [HV22] from an $O(q^6)$-loss to an $O(q)$-loss with standard CPA-secure KEMs which can be directly obtained from the underlying public-key encryption (PKE) scheme in CRYSTALS-Kyber. Moreover, we show that if the KEMs are constructed from rigid deterministic public-key encryption (PKE) schemes such as the ones in Classic McEliece and NTRU, this $O(q)$-loss can be further improved to an $O(1)$-loss. Hence, our reductions are sufficient to guarantee security in practice. According to our results, a CPA-secure KEM (which is more concise and efficient than the currently used CCA/1CCA-secure KEM) can be directly employed to construct a post-quantum TLS 1.3. Furthermore, we lift our ROM result into QROM and first prove that the CPA-secure KEMs are also sufficient for the post-quantum TLS 1.3 handshake. In particular, the techniques introduced to improve reduction tightness in this paper may be of independent interest.

2024

ASIACRYPT

Crooked Indifferentiability of the Feistel Construction
Abstract

The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks---that is, adversarial subversion---of the component round functions. Specifically, we establish that a Feistel-based construction with more than $337n/\log(1/\epsilon)$ rounds can transform a subverted random function---which disagrees with the original one at a small fraction (denoted by $\epsilon$) of inputs---into an object that is \emph{crooked-indifferentiable} from a random permutation, even if the adversary is aware of all the randomness used in the transformation. Here, $n$ denotes the length of both the input and output of the round functions that underlie the Feistel cipher. We also provide a lower bound showing that the construction cannot use fewer than $2n/\log(1/\epsilon)$ rounds to achieve crooked-indifferentiable security.

2024

ASIACRYPT

Cryptanalysis of Rank-2 Module-LIP with Symplectic Automorphisms
Abstract

At Eurocrypt'24, Mureau et al. formally defined the Lattice Isomorphism Problem for module lattices (module-LIP) in a number field $\mathbb{K}$, and proposed a heuristic randomized algorithm solving module-LIP for modules of rank 2 in $\mathbb{K}^2$ with a totally real number field $\mathbb{K}$, which runs in classical polynomial time for a large class of modules and a large class of totally real number field under some reasonable number theoretic assumptions. In this paper, by introducing a (pseudo) symplectic automorphism of the module, we successfully reduce the problem of solving module-LIP over CM number field to the problem of finding certain symplectic automorphism. Furthermore, we show that a weak (pseudo) symplectic automorphism can be computed efficiently, which immediately turns out to be the desired automorphism when the module is in a totally real number field. This directly results in a provable deterministic polynomial-time algorithm solving module-LIP for rank-2 modules in $\mathbb{K}^2$ where $\mathbb{K}$ is a totally real number field, without any assumptions or restrictions on the modules and the totally real number fields. Moreover, the weak symplectic automorphism can also be utilized to invalidate the omSVP assumption employed in HAWK's forgery security analysis, although it does not yield any actual attacks against HAWK itself.

2024

ASIACRYPT

Delegatable Anonymous Credentials From Mercurial Signatures With Stronger Privacy
Abstract

Delegatable anonymous credentials (DACs) enable a root issuer to delegate credential-issuing power, allowing a delegatee to take a delegator role. To preserve privacy, credential recipients and verifiers should not learn anything about intermediate issuers in the delegation chain. One particularly efficient approach to constructing DACs is due to Crites and Lysyanskaya (CT-RSA '19). In contrast to previous approaches, it is based on mercurial signatures (a type of equivalence-class signature), offering a conceptually simple design that does not require extensive use of zero-knowledge proofs. Unfortunately, current constructions of ``CL-type'' DACs only offer a weak form of privacy-preserving delegation: if an adversarial issuer (even an honest-but-curious one) is part of a user's delegation chain, they can detect when the user shows its credential. This is because the underlying mercurial signature schemes allows a signer to identify his public key in a delegation chain.
We propose CL-type DACs that overcome the above limitation based on a new mercurial signature scheme that provides adversarial public key class hiding which ensures that adversarial signers who participate in a user's delegation chain cannot exploit that fact to trace users. We achieve this introducing structured public parameters for each delegation level. Since the related setup produces critical trapdoors, we discuss techniques from updatable structured reference strings in zero-knowledge proof systems (Groth et al. CRYPTO '18) to guarantee the required privacy needs. In addition, we propose a simple way to realize revocation for CL-type DACs via the concept of revocation tokens. While we showcase this approach to revocation using our DAC scheme, it is generic and can be applied to any CL-type DAC system. Revocation is a vital feature that is largely unexplored and notoriously hard to achieve for DACs, thus providing it can help to make DAC schemes more attractive in practical applications.

2024

ASIACRYPT

Deletions and Dishonesty: Probabilistic Data Structures in Adversarial Settings
Abstract

Probabilistic data structures (PDS) are compact representations of high-volume data that provide approximate answers to queries about the data. They are commonplace in today's computing systems, finding use in databases, networking and more. While PDS are designed to perform well under benign inputs, they are frequently used in applications where inputs may be adversarially chosen. This may lead to a violation of their expected behaviour, for example an increase in false positive rate.
In this work, we focus on PDS that handle approximate membership queries (AMQ). We consider adversarial users with the capability of making adaptive insertions, deletions and membership queries to AMQ-PDS, and analyse the performance of AMQ-PDS under such adversarial inputs.
We argue that deletions significantly empower adversaries, presenting a challenge to enforcing honest behaviour when compared to insertion-only AMQ-PDS.To address this, we introduce a new concept of an honest setting for AMQ-PDS with deletions. By leveraging simulation-based security definitions, we then quantify how much harm can be caused by adversarial users to the functionality of AMQ-PDS. Our resulting bounds only require calculating the maximal false positive probability and insertion failure probability achievable in our novel honest setting.
We apply our results to Cuckoo filters and Counting filters. We show how to protect these AMQ-PDS at low cost, by replacing or composing the hash functions with keyed pseudorandom functions in their construction. This strategy involves establishing practical bounds for the probabilities mentioned above. Using our new techniques, we demonstrate that achieving security against adversarial users making both insertions *and* deletions remains practical.

2024

ASIACRYPT

Dense and smooth lattices in any genus
Abstract

The Lattice Isomorphism Problem (LIP) was recently introduced as a new hardness assumption for post-quantum cryptography. The strongest known efficiently computable invariant for LIP is the genus of a lattice. To instantiate LIP-based schemes one often requires the existence of a lattice that (1) lies in some fixed genus, and (2) has some good geometric properties such as a high packing density or small smoothness parameter.
In this work we show that such lattices exist. In particular, building upon classical results by Siegel (1935), we show that essentially any genus contains a lattice with a close to optimal packing density, smoothing parameter and covering radius. We present both how to efficiently compute concrete existence bounds for any genus, and asymptotically tight bounds under weak conditions on the genus.

2024

ASIACRYPT

Dictators? Friends? Forgers. Breaking and Fixing Unforgeability Definitions for Anamorphic Signature Schemes
Abstract

Anamorphic signature schemes (KPPYZ, Crypto 2023) allow users to hide encrypted messages in signatures to allow covert communication in a hypothesized scenario where encryption is outlawed by a "dictator" but authentication is permitted. We enhance the security of anamorphic signatures by proposing two parallel notions of unforgeability which close gaps in existing security definitions. The first notion considers a dictator who wishes to forge anamorphic signatures. This notion patches a divide between the definition and a stated security goal of robustness (BGHMR, Eurocrypt 2024). We port two related BGHMR constructions to the signature scheme setting and show that one is secure when built from unpredictable signature schemes while the other is broken. The second notion considers a recipient who wishes to forge signatures. To motivate this notion, we identify a gap in an existing security definition from KPPYZ and present attacks that allow parties to be impersonated when using schemes erroneously deemed secure. We then formalize our new unforgeability definition to close this gap. Interestingly, while the new definition is only modestly different from the old one, the change introduces subtle technical challenges that arise when proving security. We overcome these challenges in our reanalysis of existing anamorphic signature schemes by showing they achieve our new notion when built from chosen-randomness secure signatures or with encryption that satisfies a novel ideal-model simulatability property.

2024

ASIACRYPT

Digital Signatures with Outsourced Hashing
Abstract

Most practical signature schemes follow the hash-then-sign paradigm: First the (arbitrarily long) message is mapped to a fixed-length hash value, then a signing core derives the signature from the latter. As it is implementationally attractive, practitioners routinely exploit this structure by decoupling the two steps and distributing them among different entities; for instance, industry standards like PKCS#11 specify how security smartcards implement exclusively the core, leaving the hashing to their (untrusted) environment. At the same time, the classic security notions for signature schemes don’t consider such a decoupling, and thus don’t cover attacks involving, for instance, providing the core with maliciously chosen hash values. A first work that studied this gap appeared only recently (PKC 2024). While it could confirm for a few candidates that they remain secure when split according to PKCS#11, its syntactical abstractions and security definitions are too limited to cover most practical signature schemes (e.g., the many variants of Fiat–Shamir/Schnorr).
This article studies how the functional separation of hashing and core in signature schemes can be systematized, so that implementational demands (in the spirit of PKCS#11) and, hopefully, security can be met simultaneously. We accompany this foundational work with a case study of a variety of standardized (EC)DLP based signatures. Surprisingly, as we show, their security varies across the full spectrum between universally forgeable and provably unforgeable. For instance, for the same scheme, we demonstrate
universal forgeries when instantiated with 224-bit ECC (using an attack that completes in milliseconds), while we establish strong unforgeability for the 256-bit ECC case. Many schemes become completely insecure when the hash function is instantiated with SHA3 instead of with SHA2.

2024

ASIACRYPT

Direct FSS Constructions for Branching Programs and More from PRGs with Encoded-Output Homomorphism
Abstract

Function secret sharing (FSS) for a class $\cF$ allows to split a secret function $f \in \cal{F}$ into (succinct) secret shares $f_0,f_1$, such that for all $x\in \{0,1\}^n$ it holds $f_0(x)-f_1(x)=f(x)$. FSS has numerous applications, including private database queries, nearest neighbour search, private heavy hitters and secure computation in the preprocessing model, where the supported class $\cF$ translates to richness in the application.
Unfortunately, concretely efficient FSS constructions are only known for very limited function classes.
In this work we introduce the notion of pseudorandom generators with encoded-output homomorphism (EOH-PRGs), and give direct FSS constructions for branching programs and more based on this primitive. Further, we give constructions of FSS for deterministic finite automatas (DFAs) from a KDM secure variant of EOH-PRGs.
\begin{itemize}
\item \emph{New abstractions.} Following the work of Alamati et al.~(EUROCRYPT '19), who classify minicrypt primitives with algebraic structure and their applications, we capture the essence of our FSS constructions in the notion of EOH-PRG, paving the road towards future efficiency improvements via new instantiations of this primitive. The abstraction of EOH-PRG and its instantiations may be of independent interest, as it is an approximate substitution of an ideal homomorphic PRG.
\item \emph{Better efficiency.} We show that EOH-PRGs can be instantiated from LWE and a small-exponent variant of the DCR assumption. A theoretical analysis of our instantiations suggest efficiency improvements over the state of the art both in terms of key size and evaluation time: We show that our FSS instantiations lead to smaller key sizes, improving over previous constructions by a factor of $3.5$ and more. For branching programs our FSS constructions show considerably improved run time by avoiding the expensive generic transformation via universal circuits, shaving off a factor of $w$ and more in the number of abstract operations, where $w$ corresponds to an upper bound on the width of the underlying class of branching programs.
\item \emph{New feasibility.} We show that our instantiations of EOH-PRGs additionally support a form of KDM-security, without requiring an additional circular-security assumption. Based on this, we give the first FSS construction for DFAs which supports the evaluation of inputs of a-priori unbounded length without relying on FHE.
\item \emph{Applications.} We outline applications of our FSS constructions including pattern matching with wild cards, image matching, nearest neighbor search and regular expression matching.
\end{itemize}

2024

ASIACRYPT

Dishonest Majority Constant-Round MPC with Linear Communication from DDH
Abstract

In this work, we study constant round multiparty computation (MPC) for Boolean circuits against a fully malicious adversary who may control up to $n-1$ out of $n$ parties. Without relying on fully homomorphic encryption (FHE), the best-known results in this setting are achieved by Wang et al. (CCS 2017) and Hazay et al. (ASIACRYPT 2017) based on garbled circuits, which require a quadratic communication in the number of parties $O(|C|\cdot n^2)$. In contrast, for non-constant round MPC, the recent result by Rachuri and Scholl (CRYPTO 2022) has achieved linear communication $O(|C|\cdot n)$.
In this work, we present the first concretely efficient constant round MPC protocol in this setting with linear communication in the number of parties $O(|C|\cdot n)$. Our construction can be based on any public-key encryption scheme that is linearly homomorphic for public keys. Our work gives a concrete instantiation from a variant of the El-Gamal Encryption Scheme assuming the DDH assumption. The analysis shows that when the computational security parameter $\lambda=128$ and statistical security parameter $\kappa=80$, our protocol achieves a smaller communication than Wang et al. (CCS 2017) when there are $16$ parties for AES circuit, and $8$ parties for general Boolean circuits (where we assume that the numbers of AND gates and XOR gates are the same). When comparing with the recent work by Beck et al. (CCS 2023) that achieves constant communication complexity $O(|C|)$ in the strong honest majority setting ($t<(1/2-\epsilon)n$ where $\epsilon$ is a constant), our protocol is better as long as $n<3500$ (when $t=n/4$ for their work).

2024

ASIACRYPT

Dishonest Majority Multiparty Computation over Matrix Rings
Abstract

The privacy-preserving machine learning (PPML) has gained growing importance over the last few years. One of the biggest challenges is to improve the eﬃciency of PPML so that the communication and computation costs of PPML are aﬀordable for large machine learning models such as deep learning. As we know, linear algebra such as matrix multiplication occupies a significant part of the computation in deep learning such as deep convolutional neural networks (CNN). Thus, it is desirable to propose the MPC protocol specialized for the matrix operations. In this work, we propose a dishonest majority MPC protocol over matrix rings which supports matrix multiplication and addition. Our MPC protocol can be seen as a variant of SPDZ protocol, i.e., the MAC and global key of our protocol are vectors of length m and the secret of our protocol is an $m \times m$ matrix. Compared to the classic SPDZ protocol, our MPC protocol reduces the communication complexity by at least m times to securely compute a matrix multiplication. We also show that the communication complexity of our MPC protocol is asymptotically as good as [16] which also presented a dishonest majority MPC protocol specialized for matrix operations, i.e., the communication complexity of securely computing a multiplication gate is $O(m^2 n^2 log q)$ in the preprocessing phase and $O(m^2 n log q)$ in the online phase. The share size and the number of multiplications of our protocol are reduced by around 50% and 40% of [16], respectively. However, we take a completely different approach. The protocol in [16] uses a variant of BFV scheme to embed a whole matrix into a single ciphertext and then treats the matrix operation as the entry-wise operation in the ciphertext while our approach resorts to a variant of vector linear oblivious evaluation (VOLE) called the subﬁeld VOLE [33] which can securely compute the additive sharing of $v\bm{x}$ for $v \in F_{q^b}, \bm{x}\in F_q^a$ with sublinear communication complexity. Finally, we note that our MPC protocol can be easily extended to small ﬁelds.

2024

ASIACRYPT

Don't Use It Twice! Solving Relaxed Linear Equivalence Problems
Abstract

The Linear Code Equivalence (LCE) Problem has received increased attention in recent years due to its applicability in constructing efficient digital signatures. Notably, the LESS signature scheme based on LCE is under consideration for the NIST post-quantum standardization process, along with the MEDS signature scheme that relies on an extension of LCE to the rank metric, namely Matrix Code Equivalence (MCE) Problem. Building upon these developments, a family of signatures with additional properties, including linkable ring, group, and threshold signatures, has been proposed. These novel constructions introduce relaxed versions of LCE (and MCE), wherein multiple samples share the same secret equivalence. Despite their significance, these variations have often lacked a thorough security analysis, being assumed to be as challenging as their original counterparts. Addressing this gap, our work delves into the sample complexity of LCE and MCE --- precisely, the sufficient number of samples required for efficient recovery of the shared secret equivalence. Our findings reveal, for instance, that one should not use the same secret twice in the LCE setting since this enables a polynomial time (and memory) algorithm to retrieve the secret. Consequently, our results unveil the insecurity of two advanced signatures based on variants of the LCE Problem.

2024

ASIACRYPT

Dual Support Decomposition in the Head: Shorter Signatures from Rank SD and MinRank
Abstract

The MPC-in-the-Head (MPCitH) paradigm is widely used for building post-quantum signature schemes, as it provides a versatile way to design proofs of knowledge based on hard problems. Over the years, the MPCitH landscape has changed significantly, with the most recent improvements coming from VOLE-in-the-Head (VOLEitH) and Threshold-Computation-in-the-Head (TCitH).
While a straightforward application of these frameworks already improve the existing MPCitH-based signatures, we show in this work that we can adapt the arithmetic constraints representing the underlying security assumptions (here called the modeling) to achieve smaller sizes using these new techniques.
More precisely, we explore existing modelings for the rank syndrome decoding (RSD) and MinRank problems and we introduce a new modeling, named dual support decomposition, which achieves better sizes with the VOLEitH and TCitH frameworks by minimizing the size of the witnesses.
While this modeling is naturally more efficient than the other ones for a large set of parameters, we show that it is possible to go even further and explore new areas of parameters. With these new modeling and parameters, we obtain low-size witnesses which drastically reduces the size of the ``arithmetic part'' of the signature.
We apply our new modeling to both TCitH and VOLEitH frameworks and compare our results to RYDE, MiRitH, and MIRA signature schemes. We also note that recent techniques optimizing the sizes of GGM trees are applicable to our schemes and further reduce the signature sizes by a few hundred bytes. We obtain signature sizes below 3.5 kB for 128 bits of security with N=256 parties (a.k.a. leaves in the GGM trees) and going as low as 2.8 kB with N=2048, for both RSD and MinRank. This represents an improvement of more than 2\:kB compared to the original submissions to the 2023 NIST call for additional signatures.

