International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Papers from ASIACRYPT 2022

Year
Venue
Title
2022
ASIACRYPT
A Modular Approach to the Incompressibility of Block-Cipher-Based AEADs
Incompressibility is one of the most fundamental security goals in white-box cryptography. Given recent advances in the design of efficient and incompressible block ciphers such as SPACE, SPNbox and WhiteBlock, we demonstrate the feasibility of reducing incompressible AEAD modes to incompressible block ciphers. We first observe that several existing AEAD modes of operation, including CCM, GCM(-SIV), and OCB, would be all insecure against white-box adversaries even when used with an incompressble block cipher. This motivates us to revisit and formalize incompressibility-based security definitions for AEAD schemes and for block ciphers, so that we become able to design modes and reduce their security to that of the underlying ciphers. Our new security notion for AEAD, which we name whPRI, is an extension of the pseudo-random injection security in the black-box setting. Similar security notions are also defined for other cryptosystems such as privacy-only encryption schemes. We emphasize that whPRI ensures quite strong authenticity against white-box adversaries: existential unforgeability beyond leakage. This contrasts sharply with previous notions which have ensured either no authenticity or only universal unforgeability. For the underlying ciphers we introduce a new notion of whPRP, which extends that of PRP in the black-box setting. Interestingly, our incompressibility reductions follow from a variant of public indifferentiability. In particular, we show that a practical whPRI-secure AEAD mode can be built from a whPRP-secure block cipher: We present a SIV-like composition of the sponge construction (utilizing a block cipher as its underlying primitive) with the counter mode and prove that such a construction is (in the variant sense) public indifferentiable from a random injection. To instantiate such an AEAD scheme, we propose a 256-bit variant of SPACE, based on our conjecture that SPACE should be a whPRP-secure cipher.
2022
ASIACRYPT
A Modular Approach to the Security Analysis of Two-Permutation Constructions
Constructions based on two public permutation calls are very common in today's cryptographic community. However, each time a new construction is introduced, a dedicated proof must be carried out to study the security of the construction. In this work, we propose a new tool to analyze the security of these constructions in a modular way. This tool is built on the idea of the classical mirror theory for block cipher based constructions, such that it can be used for security proofs in the ideal permutation model. We present different variants of this public permutation mirror theory such that it is suitable for different security notions. We also present a framework to use the new techniques, which provides the bad events that need to be excluded in order to apply the public permutation mirror theory. Furthermore, we showcase the new technique on three examples: the Tweakable Even-Mansour cipher by Cogliati et al. (CRYPTO '15), the two permutation variant of the pEDM PRF by Dutta et al. (ToSC '21(2)), and the two permutation variant of the nEHtM_p MAC algorithm by Dutta and Nandi (AFRICACRYPT '20). With this new tool we prove the multi-user security of these constructions in a considerably simplified way.
2022
ASIACRYPT
A New Isogeny Representation and Applications to Cryptography
This paper focuses on isogeny representations, defined as witnesses of membership to the language of isogenous supersingular curves (the set of triples $D,E_1,E_2$ with a cyclic isogeny of degree $D$ between $E_1$ and $E_2$). This language and its proofs of membership are known to have several fundamental cryptographic applications such as the construction of digital signatures and validation of encryption keys. In the first part of this article, we reinterpret known results on isogenies in the framework of languages and proofs to show that the language of isogenous supersingular curves is in \textsf{NP} with the isogeny representation derived naturally from the Deuring correspondence. Our main contribution is the design of the suborder representation, a new isogeny representation targetted at the case of (big) prime degree. The core of our new method is the revelation of endomorphisms of smooth norm inside a well-chosen suborder of the codomain's endomorphism ring. These new membership witnesses appear to be opening interesting prospects for isogeny-based cryptography under the hardness of a new computational problem: the SubOrder to Ideal Problem (SOIP). As an application, we introduce pSIDH, a new NIKE based on the suborder representation. In the process, we also develop several heuristic algorithmic tools to solve norm equations inside a new family of quaternion orders. These new algorithms may be of independent interest.
2022
ASIACRYPT
A Non-heuristic Approach to Time-space Tradeoffs and Optimizations for BKW
Blum, Kalai and Wasserman (JACM 2003) gave the first sub-exponential algorithm to solve the Learning Parity with Noise (LPN) problem. In particular, consider the LPN problem with constant noise and dimension $n$. The BKW solves it with space complexity $2^{\frac{(1+\epsilon)n}{\log n}}$ and time/sample complexity $2^{\frac{(1+\epsilon)n}{\log n}}\cdot 2^{\Omega(n^{\frac{1}{1+\epsilon}})}$ for small constant $\epsilon\to 0^+$. We propose a variant of the BKW by tweaking Wagner's generalized birthday problem (Crypto 2002) and adapting the technique to a $c$-ary tree structure. In summary, our algorithm achieves the following: \begin{enumerate} \item {\bf (Time-space tradeoff).} We obtain the same time-space tradeoffs for LPN and LWE as those given by Esser et al. (Crypto 2018), but without resorting to any heuristics. For any $2\leq c\in\mathbb{N}$, our algorithm solves the LPN problem with time complexity $2^{\frac{\log c(1+\epsilon)n}{\log n}}\cdot 2^{\Omega(n^{\frac{1}{1+\epsilon}})}$ and space complexity $2^{\frac{\log c(1+\epsilon)n}{(c-1)\log n}}$, where one can use Grover's quantum algorithm or Dinur et al.'s dissection technique (Crypto 2012) to further accelerate/optimize the time complexity. \item {\bf (Time/sample optimization).} A further adjusted variant of our algorithm solves the LPN problem with sample, time and space complexities all kept at $2^{\frac{(1+\epsilon)n}{\log n}}$ for $\epsilon\to 0^+$, saving factor $2^{\Omega(n^{\frac{1}{1+\epsilon}})}$ in time/sample compared to the original BKW, and the variant of Devadas et al. (TCC 2017). \item {\bf (Sample reduction).} Our algorithm provides an alternative to Lyubashevsky's BKW variant (RANDOM 2005) for LPN with a restricted amount of samples. In particular, given $Q=n^{1+\epsilon}$ (resp., $Q=2^{n^{\epsilon}}$) samples, our algorithm saves a factor of $2^{\Omega(n)/(\log n)^{1-\kappa}}$ (resp., $2^{\Omega(n^{\kappa})}$) for constant $\kappa \to 1^-$ in running time while consuming roughly the same space, compared with Lyubashevsky's algorithm. \end{enumerate} In particular, the time/sample optimization benefits from a careful analysis of the error distribution among the correlated candidates, which was not studied by previous rigorous approaches such as the analysis of Minder and Sinclair (J.Cryptology 2012) or Devadas et al. (TCC 2017).
2022
ASIACRYPT
A Third is All You Need: Extended Partial Key Exposure Attack on CRT-RSA with Additive Exponent Blinding
At Eurocrypt 2022, May et al. proposed a partial key exposure (PKE) attack on CRT-RSA that efficiently factors $N$ knowing only a $\frac{1}{3}$-fraction of either most significant bits (MSBs) or least significant bits (LSBs) of private exponents $d_p$ and $d_q$ for public exponent $e \approx N^{\frac{1}{12}}$. In practice, PKE attacks typically rely on the side-channel leakage of these exponents, while a side-channel resistant implementation of CRT-RSA often uses additively blinded exponents $d^{\prime}_p = d_p + r_p(p-1)$ and $d^{\prime}_q = d_q + r_q(q-1)$ with unknown random blinding factors $r_p$ and $r_q$, which makes PKE attacks more challenging. Motivated by the above, we extend the PKE attack of May et al. to CRT-RSA with additive exponent blinding. While admitting $r_pe\in(0,N^{\frac{1}{4}})$, our extended PKE works ideally when $r_pe \approx N^{\frac{1}{12}}$, in which case the entire private key can be recovered using only $\frac{1}{3}$ known MSBs or LSBs of the blinded CRT exponents $d^{\prime}_p$ and $d^{\prime}_q$. Our extended PKE follows their novel two-step approach to first compute the key-dependent constant $k^{\prime}$ ($ed^{\prime}_p = 1 + k^{\prime}(p-1)$, $ed^{\prime}_q = 1 + l^{\prime}(q-1)$), and then to factor $N$ by computing the root of a univariate polynomial modulo $k^{\prime}p$. We extend their approach as follows. For the MSB case, we propose two options for the first step of the attack, either by obtaining a single estimate $k^{\prime}l^{\prime}$ and calculating $k^{\prime}$ via factoring, or by obtaining multiple estimates $k^{\prime}l^{\prime}_1,\ldots,k^{\prime}l^{\prime}_z$ and calculating $k^{\prime}$ probabilistically via GCD. For the LSB case, we extend their approach by constructing a different univariate polynomial in the second step of the LSB attack. A formal analysis shows that our LSB attack runs in polynomial time under the standard Coppersmith-type assumption, while our MSB attack either runs in sub-exponential time with a reduced input size (the problem is reduced to factor a number of size $e^2r_pr_q\approx N^{\frac{1}{6}}$) or in probabilistic polynomial time under a novel heuristic assumption. Under the settings of the most common key sizes (1024-bit, 2048-bit, and 3072-bit) and blinding factor lengths (32-bit, 64-bit, and 128-bit), our experiments verify the validity of the Coppersmith-type assumption and our own assumption, as well as the feasibility of the factoring step. To the best of our knowledge, this is the first PKE on CRT-RSA with experimentally verified effectiveness against 128-bit unknown exponent blinding factors. We also demonstrate an application of the proposed PKE attack using real partial side-channel key leakage targeting a Montgomery Ladder exponentiation CRT implementation.
2022
ASIACRYPT
A Universally Composable Non-Interactive Aggregate Cash System
Mimblewimble is a privacy-preserving cryptocurrency, providing the functionality of transaction aggregation. Once certain coins have been spent in Mimblewimble, they can be deleted from the UTXO set. This is desirable: now storage can be saved and computation cost can be reduced. Fuchsbauer et al. (EUROCRYPT 2019) abstracted Mimblewimble as an Aggregate Cash System (ACS) and provided security analysis via game-based definitions. In this paper, we revisit the ACS, and focus on {\em Non-interactive} ACS, denoted as NiACS. We for the first time propose a simulation-based security definition and formalize an ideal functionality for NiACS. Then, we construct a NiACS protocol in a hybrid model which can securely realize the ideal NiACS functionality in the Universal Composition (UC) framework. In addition, we propose a building block, which is a variant of the ElGamal encryption scheme that may be of independent interest. Finally, we show how to instantiate our protocol, and obtain the first NiACS system with UC security.
2022
ASIACRYPT
Additive-Homomorphic Functional Commitments and Applications to Homomorphic Signatures
Functional Commitments (FC) allow one to reveal functions of committed data in a succinct and verifiable way. In this paper we put forward the notion of additive-homomorphic FC and show two efficient, pairing-based, realizations of this primitive supporting multivariate polynomials of constant degree and monotone span programs, respectively. We also show applications of the new primitive in the contexts of homomorphic signatures: we show that additive-homomorphic FCs can be used to realize homomorphic signatures (supporting the same class of functionalities as the underlying FC) in a simple and elegant way. Using our new FCs as underlying building blocks, this leads to the (seemingly) first expressive realizations of multi-input homomorphic signatures not relying on lattices or multilinear maps.