2024

ASIACRYPT

Early Stopping Byzantine Agreement in $(1+\epsilon)\cdot f$ Rounds
Abstract

In this paper, we present two \textit{early stopping} Byzantine agreement protocols in the authenticated setting against a corrupt minority $t < n/2$, where $t$ represents the maximum number of malicious parties. Early stopping protocols ensure termination within a number of rounds determined solely by the actual number of malicious nodes $f$ present during execution, irrespective of $t$.
Our first protocol is deterministic and ensures early stopping termination in $ (d+5) \cdot (\lfloor f/d \rfloor +3)$ rounds, where $d$ is a fixed constant. For example, for all $d\ge 6$, our protocol runs in at most $(1+\epsilon )\cdot f$ rounds (where $0<\epsilon<1$), improving (for large $f$) upon the best previous early stopping deterministic broadcast protocol by Perry and Toueg~\cite{Perry}, which terminates in $2f+4$ rounds. Additionally, our second protocol is randomized, ensuring termination in an expected constant number of rounds and achieving early stopping in $(d+9) \cdot (\lfloor f/d \rfloor +2)$ rounds in the worst case. This marks a significant improvement over a similar result by Goldreich and Petrank.~\cite{GOLDREICH199045}, which \emph{always} requires an expected constant number of rounds and $O(t)$ rounds in the worst case, i.e., does not have the early stopping property.

2024

ASIACRYPT

Efficient Asymmetric PAKE Compiler from KEM and AE
Abstract

Password Authenticated Key Exchange (PAKE) allows two parties to establish a secure session key with a shared low-entropy password $pw$. Asymmetric PAKE (aPAKE) extends PAKE in the client-server setting, and the server only stores a password file instead of the plain password so as to provide additional security guarantee when the server is compromised.
In this paper, we propose a novel generic compiler from PAKE to aPAKE in the Universal Composable (UC) framework by making use of Key Encapsulation Mechanism (KEM) and Authenticated Encryption (AE).
-- Our compiler admits efficient instantiations from lattice to yield lattice-based post-quantum secure aPAKE protocols. When instantiated with Kyber (the standardized KEM algorithm by the NIST), the performances of our compiler outperform other lattice-based compilers (Gentry et al. CRYPTO 2006) in all aspects, hence yielding the most efficient aPAKE compiler from lattice. In particular, when applying our compiler to the UC-secure PAKE schemes (Santos et al. EUROCRYPT 2023, Beguinet et al. ACNS 2023), we obtain the most efficient UC-secure aPAKE schemes from lattice.
-- Moreover, the instantiation of our compiler from the tightly-secure matrix DDH (MDDH)-based KEM (Pan et al. CRYPTO 2023) can compile the tightly-secure PAKE scheme (Liu et al. PKC 2023) to a tightly-secure MDDH-based aPAKE, which serves as the first tightly UC-secure aPAKE scheme.

2024

ASIACRYPT

Efficient Fuzzy Private Set Intersection from Fuzzy Mapping
Abstract

Private set intersection (PSI) allows Sender holding a set \(X\) and Receiver holding a set \(Y\) to compute only the intersection \(X\cap Y\) for Receiver. We focus on a variant of PSI, called fuzzy PSI (FPSI), where Receiver only gets points in \(X\) that are at a distance not greater than a threshold from some points in \(Y\).
Most current FPSI approaches first pick out pairs of points that are potentially close and then determine whether the distance of each selected pair is indeed small enough to yield FPSI result. Their complexity bottlenecks stem from the excessive number of point pairs selected by the first picking process. Regarding this process, we consider a more general notion, called fuzzy mapping (Fmap), which can map each point of two parties to a set of identifiers, with closely located points having a same identifier, which forms the selected point pairs.
We initiate the formal study on Fmap and show novel Fmap instances for Hamming and \(L_\infty\) distances to reduce the number of selecte

2024

ASIACRYPT

Evasive LWE Assumptions: Definitions, Classes, and Counterexamples
Abstract

The evasive LWE assumption, proposed by Wee [Eurocrypt'22 Wee] for constructing a lattice-based optimal broadcast encryption, has shown to be a powerful assumption, adopted by subsequent works to construct advanced primitives ranging from ABE variants to obfuscation for null circuits. However, a closer look reveals significant differences among the precise assumption statements involved in different works, leading to the fundamental question of how these assumptions compare to each other. In this work, we initiate a more systematic study on evasive LWE assumptions:
(i) Based on the standard LWE assumption, we construct simple counterexamples against three private-coin evasive LWE variants, used in [Crypto'22 Tsabary, Asiacrypt'22 VWW, Crypto'23 ARYY] respectively, showing that these assumptions are unlikely to hold.
(ii) Based on existing evasive LWE variants and our counterexamples, we propose and define three classes of plausible evasive LWE assumptions, suitably capturing all existing variants for which we are not aware of non-obfuscation-based counterexamples.
(iii) We show that under our assumption formulations, the security proofs of [Asiacrypt'22 VWW] and [Crypto'23 ARYY] can be recovered, and we reason why the security proof of [Crypto'22 Tsabary] is also plausibly repairable using an appropriate evasive LWE assumption.

2024

ASIACRYPT

Evolving Secret Sharing Made Short
Abstract

Evolving secret sharing (Komargodski, Naor, and Yogev, TCC’16) generalizes the notion of secret sharing to the setting of evolving access structures, in which the share holders are added to the system in an online manner, and where the dealer does not know neither the access structure nor the maximum number of parties in advance. Here, the main difficulty is to distribute shares to the new players without updating the shares of old players; moreover, one would like to minimize the share size as a function of the number of players.
In this paper, we initiate a systematic study of evolving secret sharing in the computational setting, where the maximum number of parties is polynomial in the security parameter, but the dealer still does not know this value, neither it knows the access structure in advance. Moreover, the privacy guarantee only holds against computationally bounded adversaries corrupting an unauthorized subset of the players.
Our main result is that for many interesting, and practically relevant, evolving access structures (including graphs access structures, DNF and CNF formulas access structures, monotone circuits access structures, and threshold access structures), under standard hardness assumptions, there exist efficient secret sharing schemes with computational privacy and in which the shares are succinct (i.e., much smaller compared to the size of a natural computational representation of the evolving access structure).

2024

ASIACRYPT

Extending class group action attacks via sesquilinear pairings
Abstract

We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the O-module structure of an elliptic curve with CM by an imaginary quadratic field O. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of [CHM+23] and [FFP24].

2024

ASIACRYPT

Extractable Witness Encryption for KZG Commitments and Efficient Laconic OT
Abstract

We present a concretely efficient and simple extractable witness encryption scheme for KZG polynomial commitments.
It allows to encrypt a message towards a triple $(\mathsf{com}, \alpha, \beta)$, where $\mathsf{com}$ is a KZG commitment for some polynomial $f$.
Anyone with an opening for the commitment attesting $f(\alpha) = \beta$ can decrypt, but without knowledge of a valid opening the message is computationally hidden.
Our construction is simple and highly efficient. The ciphertext is only a single group element. Encryption and decryption both require a single pairing evaluation and a constant number of group operations.
Using our witness encryption scheme, we construct a simple and highly efficient laconic OT protocol, which significantly outperforms the state of the art in most important metrics.

2024

ASIACRYPT

Faster BGV Bootstrapping for Power-of-two Cyclotomics through Homomorphic NTT
Abstract

Power-of-two cyclotomics is a popular choice when instantiating the BGV scheme because of its efficiency and compliance with the FHE standard. However, in power-of-two cyclotomics, the linear transformations in BGV bootstrapping cannot be decomposed into sub-transformations for acceleration with existing techniques. Thus, they can be highly time-consuming when the number of slots is large, degrading the advantage brought by the SIMD property of the plaintext space. By exploiting the algebraic structure of power-of-two cyclotomics, this paper derives explicit decomposition of the linear transformations in BGV bootstrapping into NTT-like sub-transformations, which are highly efficient to compute homomorphically. Moreover, multiple optimizations are made to evaluate homomorphic linear transformations, including modified BSGS algorithms, trade-offs between level and time, and specific simplifications for thin and general bootstrapping. We implement our method on HElib. With the number of slots ranging from 4096 to 32768, we obtain a 2.4x$\sim$55.1x improvement in bootstrapping throughput, compared to previous works or the naive approach.

2024

ASIACRYPT

Faster Signatures from MPC-in-the-Head
Abstract

We revisit the construction of signature schemes using the
MPC-in-the-head paradigm. We obtain two main contributions:
– We observe that previous signatures in the MPC-in-the-head paradigm
must rely on a salted version of the GGM puncturable pseudoran-
dom function (PPRF) to avoid collision attacks. We design a new
efficient PPRF construction that is provably secure in the multi-
instance setting. The security analysis of our PPRF, in the ideal
cipher model, is quite involved and forms a core technical contri-
bution of our work. While previous constructions had to rely on a
hash function, our construction uses only a fixed-key block cipher
and is considerably more efficient as a result: we observe a 12× to
55× speed improvement for a recent signature scheme (Joux and
Huth, Crypto’24). Our improved PPRF can be used to speed up
many MPC-in-the-head signatures.
– We introduce a new signature scheme from the regular syndrome
decoding assumption, based on a new protocol for the MPC-in-
the-head paradigm, which significantly reduces communication com-
pared to previous works. Our scheme is conceptually simple, though
its security analysis requires a delicate and nontrivial combinatorial
analysis.

2024

ASIACRYPT

FLI: Folding Lookup Instances
Abstract

We introduce two folding schemes for lookup instances: FLI and FLI+SOS. Both use a PIOP to check that a matrix has elementary basis vectors as rows, with FLI+SOS adding a twist based on Lasso’s [STW23] SOS-decomposability.
FLI takes two lookup instances {a_1}, {a_2} ⊆ {t}, and expresses them as matrix equations 𝑀_𝑖 · t^T = a_i^T for i=1,2, where each matrix 𝑀_𝑖 ∈ F^{𝑚 × 𝑁} has rows which are elementary basis vectors in F^𝑁. Matrices that satisfy this condition are said to be in R_{elem}. Then, a folding scheme for R_{elem} into a relaxed relation is used, which combines the matrices 𝑀_1, 𝑀_2 as 𝑀_1 + 𝛼 𝑀_2 for a random 𝛼 ∈ F. Finally, the lookup equations are combined as (𝑀_1 + 𝛼 𝑀_2)* t^T = (a_1 + 𝛼 a_2)^T. In FLI, only the property that a matrix is in R_{elem} is folded, and this makes the FLI folding step the cheapest among existing solutions. The price to pay is in the cost for proving accumulated instances.
FLI+SOS builds upon FLI to enable folding of large SOS-decomposable [STW23] tables. This is achieved through a variation of Lasso's approach to SOS-decomposability, which fits FLI naturally. For comparison, we describe (for the first time to our knowledge) straightforward variations of Protostar [BC23] and Proofs for Deep Thought [BC24] that also benefit from SOS-decomposability. We see that for many reasonable parameter choices, and especially those arising from lookup-based zkVMs [AST23], FLI+SOS can concretely be the cheapest folding solution.

2024

ASIACRYPT

FOLEAGE: F4-OLE-Based Multi-Party Computation for Boolean Circuits
Abstract

Secure Multi-party Computation (MPC) allows two or more parties to compute any public function over their privately-held inputs, without revealing any information beyond the result of the computation. Modern protocols for MPC generate a large amount of input-independent preprocessing material called multiplication triples, in an offline phase. This preprocessing can later be used by the parties to efficiently instantiate an input-dependent online phase computing the function.
To date, the state-of-the-art secure multi-party computation protocols in the preprocessing model are tailored to secure computation of arithmetic circuits over large fields and require little communication in the preprocessing phase, typically O(N · m) to generate m triples among N parties. In contrast, when it comes to computing preprocessing for computations that are naturally represented as Boolean circuits, the state-of-the-art techniques have not evolved since the 1980s, and in particular, require every pair of parties to execute a large number of oblivious transfers before interacting to convert them to N-party triples, which induces an Ω(N^2 · m) communication overhead.
In this paper, we introduce F4OLEAGE, which addresses this gap by introducing an efficient preprocessing protocol tailored to Boolean circuits. F4OLEAGE exhibits excellent performance: it generates m multiplication triples over F2 using only N · m + O(N^2 · log m) bits of communication for N-parties, and can concretely produce over 12 million triples per second in the 2-party setting on one core of a commodity machine.
Our result builds upon an efficient Pseudorandom Correlation Generator (PCG) for multiplications triples over the field F4. Roughly speaking, a PCG enables parties to stretch a short seed into a large number of pseudorandom correlations non-interactively, which greatly improves the efficiency of the offline phase in MPC protocols. Our construction significantly outperforms the state-of-the-art, which we demonstrate via a prototype implementation. This is achieved by introducing a number of protocol-level, algorithmic-level, and implementation-level optimizations on the recent PCG construction of Bombar et al. (Crypto 2023) from the Quasi-Abelian Syndrome Decoding assumption.

2024

ASIACRYPT

Formal Definition and Verification for Combined Random Fault and Random Probing Security
Abstract

In our highly digitalized world, an adversary is not constrained to purely digital attacks but can monitor or influence the physical execution environment of a target computing device.
Such side-channel or fault-injection analysis poses a significant threat to otherwise secure cryptographic implementations. Hence, it is important to consider additional adversarial capabilities when analyzing the security of cryptographic implementations besides the default black-box model. For side-channel analysis, this is done by providing the adversary with knowledge of some internal values, while for fault-injection analysis the capabilities of the adversaries include manipulation of some internal values.
In this work, we extend probabilistic security models for physical attacks,
by introducing a general random probing model and a general random fault model to capture arbitrary leakage and fault distributions, as well as the combination of these models. Our aim is to enable a more accurate modeling of low-level physical effects. We then analyze important properties, such as the impact of adversarial knowledge on faults and compositions, and provide tool-based formal verification methods that allow the security assessment of design components. These methods are introduced as extension of previous tools VERICA and IronMask which are implemented, evaluated and compared.

2024

ASIACRYPT

General Practical Cryptanalysis of the Sum of Round-Reduced Block Ciphers and ZIP-AES
Abstract

We introduce a new approach between classical security proofs
of modes of operation and dedicated security analysis for known crypt-
analysis families: General Practical Cryptanalysis. This allows us to ana-
lyze generically the security of the sum of two keyed permutations against
known attacks. In many cases (of course, not all), we show that the se-
curity of the sum is strongly linked to that of the composition of the two
permutations. This enables the construction of beyond-birthday bound
secure low-latency PRFs by cutting a known-to-be-secure block cipher
into two equal parts. As a side result, our general analysis shows an in-
evitable difficulty for the key recovery based on differential-type attacks
against the sum, which leads to a correction of previously published at-
tacks on the dedicated design Orthros

2024

ASIACRYPT

Generalized Hybrid Search with Applications to Blockchain and Hash Function Security
Abstract

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability.
Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities—i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms recently proposed by Rosmanis. Namely, for an arbitrary distribution D on Boolean functions, the probability that an algorithm equipped with t_c classical queries and t_q quantum queries succeeds in finding a preimage of 1 for a function sampled from D is at most v_D(2sqrt(t_c) + 2t_q + 1)^2, where v_D captures the average (over D) fraction of preimages of 1.
Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a “modified Grover” in which the initial state depends on the target distribution D. We then show how to analyze its success probability for
arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.
As applications of our hardness results, we first revisit and generalize the formal security treatment of the Bitcoin protocol called the Bitcoin backbone [Eurocrypt 2015], to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we re-examine the generic security of hash functions [PKC 2016] against quantum-classical hybrid adversaries.

2024

ASIACRYPT

Generic Differential Key Recovery Attacks and Beyond
Abstract

At Asiacrypt 2022, a holistic key guessing strategy was proposed to yield the most efficient key recovery for the rectangle attack. Recently, at Crypto 2023, a new cryptanalysis technique--the differential meet-in-the-middle (MITM) attack--was introduced. Inspired by these two previous works, we present three generic key recovery attacks in this paper. First, we extend the holistic key guessing strategy from the rectangle to the differential attack, proposing the generic classical differential attack (GCDA). Next, we combine the holistic key guessing strategy with the differential MITM attack, resulting in the generalized differential MITM attack (GDMA). Finally, we apply the MITM technique to the rectangle attack, creating the generic rectangle MITM attack (GRMA). In terms of applications, we improve 12/13-round attacks on AES-256. For 12-round AES-256, by using the GDMA, we reduce the time complexity by a factor of 2^{62}; by employing the GCDA, we reduce both the time and memory complexities by factors of 2^{61} and 2^{56}, respectively. For 13-round AES-256, we present a new differential attack with data and time complexities of 2^{89} and 2^{240}, where the data complexity is 2^{37} times lower than previously published results. These are currently the best attacks on AES-256 using only two related keys. For KATAN-32, we increase the number of rounds covered by the differential attack from 115 to 151 in the single-key setting using the basic differential MITM attack (BDMA) and GDMA. Furthermore, we achieve the first 38-round rectangle attack on SKINNYe-64-256 v2 by using the GRMA.

2024

ASIACRYPT

Hard-Label Cryptanalytic Extraction of Neural Network Models
Abstract

The machine learning problem of
extracting neural network parameters
has been proposed for nearly three decades.
Functionally equivalent extraction is a crucial goal
for research on this problem.
When the adversary has access to
the raw output of neural networks, various attacks,
including those presented at CRYPTO 2020 and EUROCRYPT 2024,
have successfully achieved this goal.
However, this goal is not achieved
when neural networks operate under a hard-label setting
where the raw output is inaccessible.
In this paper,
we propose the first attack that theoretically achieves
functionally equivalent extraction under the hard-label setting,
which applies to ReLU neural networks.
The effectiveness of our attack is
validated through practical experiments
on a wide range of ReLU neural networks,
including neural networks
trained on two real benchmarking datasets
(MNIST, CIFAR10) widely used in computer vision.
For a neural network consisting of $10^5$ parameters,
our attack only requires several hours on a single core.