2022
ASIACRYPT
Algebraic Meet-in-the-Middle Attack on LowMC
By exploiting the feature of partial nonlinear layers, we propose a new technique called algebraic meet-in-the-middle (MITM) attack to analyze the security of LowMC, which can reduce the memory complexity of the simple difference enumeration attack over the state-of-the-art. Moreover, while an efficient algebraic technique to retrieve the full key from a differential trail of LowMC has been proposed at CRYPTO 2021, its time complexity is still exponential in the key size. In this work, we show how to reduce it to constant time when there are a sufficiently large number of active S-boxes in the trail. With the above new techniques, the attacks on LowMC and LowMC-M published at CRYPTO 2021 are further improved, and some LowMC instances could be broken for the first time. Our results seem to indicate that partial nonlinear layers are still not well-understood.
2022
ASIACRYPT
An Analysis of the Algebraic Group Model
The algebraic group model (AGM), formalized by Fuchsbauer, Kiltz, and Loss, has recently received significant attention. One of the appealing properties of the AGM is that it is viewed as being (strictly) weaker than the generic group model (GGM), in the sense that hardness results for algebraic algorithms imply hardness results for generic algorithms, and generic reductions in the AGM (namely, between the algebraic formulations of two problems) imply generic reductions in the~GGM. We highlight that as the GGM and AGM are currently formalized, this is not true: hardness in the AGM may not imply hardness in the GGM, and a generic reduction in the AGM may not imply a similar reduction in the~GGM.
2022
ASIACRYPT
Anonymous Public Key Encryption under Corruptions
Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What's worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_{k}\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_{k}\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with \emph{compact} ciphertexts. Furthermore, for some PKE instantiation, its security reduction is \emph{tight}.
2022
ASIACRYPT
Attaining GOD Beyond Honest Majority With Friends and Foes
In the classical notion of multiparty computation (MPC), an honest party learning private inputs of others, either as a part of protocol specification or due to a malicious party's unspecified messages, is not considered a potential breach. Several works in the literature exploit this seemingly minor loophole to achieve the strongest security of guaranteed output delivery via a trusted third party, which nullifies the purpose of MPC. Alon et al. (CRYPTO 2020) presented the notion of {\it Friends and Foes} ($\mathtt{FaF}$) security, which accounts for such undesired leakage towards honest parties by modelling them as semi-honest (friends) who do not collude with malicious parties (foes). With real-world applications in mind, it's more realistic to assume parties are semi-honest rather than completely honest, hence it is imperative to design efficient protocols conforming to the $\mathtt{FaF}$ security model. Our contributions are not only motivated by the practical viewpoint, but also consider the theoretical aspects of $\mathtt{FaF}$ security. We prove the necessity of semi-honest oblivious transfer for $\mathtt{FaF}$-secure protocols with optimal resiliency. On the practical side, we present QuadSquad, a ring-based 4PC protocol, which achieves fairness and GOD in the $\mathtt{FaF}$ model, with an optimal corruption of $1$ malicious and $1$ semi-honest party. QuadSquad is, to the best of our knowledge, the first practically efficient $\mathtt{FaF}$ secure protocol with optimal resiliency. Its performance is comparable to the state-of-the-art dishonest majority protocols while improving the security guarantee from abort to fairness and GOD. Further, QuadSquad elevates the security by tackling a stronger adversarial model over the state-of-the-art honest-majority protocols, while offering a comparable performance for the input-dependent computation. We corroborate these claims by benchmarking the performance of QuadSquad. We also consider the application of liquidity matching that deals with highly sensitive financial transaction data, where $\mathtt{FaF}$ security is apt. We design a range of $\mathtt{FaF}$ secure building blocks to securely realize liquidity matching as well as other popular applications such as privacy-preserving machine learning (PPML). Inclusion of these blocks makes QuadSquad a comprehensive framework.
2022
ASIACRYPT
Authenticated Encryption with Key Identification
Authenticated encryption with associated data (AEAD) forms the core of much of symmetric cryptography, yet the standard techniques for modeling AEAD assume recipients have no ambiguity about what secret key to use for decryption. This is divorced from what occurs in practice, such as in key management services, where a message recipient can store numerous keys and must identify the correct key before decrypting. Ad hoc solutions for identifying the intended key are deployed in practice, but these techniques can be inefficient and, in some cases, have even led to practical attacks. Notably, to date there has been no formal investigation of their security properties or efficacy. We fill this gap by providing the first formalization of nonce-based AEAD that supports key identification (AEAD-KI). Decryption now takes in a vector of secret keys and a ciphertext and must both identify the correct secret key and decrypt the ciphertext. We provide new formal security definitions, including new key robustness definitions and indistinguishability security notions. Finally, we show several different approaches for AEAD-KI and prove their security.
2022
ASIACRYPT
BLOOM: Bimodal Lattice One-Out-of-Many Proofs and Applications
We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Lyubashevsky et al. (Crypto 2022) together with an improved, over prior lattice-based one-out-of-many proofs, recursive procedure, and a novel rejection sampling proof that allows to use the efficient bimodal rejection sampling throughout the protocol. Using these new primitives and techniques, we give instantiations of the most compact lattice-based ring and group signatures schemes. The improvement in signature sizes over prior works ranges between $25\%$ and $2$X. Perhaps of even more significance, the size of the user public keys, which need to be stored somewhere publicly accessible in order for ring signatures to be meaningful, is reduced by factors ranging from $7$X to $15$X. In what could be of independent interest, we also provide noticeably improved proofs for integer relations which, together with one-out-of-many proofs are key components of confidential payment systems.
2022
ASIACRYPT
Classically Verifiable NIZK for QMA with Preprocessing
We propose three constructions of classically verifiable non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. 1. We construct a CV-NIZK for QMA in the quantum secret parameter model where a trusted setup sends a quantum proving key to the prover and a classical verification key to the verifier. It is information theoretically sound and zero-knowledge. 2. Assuming the quantum hardness of the learning with errors problem, we construct a CV-NIZK for QMA in a model where a trusted party generates a CRS and the verifier sends an instance-independent quantum message to the prover as preprocessing. This model is the same as one considered in the recent work by Coladangelo, Vidick, and Zhang (CRYPTO ’20). Our construction has the so-called dual-mode property, which means that there are two computationally in-distinguishable modes of generating CRS, and we have information theoretical soundness in one mode and information theoretical zero-knowledge property in the other. This answers an open problem left by Coladangelo et al, which is to achieve either of soundness or zero-knowledge information theoretically. To the best of our knowledge, ours is the first dual-mode NIZK for QMA in any kind of model. 3. We construct a CV-NIZK for QMA with quantum preprocessing in the quantum random oracle model. This quantum preprocessing is the one where the verifier sends a random Pauli-basis states to the prover. Our construction uses the Fiat-Shamir transformation. The quantum preprocessing can be replaced with the setup that distributes Bell pairs among the prover and the verifier, and therefore we solve the open problem by Broadbent and Grilo (FOCS ’20) about the possibility of NIZK for QMA in the shared Bell pair model via the Fiat-Shamir transformation.
2022
ASIACRYPT
Collusion-Resistant Functional Encryption for RAMs
In recent years, functional encryption (FE) has established itself as one of the fundamental primitives in cryptography. The choice of model of computation to represent the functions associated with the functional keys plays a critical role in the complexity of the algorithms of an FE scheme. Historically, the functions are represented as circuits. However, this results in the decryption time of the FE scheme growing proportional to not only the worst case running time of the function but also the size of the input, which in many applications can be quite large. In this work, we present the first construction of a public-key collusion resistant FE scheme, where the functions, associated with the keys, are represented as random access machines (RAMs). We base the security of our construction on the existence of: (i) public-key collusion-resistant FE for circuits and, (ii) public-key doubly-efficient private-information retrieval [Boyle et al., Canetti et al., TCC 2017]. Our scheme enjoys many nice efficiency properties, including input-specific decryption time. We also show how to achieve FE for RAMs in the bounded-key setting with weaker efficiency guarantees from laconic oblivious transfer, which can be based on standard cryptographic assumptions. En route to achieving our result, we present conceptually simpler constructions of succinct garbling for RAMs [Canetti et al., Chen et al., ITCS 2016] from weaker assumptions.
2022
ASIACRYPT
Compact and Tightly Selective-Opening Secure Public-key Encryption Schemes
We propose four public-key encryption schemes with tight simulation-based selective-opening security against chosen-ciphertext attacks (SIM-SO-CCA) in the random oracle model. Our schemes only consist of small constant amounts of group elements in the ciphertext, ignoring smaller contributions from symmetric-key encryption, namely, they have compact ciphertexts. Furthermore, three of our schemes have compact public keys as well. Known (almost) tightly SIM-SO-CCA secure PKE schemes are due to the work of Lyu et al. (PKC 2018) and Libert et al. (Crypto 2017). They have either linear-size ciphertexts or linear-size public keys. Moreover, they only achieve almost tightness, namely, with security loss depending on the message bit-length. Different to them, our schemes are the first ones achieving both tight SIM-SO-CCA security and compactness. Our schemes can be divided into two families: - Direct Constructions. Our first three schemes are constructed directly based on the Strong Diffie-Hellman (StDH), Computational DH (CDH), and Decisional DH assumptions. Both their ciphertexts and public keys are compact. Their security loss is a small constant. Interestingly, our CDH-based construction is the first scheme achieving all these advantages based on a weak, search assumption. - A Generic Construction. Our last scheme is the well-known Fujisaki-Okamoto transformation. We show that it can turn a lossy encryption scheme into a tightly SIM-SO-CCA secure PKE. This transformation preserves both tightness and compactness of the underlying lossy encryption, which is in contrast to the non-tight proof of Heuer et al. (PKC 2015).
2022
ASIACRYPT
Compact FE for Unbounded Attribute-Weighted Sums for Logspace from SXDH
Thispaperpresentsthefirstfunctionalencryption(FE)scheme for the attribute-weighted sum (AWS) functionality that supports the uniform model of computation. In such an FE scheme, encryption takes as input a pair of attributes (x, z) where the attribute x is public while the attribute z is private. A secret key corresponds to some weight function f, and decryption recovers the weighted sum f(x)z. This is an important functionality with a wide range of potential real-life applications, many of which require the attribute lengths to be flexible rather than being fixed at system setup. In the proposed scheme, the public attributes are considered as binary strings while the private attributes are considered as vectors over some finite field, both having arbitrary polynomial lengths that are not fixed at system setup. The weight functions are modelled as Logspace Turing machines. Prior schemes [Abdalla, Gong, and Wee, CRYPTO 2020 and Datta and Pal, ASIACRYPT 2021] could only support non-uniform Logspace. The proposed scheme is built in asymmetric prime-order bilinear groups and is proven adaptively simulation secure under the well-studied symmetric external Diffie-Hellman (SXDH) assumption against an arbitrary polynomial number of secret key queries both before and after the challenge ciphertext. This is the best possible level of security for FE as noted in the literature. As a special case of the proposed FE scheme, we also obtain the first adaptively simulation secure inner-product FE (IPFE) for vectors of arbitrary length that is not fixed at system setup. On the technical side, our contributions lie in extending the techniques of Lin and Luo [EUROCRYPT 2020] devised for payload hiding attribute-based encryption (ABE) for uniform Logspace access policies avoiding the so-called “one-use” restriction in the indistinguishability-based security model as well as the “three-slot reduction” technique for simulation- secure attribute-hiding FE for non-uniform Logspace devised by Datta and Pal [ASIACRYPT 2021] to the context of simulation-secure attribute- hiding FE for uniform Logspace.
2022
ASIACRYPT
Concurrently Composable Non-Interactive Secure Computation
We consider the feasibility of non-interactive secure two-party computation (NISC) in the plain model satisfying the notion of superpolynomial-time simulation (SPS). While stand-alone secure SPS-NISC protocols are known from standard assumptions (Badrinarayanan et al., Asiacrypt 2017), it has remained an open problem to construct a concurrently composable SPS-NISC. Prior to our work, the best protocols require 5 rounds (Garg et al., Eurocrypt 2017), or 3 simultaneous-message rounds (Badrinarayanan et al., TCC 2017). In this work, we demonstrate the first concurrently composable SPS-NISC. Our construction assumes the existence of: * a non-interactive (weakly) CCA-secure commitment, * a stand-alone secure SPS-NISC with subexponential security, and satisfies the notion of “angel-based” UC security (i.e., UC with a superpolynomial-time helper) with perfect correctness. We additionally demonstrate that both of the primitives we use (albeit only with polynomial security) are necessary for such concurrently composable SPS-NISC with perfect correctness. As such, our work identifies essentially necessary and sufficient primitives for concurrently composable SPS-NISC with perfect correctness in the plain model.
2022
ASIACRYPT
Continuously Non-Malleable Codes against Bounded-Depth Tampering
Non-malleable codes (Dziembowski, Pietrzak and Wichs, ICS 2010 & JACM 2018) allow protecting arbitrary cryptographic primitives against related-key attacks (RKAs). Even when using codes that are guaranteed to be non-malleable against a single tampering attempt, one obtains RKA security against poly-many tampering attacks at the price of assuming perfect memory erasures. In contrast, continuously non-malleable codes (Faust, Mukherjee, Nielsen and Venturi, TCC 2014) do not suffer from this limitation, as the non-malleability guarantee holds against poly-many tampering attempts. Unfortunately, there are only a handful of constructions of continuously non-malleable codes, while standard non-malleable codes are known for a large variety of tampering families including, e.g., NC0 and decision-tree tampering, AC0, and recently even bounded polynomial-depth tampering. We change this state of affairs by providing the first constructions of continuously non-malleable codes in the following natural settings: – Against decision-tree tampering, where, in each tampering attempt, every bit of the tampered codeword can be set arbitrarily after adaptively reading up to d locations within the input codeword. Our scheme is in the plain model, can be instantiated assuming the existence of one-way functions, and tolerates tampering by decision trees of depth d = O(n1/8), where n is the length of the codeword. Notably, this class includes NC0. – Against bounded polynomial-depth tampering, where in each tampering attempt the adversary can select any tampering function that can be computed by a circuit of bounded polynomial depth (and unbounded polynomial size). Our scheme is in the common reference string model, and can be instantiated assuming the existence of time-lock puzzles and simulation-extractable (succinct) non-interactive zero-knowledge proofs.
2022
ASIACRYPT
Counting Vampires: From Univariate Sumcheck to Updatable ZK-SNARK
We propose a univariate sumcheck argument $\mathfrak{Count}$ of essentially optimal communication efficiency of one group element. While the previously most efficient univariate sumcheck argument of Aurora is based on polynomial commitments, $\mathfrak{Count}$ is based on inner-product commitments. We use $\mathfrak{Count}$ to construct a new pairing-based updatable and universal zk-SNARK $\mathfrak{Vampire}$ with the shortest known argument length (four group and two finite field elements) for $\mathsf{NP}$. In addition, $\mathfrak{Vampire}$ uses the aggregated polynomial commitment scheme of Boneh et al.
2022
ASIACRYPT
Cryptographic Primitives with Hinting Property
A hinting PRG is a (potentially) stronger variant of PRG with a "deterministic" form of circular security with respect to the seed of the PRG (Koppula and Waters, CRYPTO 2019). Hinting PRGs enable many cryptographic applications, most notably CCA-secure public-key encryption and trapdoor functions. In this paper, we study cryptographic primitives with the hinting property, yielding the following results: - We present a novel and conceptually simpler approach for designing hinting PRGs from certain decisional assumptions over cyclic groups or isogeny-based group actions, which enables simpler security proofs as compared to the existing approaches for designing such primitives. - We introduce hinting weak PRFs, a natural extension of the hinting property to weak PRFs, and show how to realize circular/KDM-secure symmetric-key encryption from any hinting weak PRF. We demonstrate that our simple approach for building hinting PRGs can be extended to realize hinting weak PRFs from the same set of decisional assumptions. - We propose a stronger version of the hinting property, which we call the functional hinting property, that guarantees security even in the presence of hints about functions of the secret seed/key. We show how to instantiate functional hinting PRGs and functional hinting weak PRFs for certain (families of) functions by building upon our simple techniques for realizing plain hinting PRGs/weak PRFs. We also demonstrate the applicability of a functional hinting weak PRF with certain algebraic properties in realizing KDM-secure public-key encryption in a black-box manner. - Finally, we show the first black-box separation between hinting weak PRFs (and hinting PRGs) from public-key encryption using simple realizations of these primitives given only a random oracle.
2022
ASIACRYPT
DAG-$\Sigma$: A DAG-based Sigma Protocol for Relations in CNF
At CRYPTO 1994, Cramer, Damg{\aa}rd and Schoenmakers proposed a general method to construct proofs of knowledge (PoKs), especially for $k$-out-of-$n$ partial knowledge, of which relations can be expressed in disjunctive normal form (DNF). Since then, proofs of $k$-out-of-$n$ partial knowledge have attracted much attention and some efficient constructions have been proposed. However, many practical scenarios require efficient PoK protocols for partial knowledge in other forms. In this paper, we mainly focus on PoK protocols for $k$-conjunctive normal form ($k$-CNF) relations, which have $n$ statements and can be expressed as follows: (i) $k$ statements constitute a clause via ``OR'' operations, and (ii) the relation consists of multiple clauses via ``AND'' operations. We propose an alternative Sigma protocol (called DAG-$\Sigmaup$ protocol) for $k$-CNF relations, by turning these relations into directed acyclic graphs (DAGs). Our DAG-$\Sigmaup$ protocol achieves less communication cost and smaller computational overhead compared with Cramer et al.'s general method.
2022
ASIACRYPT
Efficient Adaptively-Secure Byzantine Agreement for Long Messages
We investigate the communication complexity of Byzantine agreement protocols for long messages against an adaptive adversary. In this setting, prior $n$-party protocols either achieved a communication complexity of $O(nl\cdot\poly(\kappa))$ or $O(nl + n^2 \cdot \poly(\kappa))$ for $l$-bit long messages and security parameter $\kappa$. We improve the state of the art by presenting protocols with communication complexity $O(nl + n \cdot \poly(\kappa))$ in both the synchronous and asynchronous communication models. The synchronous protocol tolerates $t \le (1-\epsilon) \frac{n}{2}$ corruptions and assumes a VRF setup, while the asynchronous protocol tolerates $t \le (1-\epsilon) \frac{n}{3}$ corruptions under further cryptographic assumptions. Our protocols are very simple and combine subcommittee election with the recent approach of Nayak et al. (DISC'20). Surprisingly, the analysis of our protocols is 'all but simple' and involves an interesting new application of Mc Diarmid's inequality to obtain 'almost optimal' corruption thresholds.
2022
ASIACRYPT
Efficient NIZKs from LWE via Polynomial Reconstruction and ``MPC in the Head''
All existing works building non-interactive zero-knowledge (NIZK) arguments for NP from the Learning With Errors (LWE) assumption have studied instantiating the Fiat-Shamir paradigm on a parallel repetition of an underlying honest-verifier zero knowledge (HVZK) sigma protocol, via an appropriately built correlation-intractable (CI) hash function from LWE. This technique has inherent efficiency losses that arise from parallel repetition. In this work, we show how to make use of the more efficient ``MPC in the Head'' technique for building an underlying honest-verifier protocol upon which to apply the Fiat-Shamir paradigm. To make this possible, we provide a new and more efficient construction of CI hash functions from LWE, using efficient algorithms for polynomial reconstruction as the main technical tool. We stress that our work provides a new and more efficient ``base construction'' for building LWE-based NIZK arguments for NP. Our protocol can be the building block around which other efficiency-focused bootstrapping techniques can be applied, such as the bootstrapping technique of Gentry et al. (Journal of Cryptology 2015).
2022
ASIACRYPT
Efficient Searchable Symmetric Encryption for Join Queries
The Oblivious Cross-Tags (OXT) protocol due to Cash et al. (CRYPTO 2013) is a highly scalable searchable symmetric encryption (SSE) scheme that allows fast processing of conjunctive and more general Boolean queries over encrypted relational databases. A longstanding open question has been to extend OXT to also support queries over joins of tables without pre-computing the joins. In this paper, we solve this open question without compromising on the nice properties of OXT with respect to both security and efficiency. We propose Join Cross-Tags (JXT) - a purely symmetric-key solution that supports efficient conjunctive queries over (equi-) joins of encrypted tables without any pre-computation at setup. JXT is fully compatible with OXT, and can be used in conjunction with OXT to support a wide class of SQL queries directly over encrypted relational databases. JXT incurs a storage cost (over OXT) of a factor equal to the number of potential join-attributes in a table, which is usually compensated by the fact that JXT is a fully symmetric-key solution (as opposed to OXT which relies on discrete-log hard groups). We prove the (adaptive) simulation-based security of JXT with respect to a rigorously defined leakage profile.
2022
ASIACRYPT
Efficient Zero-Knowledge Arguments in Discrete Logarithm Setting: Sublogarithmic Proof or Sublinear Verifier
We propose three interactive zero-knowledge arguments for arithmetic circuit of size N in the common random string model, which can be converted to be non-interactive by Fiat-Shamir heuristics in the random oracle model. First argument features O( log N ) communication and round complexities and O(N) computational complexity for the verifier. Second argument features O(log N ) communication and O( N ) computational complexity for the verifier. Third argument features O(log N ) communication and O( N log N ) computational complexity for the verifier. Contrary to first and second arguments, the third argument is free of reliance on pairing-friendly elliptic curves. The soundness of three arguments is proven under the standard discrete logarithm and/or the double pairing assumption, which is at least as reliable as the decisional Diffie-Hellman assumption.
2022
ASIACRYPT
Encryption to the Future A Paradigm for Sending Secret Messages to Future (Anonymous) Committees
A number of recent works have constructed cryptographic protocols with flavors of adaptive security by having a randomly-chosen anonymous committee run at each round. Since most of these protocols are stateful, transferring secret states from past committees to future, but still unknown, committees is a crucial challenge. Previous works have tackled this problem with approaches tailor-made for their specific setting, which mostly rely on using a blockchain to orchestrate auxiliary committees that aid in the state hand-over process. In this work, we look at this challenge as an important problem on its own and initiate the study of Encryption to the Future (EtF) as a cryptographic primitive. First, we define a notion of an EtF scheme where time is determined with respect to an underlying blockchain and a lottery selects parties to receive a secret message at some point in the future. While this notion seems overly restrictive, we establish two important facts: 1. if used to encrypt towards parties selected in the “far future”, EtF implies witness encryption for NP over a blockchain; 2. if used to encrypt only towards parties selected in the “near future”, EtF is not only sufficient for transferring state among committees as required by previous works, but also captures previous tailor-made solutions. To corroborate these results, we provide a novel construction of EtF based on witness encryption over commitments (cWE), which we instantiate from a number of standard assumptions via a construction based on generic cryptographic primitives. Finally, we show how to use “near future” EtF to obtain “far future” EtF with a protocol based on an auxiliary committee whose communication complexity is independent of the length of plaintext messages being sent to the future.