2024

ASIACRYPT

HARTS: High-Threshold, Adaptively Secure, and Robust Threshold Schnorr Signatures
Abstract

Threshold variants of the Schnorr signature scheme have recently been at the center of attention due to their applications to Bitcoin, Ethereum, and other cryptocurrencies.
However, existing constructions for threshold Schnorr signatures among a set of n parties with corruption threshold t_c suffer from at least one of the following drawbacks: (i) security only against static (i.e., non-adaptive) adversaries, (ii) cubic or higher communication cost to generate a single signature, (iii) strong synchrony assumptions on the network, or (iv) t_c+1 are sufficient to generate a signature, i.e., the corruption threshold of the scheme equals its reconstruction threshold. Especially (iv) turns out to be a severe limitation for many asynchronous real-world applications where t_c < n/3 is necessary to maintain liveness, but a higher signing threshold of n-t_c is needed. A recent scheme, ROAST, proposed by Ruffing et al. (ACM CCS `22) addresses (iii) and (iv), but still falls short of obtaining subcubic complexity and adaptive security.
In this work, we present HARTS, the first threshold Schnorr signature scheme to incorporate all these desiderata. More concretely:
- HARTS is adaptively secure and remains fully secure and operational even under asynchronous network conditions in the presence of up to t_c < n/3 malicious parties. This is optimal.
- HARTS outputs a Schnorr signature of size lambda with a near-optimal amortized communication cost of O(lambda n^2 log n) bits and a single online round per signature.
- HARTS is a high-threshold scheme: no fewer than t_r+1 signature shares can be combined to yield a full signature, where any t_r in [t_c,n-t_c) is supported. This especially covers the case t_r >= 2n/3 > 2t_c. This is optimal.
We prove our result in a modular fashion in the algebraic group model. At the core of our construction, we design a new simple and adaptively secure high-threshold AVSS scheme which may be of independent interest.

2024

ASIACRYPT

HELIOPOLIS: Verifiable Computation over Homomorphically Encrypted Data from Interactive Oracle Proofs is Practical
Abstract

Homomorphic encryption (HE) enables computation on encrypted data, which in turn facilitates the outsourcing of computation on private data. However, HE offers no guarantee that the returned result was honestly computed by the cloud. In order to have such guarantee, it is necessary to add verifiable computation (VC) into the system.
The most efficient recent works in VC over HE focus on verifying operations on the ciphertext space of the HE scheme, which usually lacks the algebraic structure that would make it compatible with existing VC systems. For example, multiplication of ciphertexts in the current most efficient HE schemes requires non-algebraic operations such as real division and rounding. Therefore, existing works for VC over HE have to either give up on those efficient HE schemes, or incur a large overhead (an amount of constraints proportional to the ciphertext ring's size) in order to emulate these non-algebraic operations.
In this work, we move away from that paradigm by placing the verification checks in the \emph{plaintext space} of HE, all while the prover remains computing on ciphertexts. We achieve this by introducing a general transformation for Interactive Oracle Proofs (IOPs) to work over HE, whose result we denote as HE-IOPs. We apply this same transformation to the FRI [Ben-Sasson et al., ICALP 2018] IOP of proximity and we show how to compile HE-Reed Solomon-encoded IOPs and HE-$\delta$-correlated-IOPs with HE-FRI into HE-IOPs. Furthermore, our construction is compatible with a prover that provides input in zero-knowledge, and only relies on building blocks that are plausibly quantum-safe.
Aligning the security parameters of HE and FRI is a difficult task for which we introduce several optimizations. We demonstrate their efficiency with a proof-of-concept implementation and show that we can run FRI's commit phase for 4096 encrypted Reed Solomon codewords with degree bound $2^{11}$ in just 5.4 seconds (using 32 threads) on a \texttt{c6i.metal} instance using less than 4GB of memory. Verification takes just 12.3 milliseconds (single-threaded) for the same parameter set and can be reduced to just 5.6ms with parameters optimized for the verifier.

2024

ASIACRYPT

Homomorphic sign evaluation with a RNS representation of integers
Abstract

In the context of fully-homomorphic-encryption, we consider the representation of large integers by their decomposition over a product of rings (through the Chinese Remainder Theorem) and introduce a new algorithm for the determination of the sign solely through the knowledge of ring-components. Our implementation with 128 bits of security delivers a correct result and a probability higher than 1-1.e-9 in less than 100 milliseconds for 32-bit integers on a laptop.

2024

ASIACRYPT

Honest Majority GOD MPC with O(depth(C)) Rounds and Low Online Communication
Abstract

In the context of secure multiparty computation (MPC) protocols with guaranteed output delivery (GOD) for the honest majority setting, the state-of-the-art in terms of communication is the work of (Goyal et al. CRYPTO'20), which communicates O(n|C|) field elements, where |C| is the size of the circuit being computed and n is the number of parties. Their round complexity, as usual in secret-sharing based MPC, is proportional to O(depth(C)), but only in the optimistic case where there is no cheating. Under attack, the number of rounds can increase to \Omega(n^2) before honest parties receive output, which is undesired for shallow circuits with depth(C) << n^2. In contrast, other protocols that only require O(depth(C) rounds even in the worst case exist, but the state-of-the-art from (Choudhury and Patra, Transactions on Information Theory, 2017) still requires \Omega(n^4|C|) communication in the offline phase, and \Omega(n^3|C|) in the online (for both point-to-point and broadcast channels). We see there exists a tension between efficient communication and number of rounds. For reference, the recent work of (Abraham et al., EUROCRYPT'23) shows that for perfect security and t<n/3, protocols with both linear communication and O(depth(C)) rounds exist.
We address this state of affairs by presenting a novel honest majority GOD protocol that maintains O(depth(C)) rounds, even under attack, while improving over the communication of the most efficient protocol in this setting by Choudhury and Patra. More precisely, our protocol has point-to-point (P2P) online communication of O(n|C|), accompanied by O(n|C|) broadcasted (BC) elements, while the offline has O(n^3|C|) P2P communication with O(n^3|C|) BC. This improves over the previous best result, and reduces the tension between communication and round complexity. Our protocol is achieved via a careful use of packed secret-sharing in order to improve the communication of existing verifiable secret-sharing approaches, although at the expense of weakening their robust guarantees: reconstruction of shared values may fail, but only if the adversary gives away the identities of many corrupt parties. We show that this less powerful notion is still useful for MPC, and we use this as a core building block in our construction. Using this weaker VSS, we adapt the recent secure-with-abort Turbopack protocol (Escudero et al. CCS'22) to the GOD setting without significantly sacrificing in efficiency.

2024

ASIACRYPT

Ideal-to-isogeny algorithm using 2-dimensional isogenies and its application to SQIsign
Abstract

The Deuring correspondence is a correspondence between supersingular elliptic curves and quaternion orders. Under this correspondence, an isogeny between elliptic curves corresponds to a quaternion ideal. This correspondence plays an important role in isogeny-based cryptography and several algorithms to compute an isogeny corresponding to a quaternion ideal (ideal-to-isogeny algorithms) have been proposed. In particular, SQIsign is a signature scheme based on the Deuring correspondence and uses an ideal-to-isogeny algorithm. In this paper, we propose a novel ideal-to-isogeny algorithm using isogenies of dimension $2$. Our algorithm is based on Kani's reducibility theorem, which gives a connection between isogenies of dimension $1$ and $2$. By using the characteristic $p$ of the base field of the form $2^fg - 1$ for a small odd integer $g$, our algorithm works by only $2$-isogenies and $(2, 2)$-isogenies in the operations in $\mathbb{F}_{p^2}$. We apply our algorithm to SQIsign and compare the efficiency of the new algorithm with the existing one. Our analysis shows that the key generation and the signing in our algorithm are at least twice as fast as those in the existing algorithm at the NIST security level 1. This advantage becomes more significant at higher security levels. In addition, our algorithm also improves the efficiency of the verification in SQIsign.

2024

ASIACRYPT

Improved Quantum Lifting by Coherent Measure-and-Reprogram
Abstract

We give a tighter lifting theorem for security games in the quantum random oracle model. At the core of our main result lies a novel measure-and-reprogram framework that we call coherent reprogramming. This framework gives a tighter lifting theorem for query complexity problems, that only requires purely classical reasoning. As direct applications of our lifting theorem, we first provide a quantum direct product theorem in the average case --- i.e., an enabling tool to determine the hardness of solving multi-instance security games. This allows us to derive in a straightforward manner the hardness of various security games, for example (i) the non-uniform hardness of salted games, (ii) the hardness of specific cryptographic tasks such as the multiple instance version of one-wayness and collision-resistance, and (iii) uniform or non-uniform hardness of many other games.

2024

ASIACRYPT

Interactive Line-Point Zero-Knowledge with Sublinear Communication and Linear Computation
Abstract

Studies of vector oblivious linear evaluation (VOLE)-based zero-knowledge (ZK) protocols flourish in recent years. Such ZK protocols feature optimal prover computation and a flexibility for handling arithmetic circuits over arbitrary fields. However, most of them have linear communication, which constitutes a bottleneck for handling large statements in a slow network. The pioneer work AntMan (CCS'22), achieved sublinear communication for the first time within VOLE-based ZK, but lost the advantage of fast proving. In this work, we propose two new VOLE-based ZK constructions that achieve sublinear communication and linear computation, simultaneously. Let $\mathcal{C}$ be a circuit with size $S$, input size $n$, and depth $d$. In particular, our first ZK, specialized for layered circuits, has communication $\bigO{n+d\log{S}}$, while our second ZK can be used to prove general circuits and has communication $\bigO{n+d\log{S}+d^2}$.
Our results are obtained by introducing the powerful sum-check techniques from the mature line of works on interactive proofs into the context of VOLE-based ZK for the first time. Reminiscent of the {\em non-interactive} line-point zero-knowledge proof system (ITC'21), we introduce an {\em interactive line-point zero-knowledge} (ILPZK) proof system, which serves as a bridge to VOLE-based ZK protocols. In addition, our works also enrich the studies of ZK based on interactive proofs, with new interesting features (e.g., having information-theoretic UC-security, naturally supporting any field) achieved.

2024

ASIACRYPT

Interactive Threshold Mercurial Signatures and Applications
Abstract

Mercurial signatures are an extension of equivalence class signatures that allow malleability for the public keys, messages, and signatures within the respective classes. Unfortunately, the most efficient construction to date suffers from a weak public key class-hiding property, where the original signer with the signing key can link the public keys in the same class. This is a severe limitation in their applications, where the signer is often considered untrustworthy of privacy.
This paper presents two-party and multi-party interactive threshold mercurial signatures that overcome the above limitation by eliminating the single entity who knows the signing key. For the general case, we propose two constructions. The first follows the same interactive structure as the two-party case, avoiding complex distributed computations such as randomness generation, inversion, and multiplication, and even eliminates the need for private communication between parties. The second is based on a blueprint for general multi-party computation using verifiable secret sharing, but adopting optimizations.
We show applications in anonymous credential systems that individually fit the two-party and multi-party constructions. In particular, in the two-party case, our approach provides stronger privacy by completely removing the trust in the authorities. We also discuss more applications, from blind signatures to multi-signatures and threshold ring signatures.
Finally, to showcase the practicality of our approach, we implement our interactive constructions and compare them against related alternatives.

2024

ASIACRYPT

Interval Key-Encapsulation Mechanism
Abstract

Forward-Secure Key-Encapsulation Mechanism (FS-KEM; Canetti et al. Eurocrypt 2003) allows Alice to encapsulate a key k to Bob for some time t such that Bob can decapsulate it at any time t'=<t. Crucially, a corruption of Bob's secret key after time t does not reveal k.
In this work, we generalize and extend this idea by also taking Post-Compromise Security (PCS) into account and call it Interval Key-Encapsulation Mechanism (IKEM). Thus, we do not only protect confidentiality of previous keys against future corruptions but also confidentiality of future keys against past corruptions. For this, Bob can regularly renew his secret key and inform others about the corresponding public key. IKEM enables Bob to decapsulate keys sent to him over an interval of time extending into the past, in case senders have not obtained his latest public key; forward security only needs to hold with respect to keys encapsulated before this interval. This basic IKEM variant can be instantiated based on standard KEM, which we prove to be optimal in terms of assumptions as well as ciphertext and key sizes.
We also extend this notion of IKEM for settings in which Bob decapsulates (much) later than Alice encapsulates (e.g., in high-latency or segmented networks): if a third user Charlie forwards Alice's ciphertext to Bob and, additionally, knows a recently renewed public key of Bob's, Charlie could re-encrypt the ciphertext for better PCS. We call this extended notion IKEMR. Our first IKEMR construction based on trapdoor permutations has (almost) constant sized ciphertexts in the number of re-encryptions; and our second IKEMR construction based on FS-PKE has constant sized public keys in the interval size.
Finally, to bypass our lower bound on the IKEM(R) secret key size, which must be linear in the interval size, we develop a new Interval RAM primitive with which Bob only stores a constant sized part of his secret key locally, while outsourcing the rest to a (possibly adversarial) server.
For all our constructions, we achieve security against active adversaries. For this, we obtain new insights on Replayable CCA security for KEM-type primitives, which might be of independent interest.

2024

ASIACRYPT

It’s a Kind of Magic: A Novel Conditional GAN Framework for Efficient Profiling Side-channel Analysis
Abstract

Profiling side-channel analysis (SCA) is widely used to evaluate the security of cryptographic implementations under worst-case attack scenarios. This method assumes a strong adversary with a fully controlled device clone, known as a profiling device, with full access to the internal state of the target algorithm, including the mask shares. However, acquiring such a profiling device in the real world is challenging, as secure products enforce strong life cycle protection, particularly on devices that allow the user partial (e.g., debug mode) or full (e.g., test mode) control. This enforcement restricts access to profiling devices, significantly reducing the effectiveness of profiling SCA.
To address this limitation, this paper introduces a novel framework that allows an attacker to create and learn from their own white-box reference design without needing privileged access on the profiling device.
Specifically, the attacker first implements the target algorithm on a different type of device with full control. Since this device is a white box to the attacker, they can access all internal states and mask shares. A novel conditional generative adversarial network (CGAN) framework is then introduced to mimic the feature extraction procedure from the reference device and transfer this experience to extract high-order leakages from the target device. These extracted features then serve as inputs for profiled SCA. Experiments show that our approach significantly enhances the efficacy of black-box profiling SCA, matching or potentially exceeding the results of worst-case security evaluations. Compared with conventional profiling SCA, which has strict requirements on the profiling device, our framework relaxes this threat model and, thus, can be better adapted to real-world attacks.

2024

ASIACRYPT

Jackpot: Non-Interactive Aggregatable Lotteries
Abstract

In proof-of-stake blockchains, liveness is ensured by repeatedly selecting random groups of parties as leaders, who are then in charge of proposing new blocks and driving consensus forward.
The lotteries that elect those leaders need to ensure that adversarial parties are not elected disproportionately often and that an adversary can not tell who was elected before those parties decide to speak, as this would potentially allow for denial-of-service attacks.
Whenever an elected party speaks, it needs to provide a winning lottery ticket, which proves that the party did indeed win the lottery.
Current solutions require all published winning tickets to be stored individually on-chain, which introduces undesirable storage overheads.
In this work, we introduce non-interactive aggregatable lotteries and show how these can be constructed efficiently.
Our lotteries provide the same security guarantees as previous lottery constructions, but additionally allow any third party to take a set of published winning tickets and aggregate them into one short digest.
We provide a formal model of our new primitive in the universal composability framework.
As one of our technical contributions, which may be of independent interest, we introduce aggregatable vector commitments with simulation-extractability and present a concretely efficient construction thereof in the algebraic group model in the presence of a random oracle.
We show how these commitments can be used to construct non-interactive aggregatable lotteries.
We have implemented our construction, called Jackpot, and provide benchmarks that underline its concrete efficiency.

2024

ASIACRYPT

Key Collisions on AES and Its Applications
Abstract

In this paper, we explore a new type of key collisions called target-plaintext key collisions of AES, which emerge as an open problem in the key committing security and are directly converted into single-block collision attacks on Davies-Meyer (DM) hashing mode.
For this key collision, a ciphertext collision is uniquely observed when a specific plaintext is encrypted under two distinct keys. We introduce an efficient automatic search tool designed to find target-plaintext key collisions.
This tool exploits bit-wise behaviors of differential characteristics and dependencies among operations and internal variables of both data processing and key scheduling parts.
This allows us to hierarchically perform rebound-type attacks to identify key collisions.
As a result, we demonstrate single-block collision attacks on 2/5/6-round AES-128/192/256-DM and semi-free-start collision attacks on 5/7/9-round AES-128/192/256-DM, respectively. To validate our attacks, we provide an example of fixed-target-plaintext key collision/semi-free-start collisions on 9-round AES-256-DM.
Furthermore, by exploiting a specific class of free-start collisions with our tool, we present two-block collision attacks on 3/9-round AES-128/256-DM, respectively.

2024

ASIACRYPT

Key Exchange in the Post-Snowden Era: Universally Composable Subversion-Resilient PAKE
Abstract

Password-Authenticated Key Exchange (PAKE) allows two parties to establish a common high-entropy secret from a possibly low-entropy pre-shared secret such as a password. In this work, we provide the first PAKE protocol with subversion resilience in the framework of universal composability (UC), where the latter roughly means that UC security still holds even if one of the two parties is malicious and the honest party's code has been subverted (in an undetectable manner).
We achieve this result by sanitizing the PAKE protocol from oblivious transfer (OT) due to Canetti et al. (PKC'12) via cryptographic reverse firewalls in the UC framework (Chakraborty et al., EUROCRYPT'22). This requires new techniques, which help us uncover new cryptographic primitives with sanitation-friendly properties along the way (such as OT, dual-mode cryptosystems, and signature schemes).
As an additional contribution, we delve deeper in the backbone of communication required in the subversion-resilient UC framework, extending it to the {\em unauthenticated} setting, in line with the work of Barak et al. (CRYPTO'05).