2022
ASIACRYPT
Enhancing Differential-Neural Cryptanalysis
In CRYPTO 2019, Gohr shows that well-trained neural networks can perform cryptanalytic distinguishing tasks superior to traditional differential distinguishers. Moreover, applying an unorthodox key guessing strategy, an 11-round key-recovery attack on a modern block cipher Speck32/64 improves upon the published state-of-the-art result. This calls into the next questions. To what extent is the advantage of machine learning (ML) over traditional methods, and whether the advantage generally exists in the cryptanalysis of modern ciphers? To answer the first question, we devised ML-based key-recovery attacks on more extended round-reduced Speck32/64. We achieved an improved 12-round and the first practical 13-round attacks. The essential for the new results is enhancing a classical component in the ML-based attacks, that is, the neutral bits. To answer the second question, we produced various neural distinguishers on round-reduced Simon32/64 and provided comparisons with their pure differential-based counterparts.
2022
ASIACRYPT
EvalRound Algorithm in CKKS Bootstrapping
Homomorphic encryption (HE) has open an entirely new world up in the privacy-preserving use of sensitive data by conducting computations on encrypted data. Amongst many HE schemes targeting on computation in various contexts, Cheon--Kim--Kim--Song (CKKS) scheme is distinguished since it allows computations for encrypted real number data, which have greater impact in real-world applications. CKKS scheme is a levelled homomorphic encryption scheme, consuming one level for each homomorphic multiplication. When the level runs out, a special computational circuit called bootstrapping is required in order to conduct further multiplications. The algorithm proposed by Cheon et al. has been regarded as a standard way to do bootstrapping in the CKKS scheme, and it consists of the following four steps: ModRaise, CoeffToSlot, EvalMod and SlotToCoeff. However, the steps consume a number of levels themselves, and thus optimizing this extra consumption has been a major focus of the series of recent research. Among the total levels consumed in the bootstrapping steps, about a half of them is spent in CoeffToSlot and SlotToCoeff steps to scale up the real number components of DFT matrices and round them to the nearest integers. Each scale-up factor is very large so that it takes up one level to rescale it down. Scale-up factors can be taken smaller to save levels, but the error of rounding would be transmitted to EvalMod and eventually corrupt the accuracy of bootstrapping. EvalMod aims to get rid of the superfluous $qI$ term from a plaintext $\pt + qI$ resulting from ModRaise, where $q$ is the bottom modulus and $I$ is a polynomial with small integer coefficients. EvalRound is referred to as its opposite, obtaining $qI$. We introduce a novel bootstrapping algorithm consisting of ModRaise, CoeffToSlot, EvalRound and SlotToCoeff, which yields taking smaller scale-up factors without the damage of rounding errors.
2022
ASIACRYPT
Exploring SAT for Cryptanalysis: (Quantum) Collision Attacks against 6-Round SHA-3
In this work, we focus on collision attacks against instances of \shac hash family in both classical and quantum settings. Since the 5-round collision attacks on \shacc-256 and other variants proposed by Guo \etal at JoC~2020, no other essential progress has been published. With a thorough investigation, we identify that the challenges of extending such collision attacks on \shac to more rounds lie in the inefficiency of differential trail search. To overcome this obstacle, we develop a \sat automatic search toolkit. The tool is used in multiple intermediate steps of the collision attacks and exhibits surprisingly high efficiency in differential trail search and other optimization problems encountered in the process. As a result, we present the first 6-round classical collision attack on \shakea with time complexity \cpshake, which also forms a quantum collision attack with quantum time \cpshakeq, and the first 6-round quantum collision attack on \shacc-224 and \shacc-256 with quantum time \cpshattf and \cpshatfs, where $S$ represents the hardware resources of the quantum computer. The fact that classical collision attacks do not apply to 6-round \shacc-224 and \shacc-256 shows the higher coverage of quantum collision attacks, which is consistent with that on SHA-2 observed by Hosoyamada and Sasaki at CRYPTO~2021.
2022
ASIACRYPT
Failing gracefully: Decryption failures and the Fujisaki-Okamoto transform
In known security reductions for the Fujisaki-Okamoto transformation, decryption failures are handled via a reduction solving the rather unnatural task of finding failing plaintexts given the private key, resulting in a Grover search bound. Moreover, they require an implicit rejection mechanism for invalid ciphertexts to achieve a reasonable security bound in the QROM. We present a reduction that has neither of these deficiencies: We introduce two security games related to finding decryption failures, one capturing the computationally hard task of using the public key to find a decryption failure, and one capturing the statistically hard task of searching the random oracle for key-independent failures like, e.g., large randomness. As a result, our security bounds in the QROM are tighter than previous ones with respect to the generic random oracle search attacks: The attacker can only partially compute the search predicate, namely for said key-independent failures. In addition, our entire reduction works for the explicit-reject variant of the transformation and improves significantly over all of its known reductions. Besides being the more natural variant of the transformation, security of the explicit reject mechanism is also relevant for side channel attack resilience of the implicit-rejection variant. Along the way, we prove several technical results characterizing preimage extraction and certain search tasks in the QROM that might be of independent interest.
2022
ASIACRYPT
FINAL: Faster FHE instantiated with NTRU and LWE
The NTRU problem is a promising candidate to build efficient Fully Homomorphic Encryption (FHE).However, all the existing proposals (e.g. LTV, YASHE) need so-called `overstretched' parameters of NTRU to enable homomorphic operations. It was shown by Albrecht~et~al. (CRYPTO~2016) that these parameters are vulnerable against subfield lattice attacks. Based on a recent, more detailed analysis of the overstretched NTRU assumption by Ducas and van Woerden (ASIACRYPT~2021), we construct two FHE schemes whose NTRU parameters lie outside the overstretched range.The first scheme is based solely on NTRU and demonstrates competitive performance against the state-of-the-art FHE schemes including TFHE. Our second scheme, which is based on both the NTRU and LWE assumptions, outperforms TFHE with a 28\% faster bootstrapping and 45\% smaller bootstrapping and key-switching keys.
2022
ASIACRYPT
Flashproofs: Efficient Zero-Knowledge Arguments of Range and Polynomial Evaluation with Transparent Setup
We propose Flashproofs, a new type of efficient special honest verifier zero-knowledge arguments with a transparent setup in the discrete logarithm (DL) setting. First, we put forth gas-efficient range arguments that achieve $O(N^{\frac{2}{3}})$ communication cost, and involve $O(N^{\frac{2}{3}})$ group exponentiations for verification and a slightly sub-linear number of group exponentiations for proving with respect to the range $[0, 2^N-1]$, where $N$ is the bit length of the range. For typical confidential transactions on blockchain platforms supporting smart contracts, verifying our range arguments consumes only 237K and 318K gas for 32-bit and 64-bit ranges, which are comparable to 220K gas incurred by verifying the most efficient zkSNARK with a trusted setup (EUROCRYPT \textquotesingle 16) at present. Besides, the aggregation of multiple arguments can yield further efficiency improvement. Second, we present polynomial evaluation arguments based on the techniques of Bayer \& Groth (EUROCRYPT \textquotesingle 13). We provide two zero-knowledge arguments, which are optimised for lower-degree ($D \in [3, 2^9]$) and higher-degree ($D > 2^9$) polynomials, where $D$ is the polynomial degree. Our arguments yield a non-trivial improvement in the overall efficiency. Notably, the number of group exponentiations for proving drops from $8\log D$ to $3(\log D+\sqrt{\log D})$. The communication cost and the number of group exponentiations for verification decrease from $7\log D$ to $(\log D + 3\sqrt{\log D})$. To the best of our knowledge, our arguments instantiate the most communication-efficient arguments of membership and non-membership in the DL setting among those not requiring trusted setups. More importantly, our techniques enable a significantly asymptotic improvement in the efficiency of communication and verification (group exponentiations) from $O(\log D)$ to $O(\sqrt{\log D})$ when multiple arguments satisfying different polynomials with the same degree and inputs are aggregated.
2022
ASIACRYPT
Full Quantum Equivalence of Group Action DLog and CDH, and More
Cryptographic group actions are a relaxation of standard cryptographic groups that have less structure. This lack of structure allows them to be plausibly quantum resistant despite Shor's algorithm, while still having a number of applications. The most famous example of group actions are built from isogenies on elliptic curves. Our main result is that CDH for abelian group actions is quantumly equivalent to discrete log. Galbraith et al. (Mathematical Cryptology) previously showed perfectly solving CDH to be equivalent to discrete log quantumly; our result works for any non-negligible advantage. We also explore several other questions about group action and isogeny protocols.
2022
ASIACRYPT
Functional Encryption with Secure Key Leasing
Secure software leasing is a quantum cryptographic primitive that enables us to lease software to a user by encoding it into a quantum state. Secure software leasing has a mechanism that verifies whether a returned software is valid or not. The security notion guarantees that once a user returns a software in a valid form, the user no longer uses the software. In this work, we introduce the notion of secret-key functional encryption (SKFE) with secure key leasing, where a decryption key can be securely leased in the sense of secure software leasing. We also instantiate it with standard cryptographic assumptions. More specifically, our contribution is as follows. - We define the syntax and security definitions for SKFE with secure key leasing. - We achieve a transformation from standard SKFE into SKFE with secure key leasing without using additional assumptions. Especially, we obtain bounded collusion-resistant SKFE for P/poly with secure key leasing based on post-quantum one-way functions since we can instantiate bounded collusion-resistant SKFE for P/poly with the assumption. Some previous secure software leasing schemes capture only pirate software that runs on an honest evaluation algorithm (on a legitimate platform). However, our secure key leasing notion captures arbitrary attack strategies and does not have such a limitation. As an additional contribution, we introduce the notion of single-decryptor FE (SDFE), where each functional decryption key is copy-protected. Since copy-protection is a stronger primitive than secure software leasing, this notion can be seen as a stronger cryptographic primitive than FE with secure key leasing. More specifically, our additional contribution is as follows. - We define the syntax and security definitions for SDFE. - We achieve collusion-resistant single-decryptor PKFE for P/poly from post-quantum indistinguishability obfuscation and quantum hardness of the learning with errors problem.
2022
ASIACRYPT
General Properties of Quantum Bit Commitments (Extended Abstract)
While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one. A complexity-based canonical (non-interactive) quantum bit commitment scheme refers to a kind of scheme such that the commitment consists of just a single (quantum) message from the sender to the receiver that can be opened later by uncomputing the commit stage. In this work, we study general properties of complexity-based quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two: 1. Any complexity-based quantum bit commitment scheme can be converted into the canonical (non-interactive) form (with its sum-binding property preserved). 2. Two flavors of canonical quantum bit commitments are equivalent; that is, canonical computationally-hiding statistically-binding quantum bit commitment exists if and only if the canonical statistically-hiding computationally-binding one exists. Combining this result with the first one, it immediately implies (unconditionally) that complexity-based quantum bit commitment is symmetric. Canonical quantum bit commitments can be based on quantum-secure one-way functions or pseudorandom quantum states. But in our opinion, the formulation of canonical quantum bit commitment is so clean and simple that itself can be viewed as a plausible complexity assumption as well. We propose to explore canonical quantum bit commitment from perspectives of both quantum cryptography and quantum complexity theory in future.
2022
ASIACRYPT
Group Action Key Encapsulation and Non-Interactive Key Exchange in the QROM
In the context of quantum-resistant cryptography, cryptographic group actions offer an abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) setting. In this work, we revisit the security of two previously proposed natural protocols: the Group Action Hashed ElGamal key encapsulation mechanism (GA-HEG KEM) and the Group Action Hashed Diffie-Hellman non-interactive key-exchange (GA-HDH NIKE) protocol. The latter protocol has already been considered to be used in practical protocols such as Post-Quantum WireGuard (S&P '21) and OPTLS (CCS '20). We prove that active security of the two protocols in the Quantum Random Oracle Model (QROM) inherently relies on very strong variants of the Group Action Strong CDH problem, where the adversary is given arbitrary quantum access to a DDH oracle. That is, quantum accessible Strong CDH assumptions are not only sufficient but also necessary to prove active security of the GA-HEG KEM and the GA-HDH NIKE protocols. Furthermore, we propose variants of the protocols with QROM security from the classical Strong CDH assumption, i.e., CDH with classical access to the DDH oracle. Our first variant uses key confirmation and can therefore only be applied in the KEM setting. Our second but considerably less efficient variant is based on the twinning technique by Cash et al. (EUROCRYPT '08) and in particular yields the first actively secure isogeny-based NIKE with QROM security from the standard CDH assumption.
2022
ASIACRYPT
GUC-Secure Commitments via Random Oracles: New Impossibility and Feasibility
In the UC framework, protocols must be subroutine respecting; therefore, shared trusted setup might cause security issues. To address this drawback, Generalized UC (GUC) framework is introduced by Canetti {\em et al.} (TCC 2007). In this work, we investigate the impossibility and feasibility of GUC-secure commitments using global random oracles (GRO) as the trusted setup. In particular, we show that it is impossible to have a 2-round (1-round committing and 1-round opening) GUC-secure commitment in the global observable RO model by Canetti {\em et al.} (CCS 2014). We then give a new round-optimal GUC-secure commitment that uses only Minicrypt assumptions (i.e. the existence of one-way functions) in the global observable RO model. Furthermore, we also examine the complete picture on round complexity of the GUC-secure commitments in various global RO models.
2022
ASIACRYPT
Hawk: Module LIP makes Lattice Signatures Fast, Compact and Simple
We propose the signature scheme Hawk, a concrete instantiation of proposals to use the Lattice Isomorphism Problem (LIP) as a foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows the use of lattices such as $\mathbb{Z}^n$, leading to signature algorithms with no floats, no rejection sampling, and compact precomputed distributions. Such design features are desirable for constrained devices, and when computing signatures inside FHE or MPC. The most significant change from recent LIP proposals is the use of module lattices, reusing algorithms and ideas from NTRUSign and Falcon. Its simplicity makes Hawk competitive. We provide cryptanalysis with experimental evidence for the design of Hawk and implement two parameter sets, Hawk-512 and Hawk-1024. Signing using Hawk-512 and Hawk-1024 is four times faster than Falcon on x86 architectures, produces signatures that are about 15% more compact, and is slightly more secure against forgeries by lattice reduction attacks. When floating-points are unavailable, Hawk signs 15 times faster than Falcon. We provide a worst case to average case reduction for module LIP. For certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem.
2022
ASIACRYPT
Horizontal racewalking using radical isogenies
We address three main open problems concerning the use of radical isogenies, as presented by Castryck, Decru and Vercauteren at Asiacrypt 2020, in the computation of long chains of isogenies of fixed, small degree between elliptic curves over finite fields. Firstly, we present an interpolation method for finding radical isogeny formulae in a given degree N, which by-passes the need for factoring division polynomials over large function fields. Using this method, we are able to push the range for which we have formulae at our disposal from N ≤ 13 to N ≤ 37. Secondly, using a combination of known techniques and ad-hoc manipulations, we derived optimized versions of these formulae for N ≤ 19, with some instances performing more than twice as fast as their counterparts from 2020. Thirdly, we solve the problem of understanding the correct choice of radical when walking along the surface between supersingular elliptic curves over Fp with p ≡ 7 mod 8; this is non-trivial for even N and was only settled for N = 4 by Onuki and Moriya at PKC 2022. We give a conjectural statement for all even N and prove it for N ≤ 14. The speed-ups obtained from these techniques are substantial: using 16-isogenies, the computation of long chains of 2-isogenies over 512-bit prime fields can be improved by a factor 3, and the previous implementation of CSIDH using radical isogenies can be sped up by about 12%.
2022
ASIACRYPT
Identity-Based Matchmaking Encryption from Standard Assumptions
In this work, we propose the first identity-based matchmaking encryption (IB-ME) scheme under the standard assumptions in the standard model. This scheme is proven to be secure under the symmetric external Diffie-Hellman (SXDH) assumption in prime order bilinear pairing groups. In our IB-ME scheme, all parameters have constant number of group elements and are simpler than those of previous constructions. Previous works are either in the random oracle model or based on the q-type assumptions, while ours is built directly in the standard model and based on static assumptions, and does not rely on other crypto tools. More concretely, our IB-ME scheme is constructed from a variant of two-level anonymous IBE. We observed that this two-level IBE with anonymity and unforgeability satisfies the same functionality of IB-ME, and its security properties cleverly meet the two requirements of IB-ME (Privacy and Authenticity). The privacy property of IB-ME relies on the anonymity of this two-level IBE, while the authenticity property is corresponding to the unforgeability in the 2nd level. This variant of two-level IBE is built from dual pairing vector spaces, and both security reductions rely on dual system encryption.
2022
ASIACRYPT
Improved Straight-Line Extraction in the Random Oracle Model With Applications to Signature Aggregation
The goal of this paper is to improve the efficiency and applicability of straightline extraction techniques in the random oracle model. Straightline extraction in the random oracle model refers to the existence of an extractor, which given the random oracle queries made by a prover P*(x) on some theorem x, is able to produce a witness w for x with roughly the same probability that P* produces a verifying proof. This notion applies to both zero-knowledge protocols and verifiable computation where the goal is compressing a proof. Pass (CRYPTO '03) first showed how to achieve this property for NP using a cut-and-choose technique which incurred a \lambda^2-bit overhead in communication where \lambda is a security parameter. Fischlin (CRYPTO '05) presented a more efficient technique based on ``proofs of work'' that sheds this \lambda^2 cost, but only applies to a limited class of Sigma Protocols with a ``quasi-unique response'' property, which for example, does not necessarily include the standard OR composition for Sigma protocols. With Schnorr/EdDSA signature aggregation as a motivating application, we develop new techniques to improve the computation cost of straight-line extractable proofs. Our improvements to the state of the art range from 70x--200x for the best compression parameters. This is due to a uniquely suited polynomial evaluation algorithm, and the insight that a proof-of-work that relies on multicollisions and the birthday paradox is faster to solve than inverting a fixed target. Our collision based proof-of-work more generally improves the Prover's random oracle query complexity when applied in the NIZK setting as well. In addition to reducing the query complexity of Fischlin's Prover, for a special class of Sigma protocols we can for the first time closely match a new lower bound we present. Finally we extend Fischlin's technique so that it applies to a more general class of strongly-sound Sigma protocols, which includes the OR composition. We achieve this by carefully randomizing Fischlin's technique---we show that its current deterministic nature prevents its application to certain multi-witness languages.
2022
ASIACRYPT
Improving Bounds on Elliptic Curve Hidden Number Problem for ECDH Key Exchange
Elliptic Curve Hidden Number Problem (EC-HNP) was first introduced by Boneh, Halevi and Howgrave-Graham at Asiacrypt 2001. To rigorously assess the bit security of the Diffie--Hellman key exchange with elliptic curves (ECDH), the Diffie--Hellman variant of EC-HNP, regarded as an elliptic curve analogy of the Hidden Number Problem (HNP), was presented at PKC 2017. This variant can also be used for practical cryptanalysis of ECDH key exchange in the situation of side-channel attacks. In this paper, we revisit the Coppersmith method for solving the involved modular multivariate polynomials in the Diffie--Hellman variant of EC-HNP and demonstrate that, for any given positive integer $d$, a given sufficiently large prime $p$, and a fixed elliptic curve over the prime field $\mathbb{F}_p$, if there is an oracle that outputs about $\frac{1}{d+1}$ of the most (least) significant bits of the $x$-coordinate of the ECDH key, then one can give a heuristic algorithm to compute all the bits within polynomial time in $\log_2 p$. When $d>1$, the heuristic result $\frac{1}{d+1}$ significantly outperforms both the rigorous bound $\frac{5}{6}$ and heuristic bound $\frac{1}{2}$. Due to the heuristics involved in the Coppersmith method, we do not get the ECDH bit security on a fixed curve. However, we experimentally verify the effectiveness of the heuristics on NIST curves for small dimension lattices.
2022
ASIACRYPT
Instantiability of Classical Random-Oracle-Model Encryption Transforms
Extending a line of work leveraging program obfuscation to instantiate random oracles (ROs) (\emph{e.g.}, Hohenberger \emph{et al.}, EUROCRYPT 2014, Kalai \emph{el al.}, CRYPTO 2017), we show that, using program obfuscation and other suitable assumptions, there exist standard-model hash functions that suffice to instantiate the classical RO-model encryption transforms OAEP (Bellare and Rogaway, EUROCRYPT 1994) and Fujisaki-Okamoto (EUROCRYPT 1998) under IND-CCA. Our result for Fujisaki-Okamoto employs a simple modification to the scheme that may be interesting for the current NIST PQC competition. For the most part, our instantiations do not require much stronger assumptions on the base schemes compared to their corresponding RO-model proofs. For example, to instantiate low-exponent RSA-OAEP, the assumption we need on RSA is sub-exponential partial one-wayness, matching the assumption on RSA needed by Fujisaki \emph{et al.} (J.~Cryptology 2004) in the RO model up to sub-exponentiality. Similarly, for the part of Fujisaki-Okamoto that upgrades indistinguishability under plaintext-checking to attack (OW-PCA) to IND-CCA, we again do not require much stronger assumptions up to sub-exponentiality. We obtain our hash functions in a unified way, extending a technique of Brzuska and Mittelbach (ASIACRYPT 2014). We incorporate into their technique: (1) extremely lossy functions (ELFs), a notion by Zhandry (CRYPTO 2016), and (2) \emph{multi-bit} auxiliary-input point function obfuscation (MB-AIPO). While MB-AIPO is impossible in general (Brzuska and Mittelbach, ASIACRYPT 2014), we give plausible constructions for the special cases we need, which may be of independent interest. We stress that our hash functions are not practical, but are meant to justify that when using the transforms in practice with cryptographic hashing, the end goal is plausible.
2022
ASIACRYPT
Jammin' on the deck
Currently, a vast majority of symmetric-key cryptographic schemes are built as block cipher modes. The block cipher is designed to be hard to distinguish from a random permutation and this is supported by cryptanalysis, while (good) modes can be proven secure if a random permutation takes the place of the block cipher. As such, block ciphers form an abstraction level that marks the border between cryptanalysis and security proofs. In this paper, we investigate a re-factored version of symmetric-key cryptography built not around the block ciphers but rather the deck function: a keyed function with arbitrary input and output length and incrementality properties. This allows for modes of use that are simpler to analyze and still very efficient thanks to the excellent performance of currently proposed deck functions. We focus on authenticated encryption (AE) modes with varying levels of robustness. Our modes have built-in support for sessions, but are also efficient without them. As a by-product, we define a new ideal model for AE dubbed the jammin cipher. Unlike the OAE2 security models, the jammin cipher is both a operational ideal scheme and a security reference, and addresses real-world use cases such as bi-directional communication and multi-key security.