2024

ASIACRYPT

Leakage-Resilient Incompressible Cryptography: Constructions and Barriers
Abstract

We introduce Leakage-Resilient Incompressible cryptography, which simultaneously addresses two variants of side-channel attacks that have been tackled in theoretical cryptography. Leakage-resilience seeks to provide security against an adversary who learns a part of the secret-key and the entire ciphertext or signature; conversely, incompressible cryptography provides security against an adversary who learns the entire secret-key, but only a part of the ciphertext or signature. However, constructions in either of these security models can fail against an attack in the other model. In this work, we define a new model of security that subsumes both leakage-resilient cryptography and incompressible cryptography, and we present several non-trivial positive and negative results.
On the positive side, first we present a transformation from incompressible symmetric-key encryption (SKE) to leakage-resilient incompressible SKE in the information-theoretic setting. Next, as one of our main results, we construct a leakage-resilient incompressible public-key encryption (PKE), combining an incompressible SKE and a new primitive that we call leakage-resilient non-committing key encapsulation mechanism (LR-NC-KEM). While an incompressible SKE suitable for use in both these constructions already exists in the literature (Dziembowski, CRYPTO 2006), we present a new construction with better parameters, using an appropriate notion of invertible extractors; this leads to corresponding improvements in the final parameters we obtain in these constructions. We also design a leakage-resilient incompressible signature scheme.
On the negative side, we show barriers to significantly improving the parameters we obtain, by showing impossibility of basing the security of such improved schemes on blackbox reductions.
Apart from the general framework and the specific results we obtain, some of the intermediate tools that we define and instantiate, like LR-NC-KEM and invertible extractors, may be of independent interest.

2024

ASIACRYPT

LogRobin++: Optimizing Proofs of Disjunctive Statements in VOLE-Based ZK
Abstract

In the Zero-Knowledge Proof (ZKP) of a disjunctive statement, P and V agree on B fan-in 2 circuits C_{0}, ..., C_{B−1} over a field F; each circuit has n_{in} inputs, n_{x} multiplications, and one output. P’s goal is to demonstrate the knowledge of a witness (id ∈ [B], w ∈ F^{n_{in}}), s.t. C_{id}(w) = 0 where neither w nor id is revealed. Disjunctive statements are effective, for example, in implementing ZKP based on sequential execution of CPU steps.
This paper studies ZKP (of knowledge) protocols over disjunctive statements based on Vector OLE. Denoting by λ the statistical security parameter and let ρ ≜ max{log|F|,λ}, the previous state-of-the-art protocol Robin (Yang et al. CCS’23) required (n_{in}+3n_{x})log|F|+O(ρB) bits of communication with O(1) rounds, and Mac′n′Cheese (Baum et al. CRYPTO’21) required (n_{in}+n_{x})log|F|+2n_{x}ρ+O(ρlogB) bits of communication with O(logB) rounds, both in the VOLE-hybrid model.
Our novel protocol LogRobin++ achieves the same functionality at the cost of (n_{in}+n_{x})log|F|+O(ρlogB) bits of communication with O(1) rounds in the VOLE-hybrid model. Crucially, LogRobin++ takes advantage of two new techniques – (1) an O(logB)-overhead approach to prove in ZK that an IT-MAC commitment vector contains a zero; and (2) the realization of VOLE-based ZK over a disjunctive statement, where P commits only to w and multiplication outputs of C_{id}(w) (as opposed to prior work where P commits to w and all three wires that are associated with each multiplication gate).
We implemented LogRobin++ over Boolean (i.e., F_{2}) and arithmetic (i.e., F_{2^{61}−1}) fields. In our experiments, including the cost of generating VOLE correlations, LogRobin++ achieved up to 170× optimization over Robin in communication, resulting in up to 7× (resp. 3×) wall-clock time improvements in a WAN-like (resp. LAN-like) setting.

2024

ASIACRYPT

Lova: Lattice-Based Folding Scheme from Unstructured Lattices
Abstract

Folding schemes (Kothapalli et al., CRYPTO 2022) are a conceptually simple, yet powerful cryptographic primitive that can be used as a building block to realise incrementally verifiable computation (IVC) with low recursive overhead without general-purpose non-interactive succinct arguments of knowledge (SNARK).
Most folding schemes known rely on the hardness of the discrete logarithm problem, and thus are
both not quantum-resistant and operate over large prime fields. Existing post-quantum folding schemes (Boneh, Chen, ePrint 2024/257) based on lattice assumptions instead are secure under structured lattice assumptions, such as the Module Short Integer Solution Assumption (MSIS), which also binds them to relatively complex arithmetic.
In contrast, we construct Lova, the first folding scheme whose security relies on the
(unstructured) SIS assumption. We provide a Rust implementation of Lova, which makes only use of arithmetic in hardware-friendly power-of-two moduli. Crucially, this avoids the need of implementing and performing any finite field arithmetic. At the core of our results lies a new exact Euclidean norm proof which might be of independent interest

2024

ASIACRYPT

Low Communication Threshold Fully Homomorphic Encryption
Abstract

We study constructions of threshold fully homomorphic encryption with small partial decryption shares. In this context, we discuss in details the technicalities for achieving full-fledged threshold FHE, and bring light to limitations regarding prior works, inclucing an attack against the recent construction from Boudgoust and Scholl [ASIACRYPT 2023]. In light of our observations, we generalize the definition of threshold fully homomorphic encryption by adding an algorithm which allows to sanitize evaluated ciphertexts before they are decrypted by parties. In this setting, we are able to propose a construction which offers small partial decryption shares and avoids exponential noise flooding during partial decryption. In addition, we also propose an alternative protocol based on circuit-private (non-threshold) FHE and threshold public-key encryption for private delegation of computation on joint data, but requires an additional round of communication compared to our threshold FHE construction.

2024

ASIACRYPT

Measure-Rewind-Extract: Tighter Proofs of One-Way to Hiding and CCA Security in the Quantum Random Oracle Model
Abstract

The One-Way to Hiding (O2H) theorem, first given by Unruh (J ACM 2015) and then restated by Ambainis et al. (CRYPTO 2019), is a crucial technique for solving the reprogramming problem in the quantum random oracle model (QROM). It provides an upper bound d\cdot\sqrt{\epsilon} for the distinguisher's advantage, where d is the query depth and \epsilon denotes the advantage of a one-wayness attacker. Later, in order to obtain a tighter upper bound, Kuchta et al. (EUROCRYPT 2020) proposed the Measure-Rewind-Measure (MRM) technique and then proved the Measure-Rewind-Measure O2H (MRM-O2H) theorem, which provides the upper bound d\cdot\epsilon. They also proposed an open question: Can we combine their MRM technique with Ambainis et al.'s semi-classical oracle technique (CRYPTO 2019) or Zhandry's compressed oracle technique (CRYPTO 2019) to prove a new O2H theorem with an upper bound even tighter than d\cdot\epsilon?
In this paper, we give an affirmative answer for the above question. We propose a new technique named Measure-Rewind-Extract (MRE) by combining the MRM technique with the semi-classical oracle technique. By using MRE technique, we prove the Measure-Rewind-Extract O2H (MRE-O2H) theorem, which provides the upper bound \sqrt{d}\cdot\epsilon.
As an important application of our MRE-O2H theorem, for the FO^{\slashed{\bot}}, FO_m^\slashed{\bot}, FO^{\bot} and FO_m^\bot proposed by Hofheinz et al. (TCC 2017), i.e., the key encapsulation mechanism (KEM) variants of the Fujisaki-Okamoto transformation, we prove the following results in the QROM: Their IND-CCA security can be reduced to the IND-CPA security of the underlying public key encryption (PKE) scheme without the square-root advantage loss. In particular, compared with the IND-CCA proof of FO^{\slashed{\bot}} given by Kuchta et al. (EUROCRYPT 2020), ours removes the injectivity assumption and has a tighter security bound. Under the assumption that the underlying PKE scheme is unique randomness recoverable, we for the first time prove that their IND-CCA security can be reduced to the OW-CPA security of the underlying PKE scheme without the square-root advantage loss.

2024

ASIACRYPT

Mild Asymmetric Message Franking: Illegal-Messages-Only and Retrospective Content Moderation
Abstract

In these years, many messaging platforms have integrated end-to-end (E2E) encryption into their services. This widespread adoption of E2E encryption has triggered a technical tension between user privacy and illegal content moderation. The existing solutions either support only unframeability or deniability, or they are prone to abuse (the moderator can perform content moderation for all messages, whether illegal or not), or they lack mechanisms for retrospective content moderation.
To address the above issues, we introduce a new primitive called \emph{mild asymmetric message franking} (MAMF) to establish illegal-messages-only and retrospective content moderation for messaging systems, supporting unframeability and deniability simultaneously. We provide a framework to construct MAMF, leveraging two new building blocks, which might be of independent interest.

2024

ASIACRYPT

Mind the Bad Norms: Revisiting Compressed Oracle-based Quantum Indistinguishability Proofs
Abstract

In this work, we revisit the Hosoyamada-Iwata (HI) proof for the quantum CPA security of the 4-round Luby-Rackoff construction and identify a gap that appears to undermine the security proof. We emphasize that this is not an attack, and the construction may still achieve the claimed security level. However, this gap raises concerns about the feasibility of establishing a formal security proof for the 4-round Luby-Rackoff construction. In fact, the issue persists even if the number of rounds is increased arbitrarily. On a positive note, we restore the security of the 4-round Luby-Rackoff construction in the non-adaptive setting, achieving security up to $2^{n/6}$ superposition queries. Furthermore, we establish the quantum CPA security of the 4-round MistyR and 5-round MistyL constructions, up to $2^{n/5}$ and $2^{n/7}$ superposition queries, respectively, where $n$ denotes the size of the underlying permutation.

2024

ASIACRYPT

MinRank Gabidulin encryption scheme on matrix codes
Abstract

The McEliece scheme is a generic frame which allows to use any error correcting code of which there exists an efficient decoding algorithm to design an encryption scheme by hiding the generator matrix code. Similarly, the Niederreiter frame is the dual version of the McEliece scheme, and achieves smaller ciphertexts.
In the present paper, we propose a generalization of the McEliece frame and the Niederreiter frame to matrix codes and the MinRank problem, that we apply to Gabidulin matrix codes (Gabidulin rank codes considered as matrix codes). The masking we consider consists in starting from a rank code C, to consider a matrix version of C and to concatenate a certain number of rows and columns to the matrix codes version of the rank code C and then apply to an isometry for matric codes, i.e. right and left multiplications by fixed random matrices. The security of the schemes relies on the MinRank problem to decrypt a ciphertext, and the structural security of the scheme relies on a new problem EGMC-Indistinguishability problem that we introduce and that we study in detail. The main structural attack that we propose consists in trying to recover the masked linearity over the extension field which is lost during the masking process. Overall, starting from Gabidulin codes we obtain a very appealing tradeoff between the size of ciphertext and the size of the public key. For 128b of security we propose parameters ranging from ciphertext of size 65 B (and public keys of size 98 kB) to ciphertext of size 138B (and public key of size 41 kB). Our new approach permits to achieve better trade-off between ciphertexts and public key than the classical McEliece scheme. Our new approach permits to obtain an alternative scheme to the classic McEliece scheme, to obtain very small ciphertexts, with moreover smaller public keys than in the classic McEliece scheme. For 256 bits of security, we can obtain ciphertext as low as 119B, or public key as low as 87kB.

2024

ASIACRYPT

Modelling Ciphers with Overdefined Systems of Quadratic Equations: Application to Friday, Vision, RAIN and Biscuit
Abstract

Overdefined polynomial systems have the potential to lead to reduced complexity in solving procedures. In this work, we study how to overdefine the system of equations to describe the arithmetic oriented (AO) ciphers Friday, Vision, and RAIN, as well as a special system of quadratic equations over $\mathbb F_{2^{\ell}}$ used in the post-quantum signature scheme Biscuit. Our method is inspired by Courtois-Pieprzyk's and Murphy-Robshaw's methods to model AES with overdefined systems of quadratic equations over $\mathbb F_2$ and $\mathbb F_{2^8}$, respectively. However, our method is more refined and much simplified compared with Murphy-Robshaw's method, since it can take full advantage of the low-degree $\mathbb F_2$-linearized affine polynomials used in Friday and Vision, and the overdefined system of equations over $\mathbb F_{2^{\ell}}$ can be described in a clean way with our method. For RAIN, we instead consider quadratic Boolean equations rather than equations over large finite fields $\mathbb F_{2^{\ell}}$. Specifically, we demonstrate that the special structure of RAIN allows us to set up much more linearly independent quadratic Boolean equations than those obtained only with Courtois-Pieprzyk's method. Moreover, we further demonstrate that the underlying key-recovery problem in Biscuit (NIST PQC Round 1 Additional Signatures) can also be described by solving a much overdefined system of quadratic equations over $\mathbb F_{2^{\ell}}$. On the downside, the constructed systems of quadratic equations for these ciphers cannot be viewed as semi-regular, which makes it challenging to upper bound the complexity of the Gr\"{o}bner basis attack. However, such a new modelling method can significantly improve the lower bound of the complexity of the Gr\"{o}bner basis attacks on these ciphers, i.e., we view the complexity of solving a random system of quadratic equations of the same scale as the lower bound. How to better estimate the upper and lower bounds of the Gr\"{o}bner basis attacks on these ciphers based on our modelling method is left as an open problem.

2024

ASIACRYPT

More Vulnerabilities of Linear Structure Sbox-Based Ciphers Reveal Their Inability to Resist DFA
Abstract

At Asiacrypt 2021, Baksi et al. introduced DEFAULT, the first block cipher designed to resist differential fault attacks (DFA) at the algorithm level, boasting of 64-bit DFA security. However, during Eurocrypt 2022, Nageler et al. presented a DFA attack that exposed vulnerabilities in the claimed DFA security of DEFAULT, reducing it by up to 20 bits in the case of the simple key schedule and even allowing for unique key recovery in the presence of rotating keys. In this work, we compute deterministic differential trails for up to five rounds, injecting around 5 faults into the simple key schedule for key recovery, recovering equivalent keys with just 36 faults in the DEFAULT-LAYER, and introducing a generic DFA approach suitable for round-independent keys within the DEFAULT cipher. These results represent the most efficient key recovery achieved for the DEFAULT cipher under DFA attacks so far. Additionally, we introduce a novel fault attack called the Statistical-Differential Fault Attack (SDFA), specifically tailored for linear-structured SBox-based ciphers like DEFAULT. This technique is successfully applied to BAKSHEESH, resulting in a nearly unique key recovery. Our findings emphasize the vulnerabilities present in linear-structured SBox-based ciphers and underscore the challenges in establishing robust DFA protection for such cipher designs.

2024

ASIACRYPT

Multiple-Tweak Differential Attack Against SCARF
Abstract

In this paper, we present the first third-party cryptanalysis of SCARF, a tweakable low-latency block cipher designed to thwart contention-based cache attacks through cache randomization. We focus on multiple-tweak differential attacks, exploiting biases across multiple tweaks. We establish a theoretical framework explaining biases for any number of rounds and verify this framework experimentally. Then, we use these properties to develop a key recovery attack on 7-round SCARF with a time complexity of 2^76, achieving a 98.9% success rate in recovering the 240-bit secret key. Additionally, we introduce a distinguishing attack on the full 8-round SCARF in a multi-key setting, with a complexity of c x 2^67.55, demonstrating that SCARF does not provide 80-bit security under these conditions. We also explore whether our approach could be extended to the single-key model and discuss the implications of different S-box choices on the attack success.

2024

ASIACRYPT

MuxProofs: Succinct Arguments for Machine Computation from Vector Lookups
Abstract

Proofs for machine computation prove the correct execution of arbitrary programs that operate over fixed instruction sets (e.g., RISC-V, EVM, Wasm).
A standard approach for proving machine computation is to prove a universal set of constraints that encode the full instruction set at each step of the program execution.
This approach incurs a proving cost per execution step on the order of the total sum of instruction constraints for all of the instructions in the set, despite each step of the program only executing a single instruction.
Existing proving approaches that avoid this universal cost per step (and incur only the cost of a single instruction's constraints per step) either fail to provide zero-knowledge or rely on recursive proof composition for which security relies on the heuristic instantiation of the random oracle.
We present new protocols for proving machine execution that resolve these limitations, enabling prover efficiency on the order of only the executed instructions while achieving zero-knowledge and avoiding recursive proofs.
Our core technical contribution is a new primitive that we call a succinct vector lookup argument which enables a prover to build up a machine execution ``on-the-fly''.
We propose succinct vector lookups for both univariate polynomial and multivariate polynomial commitments in which vectors are encoded on cosets of a multiplicative subgroup and on subcubes of the boolean hypercube, respectively.
We instantiate our proofs for machine computation by integrating our vector lookups with existing efficient, succinct non-interactive proof systems for NP.

2024

ASIACRYPT

Non-interactive Blind Signatures: Post-quantum and Stronger Security
Abstract

Blind signatures enable a receiver to obtain signatures on messages of its choice without revealing any message to the signer. Round-optimal blind signatures are designed as a two-round interactive protocol between a signer and receiver. Coincidentally, the choice of message is not important in many applications, and is routinely set as a random (unstructured) message by a receiver.
With the goal of designing more efficient blind signatures for such applications, Hanzlik (Eurocrypt '23) introduced a new variant called non-interactive blind signatures (NIBS). These allow a signer to asynchronously generate partial signatures for any recipient such that only the intended recipient can extract a blinded signature for a random message. This bypasses the two-round barrier for traditional blind signatures, yet enables many known applications. Hanzlik provided new practical designs for NIBS from bilinear pairings.
In this work, we propose new enhanced security properties for NIBS as well as provide multiple constructions with varying levels of security and concrete efficiency. We propose a new generic paradigm for NIBS from circuit-private leveled homomorphic encryption achieving optimal-sized signatures (i.e., same as any non-blind signature) at the cost of large public keys. We also investigate concretely efficient NIBS with post-quantum security, satisfying weaker level of privacy as proposed by Hanzlik.