2022
ASIACRYPT
Key-Reduced Variants of 3kf9 with Beyond-Birthday-Bound Security
3kf9 is a three-key CBC-type MAC that enhances the standardized integrity algorithm f9 (3GPP-MAC). It has beyond-birthday-bound security and is expected to be a possible candidate in constrained environments when instantiated with lightweight blockciphers. Two variants 2kf9 and 1kf9 were proposed to reduce key size for efficiency, but recently, Leurent et al. (CRYPTO'18) and Shen et al. (CRYPTO'21) pointed out critical flaws on these two variants and invalidated their security proofs with birthday-bound attacks. In this work, we revisit previous constructions of key-reduced variants of 3kf9 and analyze what went wrong in security analyzes. Interestingly, we find that a single doubling at the end can not only fix 2kf9 to go beyond the birthday bound, but also help 1kf9 to go beyond the birthday bound. We then propose two new key-reduced variants of 3kf9, called n2kf9 and n1kf9. By leveraging previous attempts, we prove that n2kf9 is secure up to 2^{2n/3} queries, and prove that n1kf9 is secure up to 2^{2n/3} queries when the message space is prefix-free. We also provide beyond-birthday analysis of n2kf9 in the multi-user setting. Note that compared to EMAC and CBC-MAC, the additional cost to provide a higher security guarantee is expected to be minimal for n2kf9 and n1kf9. It only requires one additional blockcipher call and one doubling.
2022
ASIACRYPT
Key-schedule Security for the TLS 1.3 Standard
Transport Layer Security (TLS) is the cryptographic backbone of secure communication on the Internet. In its latest version 1.3, the standardization process has taken formal analysis into account both due to the importance of the protocol and the experience with conceptual attacks against previous versions. To manage the complexity of TLS (the specification exceeds 100 pages), prior reduction-based analyses have focused on some protocol features and omitted others, e.g., included session resumption and omitted agile algorithms or vice versa. This article is a major step towards analysing the TLS 1.3 key establishment protocol as specified at the end of its rigorous standardization process. Namely, we provide a full proof of the TLS key schedule, a core protocol component which produces output keys and internal keys of the key exchange protocol. In particular, our model supports all key derivations featured in the standard, including its negotiated modes and algorithms that combine an optional Diffie-Hellman exchange for forward secrecy with optional pre-shared keys supplied by the application or recursively established in prior sessions. Technically, we rely on state-separating proofs (Asiacrypt '18) and introduce techniques to model large and complex derivation graphs. Our key schedule analysis techniques have been used subsequently %by Brzuska, Cornelissen and Kohbrok to analyse the key schedule of Draft 11 of the MLS protocol (S&P'22) and to propose improvements.
2022
ASIACRYPT
Knowledge Encryption and Its Applications to Simulatable Protocols With Low Round-Complexity
We introduce a new notion of public key encryption, knowledge encryption, for which its ciphertexts can be reduced to the public-key, i.e., any algorithm that can break the ciphertext indistinguishability can be used to extract the (partial) secret key. We show that knowledge encryption can be built solely on any two-round oblivious transfer with game-based security, which are known based on various standard (polynomial-hardness) assumptions, such as the DDH, the Quadratic($N^{th}$) Residuosity or the LWE assumption. We use knowledge encryption to construct the first three-round (weakly) simulatable oblivious transfer. This protocol satisfies (fully) simulatable security for the receiver, and weakly simulatable security ($(T,\epsilon)$-simulatability) for the sender in the following sense: for any polynomial $T$ and any inverse polynomial $\epsilon$, there exists an efficient simulator such that the distinguishing gap of any distinguisher of size less than $T$ is at most $\epsilon$. Equipped with these tools, we construct a variety of fundamental cryptographic protocols with low round-complexity, assuming only the existence of two-round oblivious transfer with game-based security. These protocols include three-round delayed-input weak zero knowledge argument, three-round weakly secure two-party computation, three-round concurrent weak zero knowledge in the BPK model, and a two-round commitment with weak security under selective opening attack. These results improve upon the assumptions required by the previous constructions. Furthermore, all our protocols enjoy the above $(T,\epsilon)$-simulatability (stronger than the distinguisher-dependent simulatability), and are quasi-polynomial time simulatable under the same (polynomial hardness) assumption.
2022
ASIACRYPT
Large-Precision Homomorphic Sign Evaluation using FHEW/TFHE Bootstrapping
A comparison of two encrypted numbers is an important operation needed in many machine learning applications, for example, decision tree or neural network inference/training. An efficient instantiation of this operation in the context of fully homomorphic encryption (FHE) can be challenging, especially when a relatively high precision is sought. The conventional FHE way of evaluating the comparison operation, which is based on the sign function evaluation using FHEW/TFHE bootstrapping (often referred in literature as programmable bootstrapping), can only support very small precision (practically limited to 4-5 bits or so). For higher precision, the runtime complexity scales linearly with the ciphertext (plaintext) modulus (i.e., exponentially with the modulus bit size). We propose sign function evaluation algorithms that scale logarithmically with the ciphertext (plaintext) modulus, enabling the support of large-precision comparison in practice. Our sign evaluation algorithms are based on an iterative use of homomorphic floor function algorithms, which are also derived in our work. Further, we generalize our procedures for floor function evaluation to arbitrary function evaluation, which can be used to support both small plaintext moduli (directly) and larger plaintext moduli (by using a homomorphic digit decomposition algorithm, also suggested in our work). We implement all these algorithms using the PALISADE lattice cryptography library, introducing several implementation-specific optimizations along the way, and discuss our experimental results.
2022
ASIACRYPT
Latin Dances Reloaded: Improved Cryptanalysis against Salsa and ChaCha, and the proposal of Forró
In this paper, we present 4 major contributions to ARX ciphers and in particular to the Salsa/ChaCha family of stream ciphers: a) We propose an improved differential-linear distinguisher against ChaCha. To do so, we propose a new way to approach the derivation of linear approximations by viewing the algorithm in terms of simpler subrounds. Using this idea we show that it is possible to derive almost all linear approximations from previous works from just 3 simple rules. Furthermore, we show that with one extra rule it is possible to improve the linear approximations proposed by Coutinho and Souza at Eurocrypt 2021. b) We propose a technique called Bidirectional Linear Expansions (BLE) to improve attacks against Salsa. While previous works only considered linear expansions moving forward into the rounds, BLE explores the expansion of a single bit in both forward and backward directions. Applying BLE, we propose the first differential-linear distinguishers ranging 7 and 8 rounds of Salsa and we improve PNB key-recovery attacks against 8 rounds of Salsa. c) Using all the knowledge acquired studying the cryptanalysis of these ciphers, we propose some modifications in order to provide better diffusion per round and higher resistance to cryptanalysis, leading to a new stream cipher named Forró. We show that Forró has higher security margin, this allows us to reduce the total number of rounds while maintaining the security level, thus creating a faster cipher in many platforms, specially in constrained devices. d) Finally, we developed CryptDances, a new tool for the cryptanalysis of Salsa, ChaCha, and Forró designed to be used in high performance environments with several GPUs. With CryptDances it is possible to compute differential correlations, to derive new linear approximations for ChaCha automatically, to automate the computation of the complexity of PNB attacks, among other features. We make CryptDances available for the community at https://github.com/MurCoutinho/cryptDances.
2022
ASIACRYPT
Linear-map Vector Commitments and their Practical Applications
Vector commitments (VC) are a cryptographic primitive that allow one to commit to a vector and then “open” some of its positions efficiently. Vector commitments are increasingly recognized as a central tool to scale highly decentralized networks of large size and whose content is dynamic. In this work, we examine the demands on the properties that an ideal vector commitment should satisfy in the light of the emerging plethora of practical applications and propose new constructions that improve the state-of-the-art in several dimensions and offer new tradeoffs. We also propose a unifying framework that captures several constructions and show how to generically achieve some properties from more basic ones.
2022
ASIACRYPT
Log-$\mathcal{S}$-unit lattices using Explicit Stickelberger Generators to solve Approx Ideal-SVP
In 2020, Bernard and Roux-Langlois introduced the Twisted-PHS algorithm to solve Approx-SVP for ideal lattices on any number field, based on the PHS algorithm by Pellet-Mary, Hanrot and Stehlé. They performed experiments for prime conductors cyclotomic fields of degrees at most 70, one of the main bottlenecks being the computation of a log-$\mathcal{S}$-unit lattice which requires subexponential time. Our main contribution is to extend these experiments to cyclotomic fields of degree up to 210 for most conductors $m$. Building upon new results from Bernard and Kučera on the Stickelberger ideal, we use explicit generators to construct full-rank log-$\mathcal{S}$-unit sublattices fulfilling the role of approximating the full Twisted-PHS lattice. In our best approximate regime, our results show that the Twisted-PHS algorithm outperforms, over our experimental range, the CDW algorithm by Cramer, Ducas and Wesolowski, and sometimes beats its asymptotic volumetric lower bound. Additionally, we use these explicit Stickelberger generators to remove almost all quantum steps in the CDW algorithm, under the mild restriction that the plus part of the class number verifies $h^+_m\leq O(\sqrt{m})$.
2022
ASIACRYPT
Memory-Tight Multi-Challenge Security of Public-Key Encryption
We give the first examples of public-key encryption schemes which can be proven to achieve multi-challenge, multi-user CCA security via reductions that are tight in time, advantage, and memory. Our constructions are obtained by applying the KEM-DEM paradigm to variants of Hashed ElGamal and the Fujisaki-Okamoto transformation that are augmented by adding uniformly random strings to their ciphertexts. The reductions carefully combine recent proof techniques introduced by Bhattacharyya'20 and Ghoshal-Ghosal-Jaeger-Tessaro'22. Our proofs for the augmented ECIES version of Hashed-ElGamal make use of a new computational Diffie-Hellman assumption wherein the adversary is given access to a pairing to a random group, which we believe may be of independent interest.
2022
ASIACRYPT
Mind the TWEAKEY Schedule: Cryptanalysis on SKINNYe-64-256
Designing symmetric ciphers for particular applications becomes a hot topic. At EUROCRYPT 2020, Naito, Sasaki and Sugawara invented the threshold implementation friendly cipher SKINNYe-64-256 to meet the requirement of the authenticated encryption PFB_Plus. Soon, Thomas Peyrin pointed out that SKINNYe-64-256 may lose the security expectation due the new tweakey schedule. Although the security issue of SKINNYe-64-256 is still unclear, Naito et al. decided to introduce SKINNYe-64-256 v2 as a response. In this paper, we give a formal cryptanalysis on the new tweakey schedule of SKINNYe-64-256 and discover unexpected differential cancellations in the tweakey schedule. For example, we find the number of cancellations can be up to 8 within 30 consecutive rounds, which is significantly larger than the expected 3 cancellations. This property is derived by the analysis of the updated functions (LFSRs) of the tweakey via linear algebra. Moreover, we take our new discoveries into rectangle, MITM and impossible differential attacks, and adapt the corresponding automatic tools with new constraints from our discoveries. Finally, we find a 41-round related-tweakey rectangle attack on SKINNYe-64-256 and leave a security margin of 3 rounds only. As STK accepts arbitrary tweakey size, but SKINNY and SKINNYe-64-256 v2 only support up to 4n tweakey size. We introduce a new design of tweakey schedule for SKINNY-64 to further extend the supported tweakey size. We give a formal proof that our new tweakey schedule inherits the security requirement of STK and SKINNY.