2024

ASIACRYPT

Non-Malleable Subvector Commitments
Abstract

Vector commitments are compressing commitments to vectors allowing for short local openings. Rotem and Segev (TCC'21) formalized a notion of non-malleability for vector commitments, which accounts for the information revealed by local openings when an adversary outputs its own commitment and attempts to open it to messages related to those of honest parties. They left open the problem of extending their non-malleable construction to the scenario of subvector commitments, where a committer can compactly open a significant fraction of committed vectors.
In this paper, we construct non-malleable subvector commitments by generalizing Garay {\it et al.}'s notion of simulation-sound trapdoor commitments (Eurocrypt'03) to the subvector commitment setting. We then construct simulation-sound subvector commitments from the Bilinear Diffie-Hellman assumption as well as the Strong RSA and Bilinear Strong Diffie-Hellman assumptions. These constructions allow the adversary to see equivocations on multiple tags, and thus yield re-usable (as defined by Damg\aa rd and Groth) non-malleable commitments.

2024

ASIACRYPT

NTRU-based Bootstrapping for MK-FHEs without using Overstretched Parameters
Abstract

Recent attacks on NTRU lattices given by Ducas and van Woerden (ASIACRYPT 2021) showed that for moduli $q$ larger than the so-called fatigue point $n^{2.484+o(1)}$, the security of NTRU is noticeably less than that of (ring)-LWE. Unlike NTRU-based PKE with $q$ typically lying in the secure regime of NTRU lattices (i.e., $q<n^{2.484+o(1)}$), the security of existing NTRU-based multi-key FHEs (MK-FHEs) requiring $q=O(n^k)$ for $k$ keys could be significantly affected by those attacks.
In this paper, we first propose a (matrix) NTRU-based MK-FHE for super-constant number $k$ of keys without using overstretched NTRU parameters. Our scheme is essentially a combination of two components following the two-layer framework of TFHE/FHEW:
- a simple first-layer matrix NTRU-based encryption which naturally supports multi-key NAND operations with moduli $q=O(k\cdot n^{1.5})$ only linear in the number $k$ of keys;
- and a crucial second-layer NTRU-based encryption which supports efficient hybrid product between a single-key ciphertext and a multi-key ciphertext for gate bootstrapping.
Then, by replacing the first-layer with a more efficient LWE-based multi-key encryption,
we obtain an improved MK-FHE scheme with better performance. We also employ a light key-switching technique to reduce the key-switching key size from previous $O(n^2)$ bits to $O(n)$ bits.
A proof-of-concept implementation shows that our two MK-FHE schemes outperform the state-of-the-art TFHE-like MK-FHE schemes in both computation efficiency and bootstrapping key size. Concretely, for $k=8$ at the same 100-bit security level, our improved MK-FHE scheme can bootstrap a ciphertext in {0.54s} on a laptop and only has a bootstrapping key of size {13.89}MB,
which are respectively 2.2 times faster and 7.4 times smaller than the MK-FHE scheme (which relies on a second-layer encryption from the ring-LWE assumption) due to Chen, Chillotti and Song (ASIACRYPT 2019).

2024

ASIACRYPT

On Security Proofs of Existing Equivalence Class Signature Schemes
Abstract

Equivalence class signatures (EQS; Asiacrypt '14), sign vectors of elements from a bilinear group. Anyone can transform a signature on a vector to a signature on any multiple of that vector; signatures thus authenticate equivalence classes. A transformed signature/message pair is indistinguishable from a random signature on a random message. EQS have been used to efficiently instantiate (delegatable) anonymous credentials, (round-optimal) blind signatures, ring and group signatures, anonymous tokens and contact-tracing schemes, to name a few.
The original EQS construction (J. Crypto '19) is proven secure in the generic group model, and the first scheme from standard assumptions (PKC '18) satisfies a weaker model insufficient for most applications. Two works (Asiacrypt '19, PKC '22) propose applicable schemes that assume trusted parameters. Their unforgeability is argued via a security proof from standard (or non-interactive) assumptions.
We show that their security proofs are flawed and explain the subtle issue. While the schemes might be provable in the algebraic group model (AGM), we instead show that the original construction, which is more efficient and has found applications in many works, is secure in the AGM under a parametrized non-interactive hardness assumption.

2024

ASIACRYPT

On the Complexity of Cryptographic Groups and Generic Group Models
Abstract

Ever since the seminal work of Diffie and Hellman, cryptographic (cyclic) groups have served as a fundamental building block for constructing cryptographic schemes and protocols. The security of these constructions can often be based on the hardness of (cyclic) group-based computational assumptions. Then, the generic group model (GGM) has been studied as an idealized model (Shoup, EuroCrypt 1997), which justifies the hardness of many (cyclic) group-based assumptions and shows the limits of some group-based cryptosystems. We stress that, the importance of the length of group encoding, either in a concrete group-based construction or assumption, or in the GGM, has not been studied.
In this work, we initiate a systematic study on the complexity of cryptographic groups and generic group models, varying in different lengths of group encodings, and demonstrate evidences that ``the length matters''. More concretely, we have the following results:
-- We show that there is no black-box/relativizing reduction from the CDH-secure groups (i.e., over such groups, the computational Diffie-Hellman assumption holds) with shorter encodings, to the CDH-secure groups with longer encodings, within the same security parameter. More specifically, given any arbitrary longer CDH-secure group, it is impossible to generically shorten the group encoding and obtain a shorter CDH-secure group within the same group order.
-- We show that there is a strict hierarchy of the GGMs with different lengths of encodings. That is, in the framework of indifferentiability, the shorter GGM is strictly stronger than the longer ones, even in the presence of computationally bounded adversaries.

2024

ASIACRYPT

On the Semidirect Discrete Logarithm Problem in Finite Groups
Abstract

We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem ($\SDLP$) in \emph{any} finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post-quantum cryptographic algorithms from non-abelian groups. We use a series of reduction results to show that it suffices to consider $\SDLP$ in finite simple groups. We then apply the celebrated Classification of Finite Simple Groups to consider each family. The infinite families of finite simple groups admit, in a fairly general setting, linear algebraic attacks providing a reduction to the classical discrete logarithm problem. For the sporadic simple groups, we show that their inherent properties render them unsuitable for cryptographically hard $\SDLP$ instances, which we illustrate via a Baby-Step Giant-Step style attack against $\SDLP$ in the Monster Group.
Our quantum $\SDLP$ algorithm is fully constructive, up to the computation of maximal normal subgroups, for all but three remaining cases that appear to be gaps in the literature on constructive recognition of groups; for these cases $\SDLP$ is no harder than finding a linear representation. We conclude that $\SDLP$ is not a suitable post-quantum hardness assumption for any choice of finite group.

2024

ASIACRYPT

On the Spinor Genus and the Distinguishing Lattice Isomorphism Problem
Abstract

This paper addresses the spinor genus, a previously unrecognized classification of quadratic forms in the context of cryptography, related to the lattice isomorphism problem (LIP). The spinor genus lies between the genus and equivalence class, thus refining the concept of genus. We present algorithms to determine whether two quadratic forms belong to the same spinor genus. If they do not, it provides a negative answer to the distinguishing variant of LIP. However, these algorithms have very high complexity, and we show that the proportion of genera splitting into multiple spinor genera is vanishing (assuming rank n ≥ 3). For the special case of anisotropic integral binary forms (n = 2) over number fields with class number 1, we offer an efficient quantum algorithm to test if two forms lie in the same spinor genus. Our algorithm does not apply to the HAWK protocol, which uses integral binary Hermitian forms over number fields with class number greater than 1.

2024

ASIACRYPT

One Tree to Rule Them All: Optimizing GGM Trees and OWFs for Post-Quantum Signatures
Abstract

The use of MPC-in-the-Head (MPCitH)-based zero-knowledge proofs of knowledge (ZKPoK) to prove knowledge of a preimage of a one-way function (OWF) is a popular approach towards constructing efficient post-quantum digital signatures. Starting with the Picnic signature scheme, many optimized MPCitH signatures using a variety of (candidate) OWFs have been proposed. Recently, Baum et al. (CRYPTO 2023) showed a fundamental improvement to MPCitH, called VOLE-in-the-Head (VOLEitH), which can generically reduce the signature size by at least a factor of two without decreasing computational performance or introducing new assumptions. Based on this, they designed the FAEST signature which uses AES as the underlying OWF. However, in comparison to MPCitH, the behavior of VOLEitH when using other OWFs is still unexplored.
In this work, we improve a crucial building block of the VOLEitH and MPCitH approaches, the so-called all-but-one vector commitment, thus decreasing the signature size of VOLEitH and MPCitH signature schemes. Moreover, by introducing a small Proof of Work into the signing procedure, we can improve the parameters of VOLEitH (further decreasing signature size) \emph{without} compromising the computational performance of the scheme.
Based on these optimizations, we propose three VOLEitH signature schemes FAESTER, KuMQuat, and MandaRain based on AES, MQ, and Rain, respectively. We carefully explore the parameter space for these schemes and implement each, showcasing their performance with benchmarks. Our experiments show that these three signature schemes outperform MPCitH-based competitors that use comparable OWFs, in terms of both signature size and signing/verification time.

2024

ASIACRYPT

One-More Unforgeability for Multi- and Threshold Signatures
Abstract

This paper initiates the study of one-more unforgeability for multi-signatures and threshold signatures as a stronger security goal, ensuring that $\ell$ executions of a signing protocol cannot result in more than $\ell$ signatures. This notion is widely used in the context of blind signatures, but we argue that it is a convenient way to model strong unforgeability for other types of distributed signing protocols. We provide formal security definitions for one-more unforgeability (OMUF) and show that the HBMS multi-signature scheme does not satisfy this definition, whereas MuSig and MuSig2 do. In the full version of this paper, we also show that mBCJ does not satisfy OMUF, as well as expose a subtle issue with its existential unforgeability. For threshold signatures, FROST satisfies OMUF, but ROAST does not.

2024

ASIACRYPT

Partially Non-Interactive Two-Round Lattice-Based Threshold Signatures
Abstract

This paper gives the first lattice-based two-round threshold signature based on standard lattice assumptions for which the first message is independent of the message being signed without relying on fully-homomorphic encryption, and our construction supports arbitrary thresholds.
Our construction provides a careful instantiation of a generic threshold signature construction by Tessaro and Zhu (EUROCRYPT '23) based on specific linear hash functions, which in turns can be seen as a generalization of the FROST scheme by Komlo and Goldberg (SAC '20). Our reduction techniques are new in the context of lattice-based cryptography. Also, our scheme does not use any heavy tools, such as NIZKs or homomorphic trapdoor commitments.

2024

ASIACRYPT

Password-Protected Threshold Signatures
Abstract

We witness increase in applications like cryptocurrency wallets, which involve users issuing signatures using private keys. To protect these keys from loss or compromise, users commonly outsource them to a custodial server. This creates a new point of failure, because compromise of such server leaks the user’s key, and if user authentication is implemented with a password then this password becomes open to an offline dictionary attack (ODA). A better solution is to secret-share the key among a set of servers, possibly including user’s own device(s), and implement password authentication and signature computation using threshold cryptography.
We propose a notion of augmented password protected threshold signature scheme (aptSIG) which captures the best possible security level for this setting. Using standard threshold cryptography techniques, i.e. threshold password authentication and threshold signatures, one can guarantee that compromising up to t out of n servers reveals no information on either the key or the password. However, we extend this with a novel property, namely that compromising even all n servers also does not leak any information, except via an unavoidable ODA attack, which reveals the key (and the password) only if the attacker guesses the password.
We define aptSIG in the Universally Composable (UC) framework and show that it can be constructed very efficiently, using a black-box composition of any UC threshold signature [12] and a UC augmented Password-Protected Secret Sharing (aPPSS), which we define as an extension of prior notion of PPSS [26]. As concrete instantiations we obtain secure aptSIG schemes for ECDSA and BLS signatures with very small overhead over the respective respective threshold signature.

2024

ASIACRYPT

Perfectly-Secure Multiparty Computation with Linear Communication Complexity over Any Modulus
Abstract

Consider the task of secure multiparty computation (MPC) among n parties with perfect security and guaranteed output delivery, supporting t < n/3 active corruptions. Suppose the arithmetic circuit C to be computed is defined over a finite ring Z/qZ, for an arbitrary q ∈ Z. It is known that this type of MPC over such ring is possible, with communication that scales as O(n|C|), assuming that q scales as Ω(n). However, for constant-size rings Z/qZ where q = O(1), the communication is actually O(n log n|C|) due to the need of the so-called ring extensions. In most natural settings, the number of parties is variable but the “datatypes” used for the computation are fixed (e.g. 64-bit integers). In this regime, no protocol with linear communication exists. In this work we provide an MPC protocol in this setting: perfect security, G.O.D. and t < n/3 active corruptions, that enjoys linear communication O(n|C|), even for constant-size rings Z/qZ. This includes as important particular cases small fields such as F2, and also the ring Z/2k Z. The main difficulty in achieving this result is that widely used techniques such as linear secret-sharing cannot work over constant-size rings, and instead, one must make use of ring extensions that add Ω(log n) over- head, while packing Ω(log n) ring elements in each extension element in order to amortize this cost. We make use reverse multiplication-friendly embeddings (RMFEs) for this packing, and adapt recent techniques in network routing (Goyal et al. CRYPTO’22) to ensure this can be efficiently used for non-SIMD circuits. Unfortunately, doing this naively results in a restriction on the minimum width of the circuit, which leads to an extra additive term in communication of poly(n) · depth(C). One of our biggest technical contributions lies in designing novel techniques to overcome this limitation by packing elements that are distributed across different layers. To the best of our knowledge, all works that have a notion of packing (e.g. RMFE or packed secret-sharing) group gates across the same layer, and not doing so, as in our work, leads to a unique set of challenges and complications.

2024

ASIACRYPT

Post-Quantum Asynchronous Remote Key Generation for FIDO2
Abstract

The Fast IDentity Online (FIDO) Alliance has developed
the widely adopted FIDO2 protocol suite that allows for passwordless
online authentication. Cryptographic keys stored on a user’s device (e.g.
their smartphone) are used as credentials to authenticate to services by
performing a challenge-response protocol. Yet, this approach leaves users
unable to access their accounts in case their authenticator is lost.
The device manufacturer Yubico thus proposed a FIDO2-compliant mech-
anism that allows to easily create backup authenticators. Frymann et
al. (CCS 2020) have first analyzed the cryptographic core of this pro-
posal by introducing the new primitive of Asynchronous Remote Key
Generation (ARKG) and accompanying security definitions. Later works
instantiated ARKG both from classical and post-quantum assumptions
(ACNS 2023, EuroS&P 2023).
As we will point out in this paper, the security definitions put forward
and used in these papers do not adequately capture the desired security
requirements in FIDO2-based authentication and recovery. This issue
was also identified in independent and concurrent work by Stebila and
Wilson (AsiaCCS 2024), who proposed a new framework for the analy-
sis of account recovery mechanisms, along with a secure post-quantum
instantiation from KEMs and key-blinding signature schemes.
In this work, we propose alternative security definitions for the primitive
ARKG when used inside an account recovery mechanism in FIDO2. We
give a secure instantiation from KEMs and standard signature schemes,
which may in particular provide post-quantum security. Our solution
strikes a middle ground between the compact, but (for this particular
use case) inadequate security notions put forward by Frymann et al.,
and the secure, but more involved and highly tailored model introduced
by Stebila and Wilson.

2024

ASIACRYPT

Practical Blind Signatures in Pairing-Free Groups
Abstract

Blind signatures have garnered significant attention in recent years, with several efficient constructions in the random oracle model relying on well-understood assumptions. However, this progress does not apply to pairing-free cyclic groups: fully secure constructions over cyclic groups rely on pairings, remain inefficient, or depend on the algebraic group model or strong interactive assumptions. To address this gap, Chairattana-Apirom, Tessaro, and Zhu (CTZ, Crypto 2024) proposed a new scheme based on the CDH assumption. Unfortunately, their construction results in large signatures and high communication complexity.
In this work, we propose a new blind signature construction in the random oracle model that significantly improves upon the CTZ scheme. Compared to CTZ, our scheme reduces communication complexity by a factor of more than 10 and decreases the signature size by a factor of more than 45, achieving a compact signature size of only 224~Bytes. The security of our scheme is based on the DDH assumption over pairing-free cyclic groups, and we show how to generalize it to the partially blind setting.

2024

ASIACRYPT

Proofs for Deep Thought: Accumulation for large memories and deterministic computations
Abstract

An important part in proving machine computation is to prove the correctness of the read and write operations performed from the memory, which we term memory-proving. Previous methodologies required proving Merkle Tree openings or multi-set hashes, resulting in relatively large proof circuits. We construct an efficient memory-proving Incrementally Verifiable Computation (IVC) scheme from accumulation, which is particularly useful for machine computations with large memories and deterministic steps. In our scheme, the IVC prover PIVC has cost entirely independent of the memory size T and only needs to commit to approximately 15 field elements per read/write operation, marking a more than 100X improvement over prior work. We further reduce this cost by employing a modified, accumulation-friendly version of the GKR protocol. In the optimized version, PIVC only needs to commit to 6 small memory-table elements per read/write. If the table stores 32-bit values, then this is equivalent to committing to less than one single field element per read and write. Our modified GKR protocol is also valuable for proving other deterministic computations within the context of IVC. Our memory-proving protocol can be extended to support key-value store.