2022
ASIACRYPT
Multi-Client Functional Encryption with Fine-Grained Access Control
Multi-Client Functional Encryption (\MCFE) and Multi-Input Functional Encryption (\MIFE) are very interesting extensions of Functional Encryption for practical purpose. They allow to compute joint function over data from multiple parties. Both primitives are aimed at applications in multi-user settings where decryption can be correctly output for users with appropriate functional decryption keys only. While the definitions for a single user or multiple users were quite general and can be realized for general classes of functions as expressive as Turing machines or all circuits, efficient schemes have been proposed so far for concrete classes of functions: either only for access control, \emph{i.e.} the identity function under some conditions, or linear/quadratic functions under no condition. In this paper, we target classes of functions that explicitly combine some evaluation functions independent of the decrypting user under the condition of some access control. More precisely, we introduce a framework for \MCFE with fine-grained access control and propose constructions for both single-client and multi-client settings, for inner-product evaluation and access control via Linear Secret Sharing Schemes (\textsf{LSSS}), with selective and adaptive security. The only known work that combines functional encryption in multi-user setting with access control was proposed by Abdalla \emph{et al.} (Asiacrypt '20), which relies on a generic transformation from the single-client schemes to obtain $\MIFE$ schemes that suffer a quadratic factor of $n$ (where $n$ denotes the number of clients) in the ciphertext size. We follow a different path, via $\MCFE$: we present a \emph{duplicate-and-compress} technique to transform the single-client scheme and obtain a \MCFE with fine-grained access control scheme with only a linear factor of $n$ in the ciphertext size. Our final scheme thus outperforms the Abdalla \emph{et al.}'s scheme by a factor $n$, as one can obtain \MIFE from \MCFE by making all the labels in \MCFE a fixed public constant. The concrete constructions are secure under the $\SXDH$ assumption, in the random oracle model for the \MCFE scheme, but in the standard model for the \MIFE improvement.
2022
ASIACRYPT
Multi-User Security of the Sum of Truncated Random Permutations
For several decades, constructing pseudorandom functions from pseudorandom permutations, so-called Luby-Rackoff backward construction, has been a popular cryptographic problem. Two methods are well-known and comprehensively studied for this problem: summing two random permutations and truncating partial bits of the output from a random permutation. In this paper, by combining both summation and truncation, we propose new Luby-Rackoff backward constructions, dubbed SaT1 and SaT2, respectively. SaT2 is obtained by partially truncating output bits from the sum of two independent random permutations, and SaT1 is its single permutation-based variant using domain separation. The distinguishing advantage against SaT1 and SaT2 is upper bounded by O(\sqrt{\mu q_max}/2^{n-0.5m}) and O({\sqrt{\mu}q_max^1.5}/2^{2n-0.5m}), respectively, in the multi-user setting, where n is the size of the underlying permutation, m is the output size of the construction, \mu is the number of users, and q_max is the maximum number of queries per user. We also prove the distinguishing advantage against a variant of XORP[3]~(studied by Bhattacharya and Nandi at Asiacrypt 2021) using independent permutations, dubbed SoP3-2, is upper bounded by O(\sqrt{\mu} q_max^2}/2^{2.5n})$. In the multi-user setting with \mu = O(2^{n-m}), a truncated random permutation provides only the birthday bound security, while SaT1 and SaT2 are fully secure, i.e., allowing O(2^n) queries for each user. It is the same security level as XORP[3] using three permutation calls, while SaT1 and SaT2 need only two permutation calls.
2022
ASIACRYPT
New Algorithms and Analyses for Sum-Preserving Encryption
We continue the study of sum-preserving encryption schemes, in which the plaintext and ciphertext are both integer vectors with the same sum. Such encryption schemes were recently constructed and analyzed by Tajik, Gunasekaran, Dutta, Ellia, Bobba, Rosulek, Wright, and Feng (NDSS 2019) in the context of image encryption. Our first main result is to prove a mixing-time bound for the construction given by Tajik et al. using path coupling. We then provide new sum-preserving encryption schemes by describing two practical ways to rank and unrank the values involved in sum-preserving encryption, which can then be combined with the rank-encipher-unrank technique from format-preserving encryption. Finally, we compare the efficiency of the Tajik et al. construction and our new ranking constructions based on performance tests we conducted on prototype implementations.
2022
ASIACRYPT
Non-interactive Mimblewimble transactions, revisited
Mimblewimble is a cryptocurrency protocol that promises to overcome notorious blockchain scalability issues and provides user privacy. For a long time its wider adoption has been hindered by the lack of non-interactive transactions, that is, payments for which only the sender needs to be online. Yu proposed a way of adding non-interactive transactions to stealth addresses to Mimblewimble, but this turned out to be flawed. Building on Yu and integrating ideas from Burkett, we give a fixed scheme and provide a rigorous security analysis strenghtening the previous security model from Eurocrypt'19. Our protocol is considered for implementation by MimbleWimbleCoin and a variant is now deployed as MimbleWimble Extension Blocks (MWEB) in Litecoin.
2022
ASIACRYPT
Non-Interactive Secure Computation of Inner-Product from LPN and LWE
We put forth a new cryptographic primitive for securely computing inner-products in a scalable, non-interactive fashion: any party can broadcast a public (computationally hiding) encoding of its input, and store a secret state. Given their secret state and the other party's public encoding, any pair of parties can non-interactively compute additive shares of the inner-product between the encoded vectors. We give constructions of this primitive from a common template, which can be instantiated under either the LPN (with non-negligible correctness error) or the LWE (with negligible correctness error) assumptions. Our construction uses a novel twist on the standard non-interactive key exchange based on the Alekhnovich cryptosystem, which upgrades it to a non-interactive inner product protocol almost for free. In addition to being non-interactive, our constructions have linear communication (with constants smaller than all known alternatives) and small computation: using LPN or LWE with quasi-cyclic codes, we estimate that encoding a length-2^20 vector over a 32-bit field takes less that 2s on a standard laptop; decoding amounts to a single cheap inner-product. We show how to remove the non-negligible error in our LPN instantiation using a one-time, logarithmic-communication preprocessing. Eventually, we show to to upgrade its security to the malicious model using new sublinear-communication zero-knowledge proofs for low-noise LPN samples, which might be of independent interest.
2022
ASIACRYPT
Non-Interactive Zero-Knowledge Proofs to Multiple Verifiers
In this paper, we study zero-knowledge (ZK) proofs for circuit satisfiability that can prove to $n$ verifiers at a time efficiently. The proofs are secure against the collusion of a prover and a subset of $t$ verifiers. We refer to such ZK proofs as multi-verifier zero-knowledge (MVZK) proofs and focus on the case that a majority of verifiers are honest (i.e., $t<n/2$). We construct efficient MVZK protocols in the random oracle model where the prover sends one message to each verifier, while the verifiers only exchange one round of messages. When the threshold of corrupted verifiers $t<n/2$, the prover sends $1/2+o(1)$ field elements per multiplication gate to every verifier; when $t<n(1/2-\epsilon)$ for some constant $0<\epsilon<1/2$, we can further reduce the communication to $O(1/n)$ field elements per multiplication gate per verifier. Our MVZK protocols demonstrate particularly high scalability: the proofs are streamable and only require a memory proportional to what is needed to evaluate the circuit in the clear.
2022
ASIACRYPT
Nonmalleable Digital Lockers and Robust Fuzzy Extractors in the Plain Model
We give the first constructions in the plain model of 1) nonmalleable digital lockers (Canetti and Varia, TCC 2009) and 2) robust fuzzy extractors (Boyen et al., Eurocrypt 2005) that secure sources with entropy below 1/2 of their length. Constructions were previously only known for both primitives assuming random oracles or a common reference string (CRS). We define a new primitive called a nonmalleable point function obfuscation with associated data. The associated data is public but protected from all tampering. We construct a digital locker using a similar paradigm. Our construction achieves nonmalleability over the output point by placing a CRS into the associated data and using an appropriate non-interactive zero-knowledge proof. Tampering is protected against the input point over low-degree polynomials and over any tampering to the output point and associated data. Our constructions achieve virtual black box security. These constructions are then used to create robust fuzzy extractors that can support low-entropy sources in the plain model. By using the geometric structure of a syndrome secure sketch (Dodis et al., SIAM Journal on Computing 2008), the adversary's tampering function can always be expressed as a low-degree polynomial; thus, the protection provided by the constructed nonmalleable objects suffices.
2022
ASIACRYPT
Nostradamus goes Quantum
In the Nostradamus attack, introduced by Kelsey and Kohno (Eurocrypt 2006), the adversary has to commit to a hash value y of an iterated hash function H such that, when later given a message prefix P, the adversary is able to find a suitable "suffix explanation" S with H(P||S)=y. Kelsey and Kohno show a herding attack with $2^{2n/3}$ evaluations of the compression function of H (with n bits output and state), locating the attack between preimage attacks and collision search in terms of complexity. Here we investigate the security of Nostradamus attacks for quantum adversaries. We present a quantum herding algorithm for the Nostradamus problem making approximately $\sqrt[3]{n}\cdot 2^{3n/7}$ compression function evaluations, significantly improving over the classical bound. We also prove that quantum herding attacks cannot do better than $2^{3n/7}$ evaluations for random compression functions, showing that our algorithm is (essentially) optimal. We also discuss a slightly less tight bound of roughly $2^{3n/7-s}$ for general Nostradamus attacks against random compression functions, where s is the maximal block length of the adversarially chosen suffix S.
2022
ASIACRYPT
On Module Unique-SVP and NTRU
The NTRU problem can be viewed as an instance of finding a short non-zero vector in a lattice, under the promise that it contains an exceptionally short vector. Further, the lattice under scope has the structure of a rank-2 module over the ring of integers of a number field. Let us refer to this problem as the module unique Shortest Vector Problem,or mod-uSVP for short. We exhibit two reductions that together provide evidence the NTRU problem is not just a particular case of mod-uSVP, but representative of it from a computational perspective. First, we reduce worst-case mod-uSVP to worst-case NTRU. For this, we rely on an oracle for id-SVP, the problem of finding short non-zero vectors in ideal lattices. Using the worst-case id-SVP to worst-case NTRU reduction from Pellet-Mary and Stehlé [ASIACRYPT'21],this shows that worst-case NTRU is equivalent to worst-case mod-uSVP. Second, we give a random self-reduction for mod-uSVP. We put forward a distribution D over mod-uSVP instances such that solving mod-uSVP with a non-negligible probability for samples from D allows to solve mod-uSVP in the worst-case. With the first result, this gives a reduction from worst-case mod-uSVP to an average-case version of NTRU where the NTRU instance distribution is inherited from D. This worst-case to average-case reduction requires an oracle for id-SVP.
2022
ASIACRYPT
On Rejection Sampling in Lyubashevsky's Signature Scheme
Lyubashevsky’s signatures are based on the Fiat-Shamir with aborts paradigm, whose central ingredient is the use of rejection sampling to transform secret-dependent signature samples into samples from (or close to) a secret-independent target distribution. Several choices for the underlying distributions and for the rejection sampling strategy can be considered. In this work, we study Lyubashevsky’s signatures through the lens of rejection sampling, and aim to minimize signature size given signing runtime requirements. Several of our results concern rejection sampling itself and could have other applications. We prove lower bounds for compactness of signatures given signing run- time requirements, and for expected runtime of perfect rejection sampling strategies. We also propose a Rényi-divergence-based analysis of Lyuba- shevsky’s signatures which allows for larger deviations from the target distribution, and show hyperball uniforms to be a good choice of distri- butions: they asymptotically reach our compactness lower bounds and offer interesting features for practical deployment. Finally, we propose a different rejection sampling strategy which circumvents the expected runtime lower bound and provides a worst-case runtime guarantee.