2024

ASIACRYPT

Provable Security of Linux-DRBG in the Seedless Robustness Model
Abstract

This paper studies the provable security of the deterministic random bit generator~(DRBG) utilized in Linux 6.4.8, marking the first analysis of Linux-DRBG from a provable security perspective since its substantial structural changes in Linux 4 and Linux 5.17. Specifically, we prove its security up to $O(\min\{2^{\frac{n}{2}},2^{\frac{\lambda}{2}}\})$ queries in the seedless robustness model, where $n$ is the output size of the internal primitives and $\lambda$ is the min-entropy of the entropy source. Our result implies $128$-bit security given $n=256$ and $\lambda=256$ for Linux-DRBG. We also present two distinguishing attacks using $O(2^{\frac{n}{2}})$ and $O (2^{\frac{\lambda}{2}})$ queries, respectively, proving the tightness of our security bound.

2024

ASIACRYPT

Quantum Algorithms for Fast Correlation Attacks on LFSR-Based Stream Ciphers
Abstract

This paper presents quantum algorithms for fast correlation attacks, one of the most powerful techniques for cryptanalysis on LFSR-based stream ciphers in the classical setting.
Typical fast correlation attacks recover a value related to the initial state of the underlying LFSR by solving a decoding problem on a binary linear code with the Fast Walsh-Hadamard Transform (FWHT).
Applying the FWHT on a function in the classical setting is mathematically equivalent to applying the Hadamard transform on the corresponding state in quantum computation.
While the classical FWHT on a function with $\ell$-bit inputs requires $O(\ell 2^\ell)$ operations, the Hadamard transform on $\ell$-qubit states requires only a parallel application of $O(\ell)$ basic gates.
This difference leads to the exponential speed-up by some quantum algorithms, including Simon's period finding algorithm.
Given these facts, the question naturally arises of whether a quantum speedup can also be achieved for fast correlations by replacing the classical FWHT with the quantum Hadamard transform.
We show quantum algorithms achieving speed-up in such a way, introducing a new attack model in the Q2 setting.
The new model endows adversaries with a quite strong power, but we demonstrate its feasibility by showing that certain members of the ChaCha and Salsa20 families will likely be secure in the new model.
Our attack exploits the link between LFSRs' state update and multiplication in a fine field to apply Shor's algorithm for the discrete logarithm problem.
We apply our attacks on SNOW 2.0, SNOW 3G, and Sosemanuk, observing a large speed-up from classical attacks.

2024

ASIACRYPT

Quantum Circuits of AES with a Low-depth Linear Layer and a New Structure
Abstract

In recent years quantum computing has developed rapidly. The security threat posed by quantum computing to cryptography makes it necessary to better evaluate the resource cost of attacking algorithms, some of which require quantum implementations of the attacked cryptographic building blocks. In this paper we manage to optimize quantum circuits of AES in several aspects. Firstly, based on de Brugière \textit{et al.}'s greedy algorithm, we propose an improved depth-oriented algorithm for synthesizing low-depth CNOT circuits with no ancilla qubits. Our algorithm finds a CNOT circuit of AES MixColumns with depth 10, which breaks a recent record of depth 16. In addition, our algorithm gives low-depth CNOT circuits for many MDS matrices and matrices used in block ciphers studied in related work. Secondly, we present a new structure named compressed pipeline structure to synthesize quantum circuits of AES, which can be used for constructing quantum oracles employed in quantum attacks based on Grover's and Simon's algorithms. When the number of ancilla qubits required by the round function and its inverse is not very large, our structure will have a better trade-off of $D$-$W$ cost. Moreover, our encryption oracle will have the lowest depth to date. We then give detailed encryption circuits of AES-128 under the guidance of our structure and make some comparisons with other circuits. Finally, the encryption part and the key schedule part have their own application scenarios. The Encryption oracle used in Simon's algorithm built with the former will have smaller round depth. For example, we can construct an AES-128 Encryption oracle with $T$-depth 33, while the previous best result is 60. A small variant of the latter, along with our method to make an Sbox input-invariant, can avoid the allocation of extra ancilla qubits for storing key words in the shallowed pipeline structure. Based on this, we achieve an encryption circuit of AES-128 with the lowest $TofD$-$W$ cost 130720 to date.

2024

ASIACRYPT

Quantum Money from Class Group Actions on Elliptic Curves
Abstract

We construct a quantum money/quantum lightning scheme from class group actions on elliptic curves over F_p. Our scheme, which is based on the invariant money construction of Liu et al. (Eurocrypt '23), is simple to describe and we believe it to be the most instantiable and well-defined quantum money construction known so far. The security of our quantum lightning construction is exactly equivalent to the (conjectured) hardness of constructing two uniform superpositions over elliptic curves in an isogeny class which is acted on simply transitively by an exponentially large ideal class group.
However, we needed to advance the state of the art of isogenies in order to achieve our scheme. In partcular, we show:
An efficient (quantum) algorithm for sampling a uniform superposition over a cryptographically large isogeny class.
A method for specifying polynomially many generators for the class group so that polynomial-sized products yield an exponential-sized subset of class group, modulo a seemingly very modest assumption.
Achieving these results also requires us to advance the state of the art of the (pure) mathematics of elliptic curves, and we are optimistic that the mathematical tools we developed in this paper can be used to advance isogeny-based cryptography in other ways.

2024

ASIACRYPT

Quantum Unpredictability
Abstract

Unpredictable functions (UPFs) play essential roles in classical cryptography, including message authentication codes (MACs) and digital signatures. In this paper, we introduce a quantum analog of UPFs, which we call unpredictable state generators (UPSGs). UPSGs are implied by pseudorandom function-like states generators (PRFSs), which are a quantum analog of pseudorandom functions (PRFs), and therefore UPSGs could exist even if one-way functions do not exist, similar to other recently introduced primitives like pseudorandom state generators (PRSGs), one-way state generators (OWSGs), and EFIs. In classical cryptography, UPFs are equivalent to PRFs, but in the quantum case, the equivalence is not clear, and UPSGs could be weaker than PRFSs. Despite this, we demonstrate that all known applications of PRFSs are also achievable with UPSGs. They include IND-CPA-secure secret-key encryption and EUF-CMA-secure MACs with unclonable tags. Our findings suggest that, for many applications, quantum unpredictability, rather than quantum pseudorandomness, is sufficient.

2024

ASIACRYPT

QuietOT: Lightweight Oblivious Transfer with a Public-Key Setup
Abstract

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for efficiently evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads.
Specifically, traditional OT extension uses a small number of “base” OTs, generated using any black-box OT protocol, and convert them into many OT instances using only lightweight symmetric-key primitives. Recently, a new paradigm of OT with a public-key setup has emerged, which replaces the base OTs with a non-interactive setup: Using only the public key of the other party, two parties can efficiently compute a virtually unbounded number of OT instances on-the-fly.
In this paper, we put forth a novel framework for OT extension with a public-key setup (henceforth, “public-key OT”) and concretely efficient instantiations. Implementations of our framework are 30–100× faster when compared to the previous state-of-the-art public-key OT protocols, and remain competitive even when compared to OT protocols that do not offer a public-key setup. Additionally, our instantiations result in the first public-key schemes with plausible post-quantum security.
In summary, this paper contributes:
- QuietOT: A framework for OT extension with public-key setup that uses fast, symmetric-key primitives to generate OT instances following a one-time public-key setup, and offering additional features such as precomputability.
- A public-key setup for QuietOT from the RingLWE assumption, resulting in the first post-quantum construction of OT extension with a public-key setup.
- An optimized, open-source implementation of our construction that can generate up to 1M OT extensions per second on commodity hardware. In contrast, the state-of-the-art public-key OT protocol is limited to at most 20K OTs per second.
- The first formal treatment of the security of OT with a public-key setup in a multi-party setting, which addresses several subtleties that were overlooked in prior work.

2024

ASIACRYPT

Randomness in Private Sequential Stateless Protocols
Abstract

A significant body of work in information-theoretic cryptography has been devoted to the fundamental problem of understanding the power of randomness in private computation. This has included both in-depth study of the randomness complexity of specific functions (e.g., Couteau and Rosén, ASIACRYPT 2022, gives an upper bound of 6 for n-party AND), and results for broad classes of functions (e.g., Kushilevitz et al., STOC 1996, gives an O(1) upper bound for all functions with linear-sized circuits). In this work, we make further progress on both fronts by studying randomness complexity in a new simple model of secure computation called Private Sequential Stateless (PSS) model.
We show that functions with O(1) randomness complexity in the PSS model are exactly those with constant-width branching programs, restricting to “speak-constant-times” protocols and to “read-constant-times” branching programs.
Towards this our main construction is a novel PSS protocol for “strongly regular branching programs” (SRBP). As we show, any constant-width branching program can be converted to a constant-width SRBP, yielding one side of our characterization. The converse direction uses ideas from Kushilevitz et al. to translate randomness to communication.
Our protocols are concretely efficient, has a simple structure, covers the broad class of functions with small-width, read-once (or read-a-few-times) branching programs, and hence may be of practical interest when 1-privacy is considered adequate. Also, as a consequence of our general result for SRBPs, we obtain an improvement over the protocol of Couteau and Rosén for AND in certain cases — not in terms of the number of bits of randomness, but in terms of a simpler protocol structure (sequential, stateless).

2024

ASIACRYPT

Rare structures in tensor graphs - Bermuda triangles for cryptosystems based on the Tensor Isomorphism problem
Abstract

Recently, there has been a lot of interest in improving the understanding of the practical hardness of the 3-Tensor Isomorphism (3-TI) problem, which, given two 3-tensors, asks for an isometry between the two. The current state-of-the-art for solving this problem is the algebraic algorithm of Ran et al. '23 and the graph-theoretic algorithm of Narayanan et al. '24 that have both slightly reduced the security of the signature schemes MEDS and ALTEQ, based on variants of the 3-TI problem (Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE) respectively).
In this paper, we propose a new combined technique for solving the 3-TI problem. Our algorithm, as typically done in graph-based algorithms, looks for an invariant in the graphs of the isomorphic tensors that can be used to recover the secret isometry. However, contrary to usual combinatorial approaches, our approach is purely algebraic. We model the invariant as a system of non-linear equations and solve it. Using this modelling we are able to find very rare invariant objects in the graphs of the tensors — cycles of length 3 (triangles) — that exist with probability approximately 1/q. For solving the system of non-linear equations we use Gröbner-basis techniques adapted to tri-graded polynomial rings. We analyze the algorithm theoretically, and we provide lower and upper bounds on its complexity. We further provide experimental support for our complexity claims. Finally, we describe two dedicated versions of our algorithm tailored to the specifics of the MCE and the ATFE problems.
The implications of our algorithm are improved cryptanalysis of both MEDS and ALTEQ for the cases when a triangle exists, i.e. in approximately 1/q of the cases. While for MEDS, we only marginally reduce the security compared to previous work, for ALTEQ our results are much more significant with at least 60 bits improvement compared to previous work for all security levels.
For Level I parameters, our attack is practical, and we are able to recover the secret key in only 1501 seconds. The code is available for testing and verification of our results.

2024

ASIACRYPT

Reducing the Number of Qubits in Quantum Information Set Decoding
Abstract

This paper presents an optimization of the memory cost of the quantum \emph{Information Set Decoding} (ISD) algorithm proposed by Bernstein (PQCrypto 2010), obtained by combining Prange's ISD with Grover's quantum search.
When the code has constant rate and length $n$, this algorithm essentially performs a quantum search which, at each iterate, solves a linear system of dimension $\mathcal{O}(n)$. The typical code lengths used in post-quantum public-key cryptosystems range from $10^3$ to $10^5$. Gaussian elimination, which was used in previous works, needs $\mathcal{O}(n^2)$ space to represent the matrix, resulting in millions or billions of (logical) qubits for these schemes.
In this paper, we propose instead to use the algorithm for sparse matrix inversion of Wiedemann (IEEE Trans. inf. theory 1986). The interest of Wiedemann's method is that one relies only on the implementation of a matrix-vector product, where the matrix can be represented in an implicit way. This is the case here.
We propose two main trade-offs, which we have fully implemented, tested on small instances, and benchmarked for larger instances. The first one is a quantum circuit using $\mathcal{O}(n)$ qubits, $\mathcal{O}(n^3)$ Toffoli gates like Gaussian elimination, and depth $\mathcal{O}(n^2 \log n)$. The second one is a quantum circuit using $\mathcal{O}(n \log^2 n)$ qubits, $\mathcal{O}(n^3)$ gates in total but only $\mathcal{O}( n^2 \log^2 n)$ Toffoli gates, which relies on a different representation of the search space.
As an example, for the smallest Classic McEliece parameters we estimate that the Quantum Prange's algorithm can run with 18098 qubits, while previous works would have required at least half a million qubits.

2024

ASIACRYPT

Registered FE beyond Predicates: (Attribute-Based) Linear Functions and more
Abstract

This paper introduces the first registered functional encryption RFE scheme tailored for linear functions. Distinctly different from classical functional encryption (FE), RFE addresses the key-escrow issue and negates the master key exfiltration attack. Instead of relying on a centralized trusted authority, it introduces a “key curator” - a fully transparent entity that does not retain secrets. In an RFE framework, users independently generate secret keys and subsequently register their respective public keys, along with their authorized functions, with the key curator. This curator consolidates public keys from various users into a unified, concise master public key. For decryption, users occasionally secure helper decryption keys from the key curator, which they use in conjunction way with their private keys. It is imperative that the aggregate public key, helper decryption keys, ciphertexts, and the times for encryption/decryption are polylogarithmic in the number of registered users.
All existing RFE designs were confined to predicates where given the correct credentials a user can retrieve the entire payload from a ci- phertext or gain no information about it otherwise. Contrarily, our RFE scheme facilitates the computation of linear functions on encrypted con- tent and extraction of only the computation results. Recognizing poten- tial leaks from linear functions, we further enhance our RFE by incor- porating an attribute-based access control mechanism. The outcome is the first registered attribute-based linear FE (RABIPFE), which sup- ports access policies depicted as linear secret sharing schemes LSSS. Our proposed schemes are realized in the common reference string (CRS) model as introduced by Hohenberger et al.[EUROCRYPT 2023], employ simple tools and black-box methods. Specifically, our constructions op- erate in asymmetric prime-order bilinear group setting and are proven secure in the generic bilinear group model. Aligning with all pre-existing black-box RFE designs within the CRS model, our schemes cater to a predetermined maximum user count. A notable variant of our RABIPFE scheme also yields the first efficient registered ABE (RABE) system for LSSS access policies in asymmetric prime-order bilinear groups. Conclusively, demonstrating feasibility, we formulated an RFE blueprint that supports general functionalities and an infinite user base, leveraging indistinguishability obfuscation and one-way functions.

2024

ASIACRYPT

Relaxed Functional Bootstrapping: A New Perspective on BGV/BFV Bootstrapping
Abstract

BGV and BFV are among the most widely used fully homomorphic encryption (FHE) schemes, supporting evaluations over a finite field. To evaluate a circuit with arbitrary depth, bootstrapping is needed. However, despite the recent progress, bootstrapping of BGV/BFV still remains relatively impractical, compared to other FHE schemes.
In this work, we inspect the BGV/BFV bootstrapping procedure from a different angle. We provide a generalized bootstrapping definition that relaxes the correctness requirement of regular bootstrapping, allowing constructions that support only certain kinds of circuits with arbitrary depth. In addition, our definition captures a form of functional bootstrapping. In other words, the output encrypts a function evaluation of the input instead of the input itself.
Under this new definition, we provide a bootstrapping procedure supporting different types of functions. Our construction is 1-2 orders of magnitude faster than the state-of-the-art BGV/BFV bootstrapping algorithms, depending on the evaluated function.
Of independent interest, we show that our technique can be used to improve the batched FHEW/TFHE bootstrapping construction introduced by Liu and Wang (Asiacrypt 2023). Our optimization provides a speed-up of 6x in latency and 3x in throughput for binary gate bootstrapping and a plaintext-space-dependent speed-up for functional bootstrapping with plaintext space smaller than Z_{512}.

2024

ASIACRYPT

Revisiting Key Decomposition Techniques for FHE: Simpler, Faster and More Generic
Abstract

Ring-LWE based homomorphic encryption computations in large depth use a combination of two techniques: 1) decomposition of big numbers into small limbs/digits, and 2) efficient cyclotomic multiplications modulo $X^N+1$. It was long believed that the two mechanisms had to be strongly related, like in the full-RNS setting that uses a CRT decomposition of big numbers over an NTT-friendly family of prime numbers, and NTT over the same primes for multiplications.
However, in this setting, NTT was the bottleneck of all large-depth FHE computations. A breakthrough result from Kim et al. (Crypto'2023) managed to overcome this limitation by introducing a second gadget decomposition and showing that it indeed shifts the bottleneck and renders the cost of NTT computations negligible compared to the rest of the computation. In this paper, we extend this result (far) beyond the Full-RNS settings and show that we can completely decouple the big number decomposition from the cyclotomic arithmetic aspects. As a result, we get modulus switching/rescaling for free. We verify both in theory and in practice that the performance of key-switching, external and internal products and automorphisms using our representation are faster than the one achieved by Kim et al., and we discuss the high impact of these results for low-level or hardware optimizations as well as the benefits of the new parametrizations for FHE compilers. We even manage to lower the running time of the gate bootstrapping of $\TFHE$ by eliminating one eighth of the FFTs and one sixth of the linear operations, which lowers the running time below 5.5ms on recent CPUs.

2024

ASIACRYPT

Revisiting OKVS-based OPRF and PSI: Cryptanalysis and Better Construction
Abstract

Oblivious pseudorandom function (OPRF) is a two-party cryptographic protocol that allows the receiver to input $x$ and learn $F(x)$ for some PRF $F$, only known to the sender. For private set intersection (PSI) applications, OPRF protocols have evolved to enhance efficiency, primarily using symmetric key cryptography. Current state-of-the-art protocols, such as those by Rindal and Schoppmann (Eurocrypt~'21), leverage vector oblivious linear evaluation (VOLE) and oblivious key-value store (OKVS) constructions.
In this work, we identify a flaw in an existing security proof, and present practical attacks in the malicious model, which results in additional PRF evaluations than the previous works' claim. In particular, the attack for malicious model is related to the concept of OKVS overfitting, whose hardness is conjectured in previous works. Our attack is the first one to discuss the concrete hardness of OKVS overfitting problem.
As another flavour of contribution, we generalize OKVS-based OPRF constructions, suggesting new instantiations using a VOLE protocol with only Minicrypt assumptions. Our generalized construction shows improved performance in high-speed network environments, narrowing the efficiency gap between the OPRF constructions over Cryptomania and Minicrypt.

2024

ASIACRYPT

Revisiting Pairing-Friendly Curves with Embedding Degrees 10 and 14
Abstract

Since 2015, there has been a significant decrease in the asymptotic complexity of computing discrete logarithms in finite fields. As a result, the key sizes of many mainstream pairing-friendly curves have to be updated to maintain the desired security level. In PKC'20, Guillevic conducted a comprehensive assessment of the security of a series of pairing-friendly curves with embedding degrees ranging from $9$ to $17$. In this paper, we focus on five pairing-friendly curves with embedding degrees 10 and 14 at the 128-bit security level, with BW14-351 emerging as the most competitive candidate. First, we extend the optimized formula for the optimal pairing on BW13-310, a 128-bit secure curve with a prime $p$ in 310 bits and embedding degree $13$, to our target curves. This generalization allows us to compute the optimal pairing in approximately $\log r/(2\varphi(k))$ Miller iterations, where $r$ and $k$ are the order of pairing groups and the embedding degree respectively. Second, we develop optimized algorithms for cofactor multiplication for $\G_1$ and $\G_2$, as well as subgroup membership testing for $\G_2$ on these curves. Finally, we provide detailed performance comparisons between BW14-351 and other popular curves on a 64-bit platform in terms of pairing computation, hashing to $\G_1$ and $\G_2$, group exponentiations, and subgroup membership testings. Our results demonstrate that BW14-351 is a strong candidate for building pairing-based cryptographic protocols.

2024

ASIACRYPT

Robust AE With Committing Security
Abstract

There has been a recent interest to develop and standardize Robust Authenticated Encryption schemes. NIST, for example, is considering an Accordion mode for (wideblock) tweakable blockcipher, with Robust AE as a primary application. At the same time, recent attacks and applications suggest that encryption context needs to be committed. Indeed, committing security is also a design consideration in Accordion mode.
In this work, we give a modular solution for this problem. We first show how to transform any wideblock tweakable blockcipher TE to a Robust AE scheme SE that commits just the key.
The overhead is cheap, just a few finite-field multiplications and blockcipher calls. If one wants to commit the entire encryption context, one can simply hash the context to derive a 256-bit subkey,
and uses SE on that subkey. The use of 256-bit key on SE only means that it has to rely on AES-256 but doesn't require TE to have 256-bit key.
Our approach frees the Accordion designs from consideration of committing security. Moreover, it gives a big saving for several key-committing applications that don't want to pay the inherent hashing cost of full committing.

2024

ASIACRYPT

RoK, Paper, SISsors – Toolkit for Lattice-based Succinct Arguments
Abstract

Lattice-based succinct arguments allow to prove bounded-norm satisfiability of relations, such as $f(\mathbf{s}) = \mathbf{t} \bmod q$ and $\|\mathbf{s}\|\leq \beta$, over specific cyclotomic rings $\mathcal{O}_\mathcal{K}$, with proof size polylogarithmic in the witness size. However, state-of-the-art protocols require either 1) a super-polynomial size modulus $q$ due to a soundness gap in the security argument, or 2) a verifier which runs in time linear in the witness size. Furthermore, construction techniques often rely on specific choices of $\mathcal{K}$ which are not mutually compatible. In this work, we exhibit a diverse toolkit for constructing efficient lattice-based succinct arguments:
\begin{enumerate}
\item We identify new subtractive sets for general cyclotomic fields $\mathcal{K}$ and their maximal real subfields $\mathcal{K}^+$, which are useful as challenge sets, e.g. in arguments for exact norm bounds.
\item We construct modular, verifier-succinct reductions of knowledge for the bounded-norm satisfiability of structured-linear/inner-product relations, without any soundness gap, under the vanishing SIS assumption, over any $\mathcal{K}$ which admits polynomial-size subtractive sets.
\item We propose a framework to use twisted trace maps, i.e. maps of the form $\tau(z) = \frac{1}{N} \cdot \mathsf{Trace}_{\mathcal{K}/\mathbb{Q}}( \alpha \cdot z )$, to embed $\mathcal{R}$-inner-products as $\mathcal{R}$-inner-products for some structured subrings $\mathcal{R} \subseteq \mathcal{O}_\mathcal{K}$ whenever the conductor has a square-free odd part.
\item We present a simple extension of our reductions of knowledge for proving the consistency between the coefficient embedding and the Chinese Remainder Transform (CRT) encoding of $\vec{s}$ over any cyclotomic field $\mathcal{K}$ with a smooth conductor, based on a succinct decomposition of the CRT map into automorphisms, and a new, simple succinct argument for proving automorphism relations.
\end{enumerate}
Combining all techniques, we obtain, for example, verifier-succinct arguments for proving that $\vec{s}$ satisfying $f(\mathbf{s}) = \mathbf{t} \bmod q$ has binary coefficients, without soundness gap and with polynomial-size modulus $q$.

2024

ASIACRYPT

Signature-based Witness Encryption with Compact Ciphertext
Abstract

Signature-based witness encryption (SWE) is a recently proposed notion that allows to encrypt a message with respect to a tag $T$ and a set of signature verification keys. The resulting ciphertext can only be decrypted by a party who holds at least $k$ different valid signatures w.r.t. $T$ and $k$ different verification keys out of the $n$ keys specified at encryption time. Natural applications of this primitive involve distributed settings (e.g., blockchains), where multiple parties sign predictable messages, such as polling or randomness beacons. However, known SWE schemes without trusted setup have ciphertexts that scale linearly in the number of verification keys. This quickly becomes a major bottleneck as the system gets more distributed and the number of parties increases.
Towards showing the feasibility of SWE with ciphertext size sub-linear in the number of keys, we give a construction based on indistinguishability obfuscation (iO) for Turing machines and a new flavour of puncturable signatures that we call \emph{strongly} puncturable signatures (SPS). SPS allows to generate key pairs which are strongly punctured at a message $T$, meaning that with overwhelming probability no valid signature exists for message $T$ under the punctured key pair. Moreover, punctured keys are indistinguishable from standard non-punctured keys.

2024

ASIACRYPT

SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies
Abstract

We introduce SQIPrime, a post-quantum digital signature scheme based on the Deuring correspondence and Kani's Lemma.
Compared to its predecessors that are SQISign and especially SQISignHD, SQIPrime further expands the use of high dimensional isogenies, already in use in the verification in SQISignHD, to all its subroutines.
In doing so, it no longer relies on smooth degree isogenies (of dimension 1). Intriguingly, this includes the challenge isogeny which is also a non-smooth degree isogeny, but has an accessible kernel. The fact that the isogenies do not have rational kernel allows to fit more rational power 2 torsion points which are necessary when computing and representing the response isogeny.
SQIPrime operates with prime numbers of the form $p = 2^\alpha f-1$.
We describe two variants of SQIPrime. SQIPrime4D which incorporates the novelties described above and uses dimension 4 isogenies to represent the response isogeny. The runtime of higher dimensional isogeny computation is exponential in the dimension, hence the smaller the dimension the better for efficiency. The second variant, SQIPrime2D, solely uses dimension 2 isogenies. This is achieved by setting the degree of the secret isogeny to be equal to that of the challenge isogeny and further exploiting Kani's Lemma. SQIPrime2D is more efficient compared to SQIPrime4D and to SQISignHD, at the cost of being comparatively less compact, but still very compact compared to non isogeny based post-quantum signatures.

2024

ASIACRYPT

SQIsign2D-East: A New Signature Scheme Using 2-dimensional Isogenies
Abstract

Isogeny-based cryptography is cryptographic schemes whose security is based on the hardness of a mathematical problem called the isogeny problem, and is attracting attention as one of the candidates for post-quantum cryptography. A representative isogeny-based cryptography is the signature scheme called SQIsign, which was submitted to the NIST PQC standardization competition. SQIsign has attracted much attention because of its very short signature and key size among the candidates for the NIST PQC standardization. Recently, a lot of new schemes have been proposed that use high-dimensional isogenies. Among them, the signature scheme called SQIsignHD has an even shorter signature size than SQIsign. However, it requires 4-dimensional isogeny computations for the signature verification. In this paper, we propose a new signature scheme, SQIsign2D-East, which requires only two-dimensional isogeny computations for verification, thus reducing the computational cost of verification. First, we generalized an algorithm called RandIsogImg, which computes a random isogeny of non-smooth degree. Then, by using this generalized RandIsogImg, we construct a new signature scheme SQIsign2D-East.

2024

ASIACRYPT

SQIsign2D-West: The Fast, the Small, and the Safer
Abstract

We introduce SQIsign2D-West, a variant of SQIsign using two-dimensional isogeny representations.
SQIsignHD was the first variant of SQIsign to use higher dimensional isogeny representations. Its eight-dimensional variant is geared towards provable security but is deemed unpractical. Its four-dimensional variant is geared towards efficiency and has significantly faster signing times than SQIsign, but considerably slower verification owing to the complexity of the four-dimensional representation. Its authors commented on the apparent difficulty of getting any improvement over SQIsign by using two-dimensional representations.
In this work, we introduce new algorithmic tools that make two-dimensional representations a viable alternative. These lead to a signature scheme with sizes comparable to SQIsignHD, slightly slower signing than SQIsignHD but still much faster than SQIsign, and the fastest verification of any known variant of SQIsign. We achieve this without compromising on the security proof: the assumptions behind SQIsign2D-West are similar to those of the eight-dimensional variant of SQIsignHD. Additionally, like SQIsignHD, SQIsign2D-West favourably scales to high levels of security.
Concretely, for NIST level I we achieve signing times of 80ms and verifying times of 4.5ms, using optimised arithmetic based on intrinsics available to the Ice Lake architecture. For NIST level V, we achieve 470ms for signing and 31ms for verifying.

2024

ASIACRYPT

Strongly Secure Universal Thresholdizer
Abstract

A universal thresholdizer (UT), constructed from a threshold fully homomorphic
encryption by Boneh et. al, Crypto 2018, is a general framework for universally
thresholdizing many cryptographic schemes. However, their framework
is insufficient to construct strongly secure threshold schemes, such as threshold
signatures and threshold public-key encryption, etc.
In this paper, we strengthen the security definition for a universal thresholdizer
and propose a scheme which satisfies our stronger security notion. Our UT
scheme is an improvement of Boneh et. al ’s construction in the level of threshold
fully homomorphic encryption using a key homomorphic pseudorandom function.
We apply our strongly secure UT scheme to construct strongly secure
threshold signatures and threshold public-key encryption.

2024

ASIACRYPT

The Boomerang Chain Distinguishers: New Record for 6-Round AES
Abstract

AES is the most used block cipher, and its round-reduced variants are popular underlying components to design cryptographic schemes. How to effectively distinguish round-reduced AES from random permutations has always been a hot research topic. Currently, the longest rounds of AES can be distinguished is 6 rounds, where the best result is the 6-round exchange distinguisher with the data complexity 2^{84}. In this paper, we extend the classical boomerang distinguisher which uses only one boomerang property to use two or more related boomerangs and the technique of `friend pairs' to enhance the distinguishing effect. We propose the frameworks of the re-boomerang and boomerang chain distinguishers and apply to 6-round AES. The re-boomerang distinguisher uses two related boomerangs sequentially, which have the same upper truncated differential trail in the forward direction. A plaintext pair is called a right pair if it follows this truncated differential trail. By the first boomerang, a target set of plaintext pairs containing one right pair can be obtained. Then for each pair in the target set, construct its `friend pairs' as the input of the second boomerang to distinguish the cipher. Due to the dependence of the two boomerangs, all `friend pairs' of the right pair are right pairs, so the probability of the second boomerang is increased. To further improve the complexity, we insert a new boomerang in the middle of the re-boomerang and repeat it to reduce the target set. Combining the strategies of using more data in each boomerang and repeating the distinguishing process several times, we give a boomerang chain distinguisher on 6-round AES with success probability 60% and complexity 2^{76.57}, reduced by a factor of 172 compared with the previous best result. This is a new record for the secret-key distinguisher on 6-round AES.

2024

ASIACRYPT

The Concrete Security of Two-Party Computation: Simple Definitions, and Tight Proofs for PSI and OPRFs
Abstract

This paper aims to give tight proofs, and thus concrete-security improvements, for protocols for two-party computation. Our first step is to suggest, as target, a simple, indistinguishability-based, concrete-security-friendly definition we call InI. This would of course be a poor choice if InI were weaker than the standard simulation-based definition, but it is not; we show that for functionalities of practical interest like PSI and its variants, the two definitions are equivalent. Based on this, we move forward to study a canonical OPRF-based construction of PSI, giving a tight proof of InI security of the constructed PSI protocol based on the security of the OPRF. This leads us to the concrete security of OPRFs, where we show how different DH-style assumptions on the underlying group yield proofs of different degrees of tightness, including one that is tight, for the well-known and efficient 2H-DH OPRF.

2024

ASIACRYPT

The First Practical Collision for 31-Step SHA-256
Abstract

SHA-256 is a hash function standardized by NIST and has been widely deployed in real-world applications, e.g., Bitcoin. Recently, an improved collision attack on 31-step SHA-256 was proposed by Li- Liu-Wang at EUROCRYPT 2024, whose time and memory complexity are 2^{49.8} and 2^{48}, respectively. Such a result indicates that we are close to a practical collision attack on 31-step SHA-256, and that the current bottleneck is the memory complexity. To overcome such an obstacle, we develop a novel memory-efficient attack in this paper, which allows us to find the first practical colliding message pair for 31-step SHA-256 in only 1.2 hours with 64 threads and negligible memory. This technique is general and Li-Liu-Wang’s collision attack on 31-step SHA-512 can also be significantly improved, i.e., the time and memory complexity can be improved by a factor of 2^{20.9} and 2^{42.1}, respectively. Although we have set a new record in the practical collision attack on SHA-256, which improves the previous best practical attack published at EUROCRYPT 2013 by 3 steps, the attack is still far from threatening the security of SHA-256 since it has 64 steps in total. On the other hand, our new attack shows that nearly half of full SHA-256 can be practically cracked now, and it should be viewed as a major progress in the cryptanalysis of SHA-256 since 2013.

2024

ASIACRYPT

Threshold PAKE with Security against Compromise of all Servers
Abstract

We revisit the notion of Threshold Password-Authenticated Key Exchange (tPAKE), and we extend it to augmented tPAKE (atPAKE), which protects password information even in case of compromise of all servers, except for allowing an (inevitable) offline dictionary attack. Compared to prior notions of tPAKE this is analogous to replacing symmetric PAKE, where the server stores the user’s password, with an augmented (or asymmetric) PAKE, like OPAQUE [39], where the server stores a password hash, which can be used only as a target in an offline dictionary search for the password. An atPAKE scheme also strictly improves on security of an aPAKE, by secret-sharing the password hash among a set of servers. Indeed, our atPAKE protocol is a natural realization of threshold OPAQUE.
We formalize atPAKE in the framework of Universal Composability (UC), and show practical ways to realize it. All our schemes are generic compositions which interface to any aPAKE used as a sub-protocol, making them easier to adopt. Our main scheme relies on threshold Oblivious Pseudorandom Function (tOPRF), and our independent contribution fixes a flaw in the UC tOPRF notion of [36] and upgrades the tOPRF scheme therein to achieve the fixed definition while preserving its minimal cost and round complexity. The technique we use enforces implicit agreement on arbitrary context information within threshold computation, and it is of general interest.

2024

ASIACRYPT

Tighter Proofs for PKE-to-KEM Transformation in the Quantum Random Oracle Model
Abstract

In this work, we provide new, tighter proofs for the $T_{RH}$-transformation by Jiang {et al.} (ASIACRYPT 2023), which converts OW-CPA secure PKEs into KEMs with IND-1CCA security, a variant of typical IND-CCA security where only a single decapsulation query is allowed. Such KEMs are efficient and have been shown sufficient for real-world applications by Huguenin-Dumittan and Vaudenay at EUROCRYPT 2022. We reprove Jiang {et al.}'s $T_{RH}$-transformation in both the random oracle model (ROM) and the quantum random oracle model (QROM), for the case where the underlying PKE is rigid deterministic. In both ROM and QROM models, our reductions achieve security loss factors of $\bigO{1}$, significantly improving Jiang {et al.}'s results which have security loss factors of $\bigO{q}$ in the ROM and $\bigO{q^2}$ in the QROM respectively. Notably, central to our tight QROM reduction is a new tool called ``reprogram-after-measure'', which overcomes the reduction loss posed by oracle reprogramming in QROM proofs. This technique may be of independent interest and useful for achieving tight QROM proofs for other post-quantum cryptographic schemes. We remark that our results also improve the reduction tightness of the $T_{H}$-transformation (which also converts PKEs to KEMs) by Huguenin-Dumittan and Vaudenay (EUROCRYPT 2022), as Jiang {et al.} provided a tight reduction from $T_H$-transformation to $T_{RH}$-transformation (ASIACRYPT 2023).

2024

ASIACRYPT

Tightly Secure Non-Interactive BLS Multi-Signatures
Abstract

Due to their simplicity, compactness, and algebraic structure, BLS signatures are among the most widely used signatures in practice.
For example, used as multi-signatures, they are integral in Ethereum's proof-of-stake consensus.
From the perspective of concrete security, however, BLS (multi-)signatures suffer from a security loss linear in the number of signing queries. It is well-known that this loss can not be avoided using current proof techniques.
In this paper, we introduce a new variant of BLS multi-signatures that achieves tight security while remaining fully compatible with regular BLS. In particular, our signatures can be seamlessly combined with regular BLS signatures, resulting in regular BLS signatures.
Moreover, it can easily be implemented using existing BLS implementations in a black-box way.
Our scheme is also one of the most efficient non-interactive multi-signatures, and in particular more efficient than previous tightly secure schemes.
We demonstrate the practical applicability of our scheme by showing how proof-of-stake protocols that currently use BLS can adopt our variant for fully compatible opt-in tight security.

2024

ASIACRYPT

Tightly-Secure Group Key Exchange with Perfect Forward Secrecy
Abstract

In this work, we present a new paradigm for constructing Group Authenticated Key Exchange (GAKE). This result is the first tightly secure GAKE scheme in a strong security model that allows maximum exposure attacks (MEX) where the attacker is allowed to either reveal the secret session state or the long-term secret of all communication partners. Moreover, our protocol features the strong and realistic notion of (full) perfect forward secrecy (PFS), that allows the attacker to actively modify messages before corrupting parties. We obtain our results via a series of tightly secure transformations. Our first transformation is from weakly secure KEMs to unilateral authenticated key exchange (UAKE) with weak forward secrecy (WFS). Next, we show how to turn this into an UAKE with PFS in the random oracle model. Finally, and as one of our major novel conceptual contributions, we describe how to build GAKE protocols from UAKE protocols, also in the random oracle model. We apply our transformations to obtain two practical GAKE protocols with tight security. The first is based on the DDH assumption and features low message complexity. Our second result is based on the LWE assumption. In this way, we obtain the first GAKE protocol from a post-quantum assumption that is tightly secure in a strong model of security allowing MEX attacks.

2024

ASIACRYPT

Timed Secret Sharing
Abstract

This paper introduces the notion of timed secret sharing (TSS), which establishes lower and upper time bounds for secret reconstruction in a threshold secret sharing scheme. Such time bounds are particularly useful in scenarios where an early or late reconstruction of a secret matters. We propose several new constructions that offer different security properties and show how they can be instantiated efficiently using novel techniques. We highlight how our ideas can be used to break the public goods game, which is an issue inherent to threshold secret sharing-based systems, without relying on incentive mechanism. We achieve this through an upper time bound that can be implemented either via short-lived proofs, or the gradual release of additional shares, establishing a trade-off between time and fault tolerance. The latter independently provides robustness in the event of dropout by some portion of shareholders.

2024

ASIACRYPT

Tiresias: Large Scale, UC-Secure Threshold Paillier
Abstract

In the threshold version of Paillier's encryption scheme, a set of parties collectively holds the secret decryption key through a secret sharing scheme.
Whenever a ciphertext is to be decrypted, the parties send their decryption shares, which are then verified for correctness and combined into the plaintext.
The scheme has been widely adopted in various applications, from secure voting to general purpose MPC protocols.
However, among the handful of existing proposals for a maliciously secure scheme, one must choose between an efficient implementation that relies on non-standard assumptions or a computationally expensive implementation that relies on widely acceptable assumptions.
In this work, we show that one can enjoy the benefits of both worlds.
Specifically, we adjust a scheme by Damgard et al. (Int. J. Inf. Secur. 2010) to get a practical distributed key generation (DKG). While the original scheme was only known to be secure under ad-hoc non-standard assumptions, we prove that the adjusted scheme is in fact secure under the decisional composite residuosity (DCR) assumption alone, required for the semantic security of the Pallier encryption scheme itself.
This is possible thanks to a novel reduction technique, from computing and proving a false decryption share, to the factoring problem. Specifically, while there may exist false decryption shares for which the zk-proof verifies with non-negligible probability, they are computationally hard to find.
Furthermore, we use similar ideas to prove that batching techniques by Aditya et al. (ACNS 2004), which allows a prover to batch several statements into a single proof, can be applied to our adjusted scheme. This enables a batched threshold Paillier decryption in the fully distributed setting for the first time.
Until now, verifying that a decryption share is correct was the bottleneck of threshold Paillier schemes and hindered real world deployments (unless one is willing to rely on a trusted dealer).
Our work accumulates to shifting the bottleneck back to the plaintext reconstruction, just like in the semi-honest setting, and renders threshold Paillier practical for the first time, supporting large scale deployments.
We exemplify this shift by implementing the scheme and report our evaluation with up to 1000 parties, in the dishonest majority setting.
Over an EC2 c6i machine, we get a throughput of about 50 and 3.6 decryptions per second, when run over a network of 100 and 1000 parties, respectively.

2024

ASIACRYPT

Toward Full n-bit Security and Nonce Misuse Resistance of Block Cipher-based MACs
Abstract

In this paper, we study the security of MAC constructions among those classified by Chen {\it et al.} in ASIACRYPT '21. Precisely, $F^{\text{EDM}}_{B_2}$~(or $\ewcdm$ as named by Cogliati and Seurin in CRYPTO '16), $F^{\text{EDM}}_{B_3}$, $F^{\text{SoP}}_{B_2}$, $F^{\text{SoP}}_{B_3}$ (all as named by Chen {\it et al.}) are proved to be fully secure up to $2^n$ MAC queries in the nonce-respecting setting, improving the previous bound of $\frac{3n}{4}$-bit security. In particular, $F^{\text{SoP}}_{B_2}$ and $F^{\text{SoP}}_{B_3}$ enjoy graceful degradation as the number of queries with repeated nonces grows (when the underlying universal hash function satisfies a certain property called \emph{multi-xor-collision resistance}). To do this, we develop a new tool, namely extended Mirror theory based on two independent permutations to a wide range of $\xi_{\max}$ including inequalities.
We also present matching attacks on $F^{\text{EDM}}_{B_4}$ and $F^{\text{EDM}}_{B_5}$ using $O(2^{3n/4})$ MAC queries and $O(1)$ verification query without using repeated nonces.

2024

ASIACRYPT

Traitor Tracing without Trusted Authority from Registered Functional Encryption
Abstract

Traitor-tracing systems allow identifying the users who contributed to building a rogue decoder in a broadcast environment. In a traditional traitor-tracing system, a key authority is responsible for generating the global public parameters and issuing secret keys to users. All security is lost if the \emph{key authority itself} is corrupt. This raises the question: Can we construct a traitor-tracing scheme, without a trusted authority?
In this work, we propose a new model for traitor-tracing systems where, instead of having a key authority, users could generate and register their own public keys. The public parameters are computed by aggregating all user public keys. Crucially, the aggregation process is \emph{public}, thus eliminating the need of any trusted authority. We present two new traitor-tracing systems in this model based on bilinear pairings. Our first scheme is proven adaptively secure in the generic group model. This scheme features a {\it transparent} setup, ciphertexts consisting of $6\sqrt{L}+4$ group elements, and a public tracing algorithm. Our second scheme supports a bounded collusion of traitors and is proven selectively secure in the standard model. Our main technical ingredients are new registered functional encryption (RFE) schemes for quadratic and linear functions which, prior to this work, were known only from indistinguishability obfuscation.
To substantiate the practicality of our approach, we evaluate the performance a proof of concept implementation. For a group of $L = 1024$ users, encryption and decryption take roughly 50ms and 4ms, respectively, whereas a ciphertext is of size 6.7KB.

2024

ASIACRYPT

Ultrametric integral cryptanalysis
Abstract

A systematic method to analyze divisibility properties is proposed. In integral cryptanalysis, divisibility properties interpolate between bits that sum to zero (divisibility by two) and saturated bits (divisibility by $2^{n - 1}$ for $2^n$ inputs). From a theoretical point of view, we construct a new cryptanalytic technique that is a non-Archimedean multiplicative analogue of linear cryptanalysis. It lifts integral cryptanalysis to characteristic zero in the sense that, if all quantities are reduced modulo two, then one recovers the algebraic theory of integral cryptanalysis. The new technique leads to a theory of trails. We develop a tool based on off-the-shelf solvers that automates the analysis of these trails and use it to show that many integral distinguishers on Present and Simon are stronger than expected.

2024

ASIACRYPT

Unbounded ABE for Circuits from LWE, Revisited
Abstract

We introduce new lattice-based techniques for building ABE for circuits with unbounded attribute length based on the LWE assumption, improving upon the previous constructions of Brakerski and Vaikuntanathan (CRYPTO 16) and Goyal, Koppula, and Waters (TCC 16). Our main result is a simple and more efficient unbounded ABE scheme for circuits where only the circuit depth is fixed at set-up; this is the first unbounded ABE scheme for circuits that rely only on black-box access to cryptographic and lattice algorithms. The scheme achieves semi-adaptive security against unbounded collusions under the LWE assumption. The encryption time and ciphertext size are roughly 3x larger than the prior bounded ABE of Boneh et al (EUROCRYPT 2014), substantially improving upon the encryption times in prior works. As a secondary contribution, we present an analogous result for unbounded inner product predicate encryption that satisfies weak attribute-hiding.

2024

ASIACRYPT

Unclonable Non-Interactive Zero-Knowledge
Abstract

A non-interactive ZK (NIZK) proof enables verification of NP statements without revealing secrets about them. However, an adversary that obtains a NIZK proof may be able to clone this proof and distribute arbitrarily many copies of it to various entities: this is inevitable for any proof that takes the form of a classical string. In this paper, we ask whether it is possible to rely on quantum information in order to build NIZK proof systems that are impossible to clone.
We define and construct unclonable non-interactive zero-knowledge arguments (of knowledge) for NP, addressing a question first posed by Aaronson (CCC 2009). Besides satisfying the zero-knowledge and argument of knowledge properties, these proofs additionally satisfy unclonability. Very roughly, this ensures that no adversary can split an honestly generated proof of membership of an instance x in an NP language L and distribute copies to multiple entities that all obtain accepting proofs of membership of x in L. Our result has applications to unclonable signatures of knowledge, which we define and construct in this work; these non-interactively prevent replay attacks.

2024

ASIACRYPT

Unclonable Secret Sharing
Abstract

Unclonable cryptography utilizes the principles of quantum mechanics to addresses cryptographic tasks that are impossible classically. We introduce a novel unclonable primitive in the context of secret sharing, called unclonable secret sharing (USS). In a USS scheme, there are
shareholders, each holding a share of a classical secret represented as a quantum state. They can recover the secret once all parties (or at least
parties) come together with their shares. Importantly, it should be infeasible to copy their own shares and send the copies to two non-communicating parties, enabling both of them to recover the secret.
Our work initiates a formal investigation into the realm of unclonable secret sharing, shedding light on its implications, constructions, and inherent limitations.
** Connections: We explore the connections between USS and other quantum cryptographic primitives such as unclonable encryption and position verification, showing the difficulties to achieve USS in different scenarios.
**Limited Entanglement: In the case where the adversarial shareholders do not share any entanglement or limited entanglement, we demonstrate information-theoretic constructions for USS.
**Large Entanglement: If we allow the adversarial shareholders to have unbounded entanglement resources (and unbounded computation), we prove that unclonable secret sharing is impossible. On the other hand, in the quantum random oracle model where the adversary can only make a bounded polynomial number of queries, we show a construction secure even with unbounded entanglement.
Furthermore, even when these adversaries possess only a polynomial amount of entanglement resources, we establish that any unclonable secret sharing scheme with a reconstruction function implementable using Cliffords and logarithmically many T-gates is also unattainable.

2024

ASIACRYPT

Updatable Privacy-Preserving Blueprints
Abstract

Privacy-preserving blueprint schemes (Kohlweiss et al., EUROCRYPT'23) offer a mechanism for safeguarding user's privacy while allowing for specific legitimate controls by a designated auditor agent. These schemes enable users to create escrows encrypting the result of evaluating a function y=P(t,x), with P being publicly known, t a secret used during the auditor's key generation, and x the user's private input.
Crucially, escrows only disclose the blueprinting result y=P(t,x) to the designated auditor, even in cases where the auditor is fully compromised.
The original definition and construction only support the evaluation of functions P on an input x provided by a single user.
We address this limitation by introducing updatable privacy-preserving blueprint schemes (UPPB), which enhance the original notion with the ability for multiple users to non-interactively update the private user input x while blueprinting.
Moreover, UPPBs contain a proof that y is the result of a sequence of valid updates, while revealing nothing else about the private inputs {x_i} of updates.
As in the case of privacy-preserving blueprints, we first observe that UPPBs can be realized via a generic construction for arbitrary predicates P based on FHE and NIZKs.
Our main result is uBlu, an efficient instantiation for a specific predicate comparing the values x and t, where x is the cumulative sum of users' private inputs and t is a fixed private value provided by the auditor in the setup phase.
This rather specific setting already finds interesting applications
such as privacy-preserving anti-money laundering and location tracking, and can be extended to support more generic predicates.
From the technical perspective, we devise a novel technique to keep the escrow size concise, independent of the number of updates, and reasonable for practical applications. We achieve this via a novel characterization of malleability for the algebraic NIZK by Couteau and Hartmann (CRYPTO’20) that allows for an additive update function.

2024

ASIACRYPT

Updatable Private Set Intersection Revisited: Extended Functionalities, Deletion, and Worst-Case Complexity
Abstract

Private set intersection (PSI) allows two mutually distrusting parties each holding a private set of elements, to learn the intersection of their sets without revealing anything beyond the intersection. Recent work (Badrinarayanan et al., PoPETS'22) initiates the study of updatable PSI (UPSI), which allows the two parties to compute PSI on a regular basis with sets that constantly get updated, where both the computation and communication complexity only grow with the size of the small updates and not the large entire sets. However, there are several limitations of their presented protocols. First, they can only be used to compute the plain PSI functionality and do not support extended functionalities such as PSI-Cardinality and PSI-Sum. Second, they only allow parties to add new elements to their existing set and do not support arbitrary deletion of elements. Finally, their addition-only protocols either require both parties to learn the output or only achieve low complexity in an amortized sense and incur linear worst-case complexity.
In this work, we address all the above limitations. In particular, we study UPSI with semi-honest security in both the addition-only and addition-deletion settings. We present new protocols for both settings that support plain PSI as well as extended functionalities including PSI-Cardinality and PSI-Sum, achieving one-sided output (which implies two-sided output). In the addition-only setting, we also present a protocol for a more general functionality Circuit-PSI that outputs secret shares of the intersection. All of our protocols have worst-case computation and communication complexity that only grow with the set updates instead of the entire sets (except for a polylogarithmic factor). We implement our new UPSI protocols and compare with the state-of-the-art protocols for PSI and extended functionalities. Our protocols compare favorably when the total set sizes are sufficiently large, the new updates are sufficiently small, or in networks with low bandwidth.

2024

ASIACRYPT

Verifiable Oblivious Pseudorandom Functions from Lattices: Practical-ish and Thresholdisable
Abstract

We revisit the lattice-based verifiable oblivious PRF construction from PKC’21 and remove or mitigate its central three sources of inefficiency. First, applying R´enyi divergence arguments, we eliminate one superpolynomial factor from the ciphertext modulus q, allowing us to reduce the overall bandwidth consumed by RLWE samples by about a factor of four. This necessitates us introducing intermediate unpredictability notions to argue PRF security of the final output in the Random Oracle model. Second, we remove the reliance on the 1D-SIS assumption, which reduces another superpolynomial factor, albeit to a factor that is still superpolynomial. Third, by applying the state-of-the-art in zero-knowledge proofs for lattice statements, we achieve a reduction in
bandwidth of several orders of magnitude for this material. Finally, we give a t-out-of-n threshold variant of the VOPRF for constant t and with trusted setup, based on a n-out-of-n distributed variant of the VOPRF (and without trusted setup).

2024

ASIACRYPT

Verifiable Secret Sharing from Symmetric Key Cryptography with Improved Optimistic Complexity
Abstract

In this paper we propose verifiable secret sharing (VSS) schemes
secure for any honest majority in the synchronous model, and that only use \textit{symmetric-key} cryptographic tools, therefore having plausibly post-quantum security. Compared to the state-of-the-art scheme with these features (Atapoor et al., Asiacrypt `23), our main improvement lies on the complexity of the \textit{``optimistic''} scenario where the dealer and all but a small number of receivers behave honestly in the sharing phase: in this case, the running time and download complexity (amount of information read) of each honest verifier is \textit{polylogarithmic} and the total amount of broadcast information by the dealer is \textit{logarithmic}; all these complexities were linear in the aforementioned work by Atapoor et al. At the same time, we preserve these complexities with respect to the previous work for the ``pessimistic'' case where the dealer or $O(n)$ receivers cheat actively.
The new VSS protocol is of interest in multiparty computations where each party runs one VSS as a dealer, such as distributed key generation protocols.
Our main technical handle is a distributed zero-knowledge proof of low degreeness of a polynomial, in the model of Boneh et al. (Crypto `19) where the statement (in this case the evaluations of the witness polynomial) is distributed among several verifiers, each knowing one evaluation. Using folding techniques similar to FRI (Ben-Sasson et al., ICALP `18) we construct such a proof where each verifier receives polylogarithmic information and runs in polylogarithmic time.

2024

ASIACRYPT

ZKFault: Fault attack analysis on zero-knowledge-based post-quantum digital signature schemes
Abstract

Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against quantum computers. However, these schemes are often considered impractical for real-world deployment due to large key sizes and inefficient computation time. In the recent call for standardization of additional post-quantum digital signatures by the National Institute of Standards and Technology, several code-based candidates have been proposed, including LESS, CROSS, and MEDS. These schemes are designed on the relatively new zero-knowledge framework. Although several works analyze the hardness of these schemes, there is hardly any work that examines the security of these schemes in the presence of physical attacks.
In this work, we analyze these signature schemes from the perspective of fault attacks. All these schemes use a similar tree-based construction to compress the signature size. We attack this component of these schemes. Therefore, our
attack is applicable to all of these schemes. In this work, we first analyze the LESS signature scheme and devise our attack. Furthermore, we showed how this attack can be extended to the CROSS signature scheme. Our attacks are built on very simple fault assumptions. Our results show that we can recover the entire secret key of LESS and CROSS using as little as a single fault. Finally, we propose various countermeasures to prevent these kinds of attacks and discuss their efficiency and shortcomings.