2022
ASIACRYPT
On Secure Ratcheting with Immediate Decryption
Ratcheting protocols let parties securely exchange messages in environments in which state exposure attacks are anticipated. While, unavoidably, some promises on confidentiality and authenticity cannot be upheld once the adversary obtains a copy of a party's state, ratcheting protocols aim at confining the impact of state exposures as much as possible. In particular, such protocols provide forward security (after state exposure, past messages remain secure) and post-compromise security (after state exposure, participants auto-heal and regain security). Ratcheting protocols serve as core components in most modern instant messaging apps, with billions of users per day. Most instances, including Signal, guarantee immediate decryption (ID): Receivers recover and deliver the messages wrapped in ciphertexts immediately when they become available, even if ciphertexts arrive out-of-order and preceding ciphertexts are still missing. This ensures the continuation of sessions in unreliable communication networks, ultimately contributing to a satisfactory user experience. While initial academic treatments consider ratcheting protocols without ID, Alwen et al (EC'19) propose the first ID-aware security model, together with a provably secure construction. Unfortunately, as we note, in their protocol a receiver state exposure allows for the decryption of all prior undelivered ciphertexts. As a consequence, from an adversary's point of view, intentionally preventing the delivery of a fraction of the ciphertexts of a conversation, and corrupting the receiver (days) later, allows for correctly decrypting all suppressed ciphertexts. The same attack works against Signal. We argue that the level of (forward-)security realized by the protocol of Alwen et al, and mandated by their security model, is considerably lower than both intuitively expected and technically possible. The main contributions of our work are thus a careful revisit of the security notions for ratcheted communication in the ID setting, together with a provably secure proof-of-concept construction. One novel component of our model is that it reflects the progression of physical time. This allows for formally requiring that (undelivered) ciphertexts automatically expire after a configurable amount of time.
2022
ASIACRYPT
On the Field-Based Division Property: Applications to MiMC, Feistel MiMC and GMiMC
Recent practical applications using advanced cryptographic protocols such as multi-party computation (MPC) and zero-knowledge proofs (ZKP) have prompted a range of novel symmetric primitives described over large finite fields, characterized as arithmetization-oriented (AO) ciphers. Such designs, aiming to minimize the number of multiplications over fields, have a high risk of being vulnerable to algebraic attacks, especially to the higher-order differential attack. Thus, it is significant to carefully evaluate the growth of the algebraic degree. However, degree estimation for AO ciphers has been a challenge for cryptanalysts due to the lack of general and accurate methods. In this paper, we extend the division property, a state-of-the-art frame- work for finding the upper bound of the algebraic degree over binary fields, to the scope of F2n, called general monomial prediction. It is a generic method to detect the algebraic degree for AO ciphers, even applicable to Feistel ciphers which have no better bounds than the trivial exponential one. In the general monomial prediction, our idea is to evaluate whether the polynomial representation of a block cipher contains some specific monomials. With a deep investigation of the arithmetical feature, we introduce the propagation rules of monomials for field-based operations, which can be efficiently modeled using the bit-vector theory of SMT. Then the new searching tool for degree estimation can be constructed due to the relationship between the algebraic degree and the exponents of monomials. We apply our new framework to some important AO ciphers, including Feistel MiMC, GMiMC, and MiMC. For Feistel MiMC, we show that the algebraic degree grows significantly slower than the native exponential bound. For the first time, we present a secret-key higher-order differential distinguisher for up to 124 rounds, much better than the 83-round distinguisher for Feistel MiMC permutation proposed at CRYPTO 2020. We also exhibit a full-round zero-sum distinguisher with a data complexity of 2^{251}. Our method can be further extended for the general Feistel structure with more branches and exhibit higher-order differential distinguishers against the practical instance of GMiMC for up to 50 rounds. For MiMC in SP-networks, our results correspond to the exact algebraic degree proved by Bouvier. We also point out that the number of rounds in MiMC specification is not necessary to guarantee the security against the higher-order differential attack for MiMC-like schemes with different exponents. The investigation of different exponents provides some guidance on the cipher design.
2022
ASIACRYPT
Optimising Linear Key Recovery Attacks with Affine Walsh Transform Pruning
Linear cryptanalysis is one of the main families of key-recovery attacks on block ciphers. Several publications have drawn attention towards the possibility of reducing their time complexity using the fast Walsh transform. These previous contributions ignore the structure of the key recovery rounds, which are treated as arbitrary boolean functions. In this paper, we optimise the time and memory complexities of these algorithms by exploiting zeroes in the Walsh spectra of these functions using a novel affine pruning technique for the Walsh Transform. These new optimisation strategies are then showcased with two application examples: an improved attack on the DES and the first known atttack on 29-round PRESENT-128.
2022
ASIACRYPT
Optimizing Rectangle Attacks: A Unified and Generic Framework for Key Recovery
The rectangle attack has shown to be a very powerful form of cryptanalysis against block ciphers. Given a rectangle distinguisher, one expects to mount key recovery attacks as efficiently as possible. In the literature, there have been four algorithms for rectangle key recovery attacks. However, their performance vary from case to case. Besides, numerous are the applications where the attacks lack optimality. In this paper, we investigate the rectangle key recovery in depth and propose a unified and generic key recovery algorithm, which supports any possible attacking parameters. Notably, it not only covers the four previous rectangle key recovery algorithms, but also unveils five types of new attacks which were missed previously. Along with the new key recovery algorithm, we propose a framework for automatically finding the best attacking parameters, with which the time complexity of the rectangle attack will be minimized using the new algorithm. To demonstrate the efficiency of the new key recovery algorithm, we apply it to Serpent, CRAFT, SKINNY and Deoxys-BC-256 based on existing distinguishers and obtain a series of improved rectangle attacks.
2022
ASIACRYPT
PointProofs, Revisited
Vector commitments allow a user to commit to a vector of length n using a constant-size commitment while being able to locally open the commitment to individual vector coordinates. Importantly, the size of position-wise openings should be independent of the dimension n. Gorbunov, Reyzin, Wee, and Zhang recently proposed PointProofs (CCS 2020), a vector commitment scheme that supports non-interactive aggregation of proofs across multiple commitments, allowing to drastically reduce the cost of block propagation in blockchain smart contracts. Gorbunov et al. provide a security analysis combining the algebraic group model and the random oracle model, under the weak n-bilinear Diffie- Hellman Exponent assumption (n-wBDHE) assumption. In this work, we propose a novel analysis that does not rely on the algebraic group model. We prove the security in the random oracle model under the n- Diffie-Hellman Exponent (n-DHE) assumption, which is implied by the n-wBDHE assumption considered by Gorbunov et al. We further note that we do not modify their scheme (and thus preserve its efficiency) nor introduce any additional assumption. Instead, we prove the security of the scheme as it is via a strictly improved analysis.
2022
ASIACRYPT
Practical Provably Secure Flooding for Blockchains
In recent years, permisionless blockchains have received a lot of attention both from industry and academia, where substantial effort has been spent to develop consensus protocols that are secure under the assumption that less than half (or a third) of a given resource (e.g., stake or computing power) is controlled by corrupted parties. The security proofs of these consensus protocols usually assume the availability of a network functionality guaranteeing that a block sent by an honest party is received by all honest parties within some bounded time. To obtain an overall protocol that is secure under the same corruption assumption, it is therefore necessary to combine the consensus protocol with a network protocol that achieves this property under that assumption. In practice, however, the underlying network is typically implemented by flooding protocols that are not proven to be secure in the setting where a fraction of the considered total weight can be corrupted. This has led to many so-called eclipse attacks on existing protocols and tailor-made fixes against specific attacks. To close this apparent gap, we present the first practical flooding protocol that provably delivers sent messages to all honest parties after a logarithmic number of steps. We prove security in the setting where all parties are publicly assigned a positive weight and the adversary can corrupt parties accumulating up to a constant fraction of the total weight. This can directly be used in the proof-of-stake setting, but is not limited to it. To prove the security of our protocol, we combine known results about the diameter of Erdős–Rényi graphs with reductions between different types of random graphs. We further show that the efficiency of our protocol is asymptotically optimal. The practicality of our protocol is supported by extensive simulations for different numbers of parties, weight distributions, and corruption strategies. The simulations confirm our theoretical results and show that messages are delivered quickly regardless of the weight distribution, whereas protocols that are oblivious of the parties' weights completely fail if the weights are unevenly distributed. Furthermore, the average message complexity per party of our protocol is within a small constant factor of such a protocol.
2022
ASIACRYPT
Privacy-Preserving Authenticated Key Exchange in the Standard Model
Privacy-Preserving Authenticated Key Exchange (PPAKE) provides protection both for the session keys and the identity information of the involved parties. In this paper, we introduce the concept of robustness into PPAKE. Robustness enables each user to confirm whether itself is the target recipient of the first round message in the protocol. With the help of robustness, a PPAKE protocol can successfully avoid the heavy redundant communications and computations caused by the ambiguity of communicants in the existing PPAKE, especially in broadcast channels. We propose a generic construction of robust PPAKE from key encapsulation mechanism (KEM), digital signature (SIG), message authentication code (MAC), pseudo-random generator (PRG) and symmetric encryption (SE). By instantiating KEM, MAC, PRG from the DDH assumption and SIG from the CDH assumption, we obtain a specific robust PPAKE scheme in the standard model, which enjoys forward security for session keys, explicit authentication and forward privacy for user identities. Thanks to the robustness of our PPAKE, the number of broadcast messages per run and the computational complexity per user are constant, and in particular, independent of the number of users in the system.
2022
ASIACRYPT
Puncturable Key Wrapping and Its Applications
We introduce puncturable key wrapping (PKW), a new cryptographic primitive that supports fine-grained forward security properties in symmetric key hierarchies. We develop syntax and security definitions, along with provably secure constructions for PKW from simpler components (AEAD schemes and puncturable PRFs). We show how PKW can be applied in two distinct scenarios. First, we show how to use PKW to achieve forward security for TLS 1.3 0-RTT session resumption, even when the server's long-term key for generating session tickets gets compromised. This extends and corrects a recent work of Aviram, Gellert, and Jager (Journal of Cryptology, 2021). Second, we show how to use PKW to build a protected file storage system with file shredding, wherein a client can outsource encrypted files to a potentially malicious or corrupted cloud server whilst achieving strong forward-security guarantees, relying only on local key updates.
2022
ASIACRYPT
Random Sources in Private Computation
We consider multi-party information-theoretic private computation. Such computation inherently requires the use of local randomness by the parties, and the question of minimizing the total number of random bits used for given private computations has received considerable attention in the literature. In this work we are interested in another question: given a private computation, we ask how many of the players need to have access to a random source, and how many of them can be deterministic parties. We are further interested in the possible interplay between the number of random sources in the system and the total number of random bits necessary for the computation. We give a number of results. We first show that, perhaps surprisingly, t players (rather than t+1) with access to a random source are sufficient for the information-theoretic t-private computation of any deterministic functionality over n players for any t<n/2; by a result of (Kushilevitz and Mansour, PODC'96), this is best possible. This means that, counter intuitively, while private computation is impossible without randomness, it is possible to have a private computation even when the adversary can control *all* parties who can toss coins (and therefore sees all random coins). For randomized functionalities we show that t+1 random sources are necessary (and sufficient). We then turn to the question of the possible interplay between the number of random sources and the necessary number of random bits. Since for only very few settings in private computation meaningful bounds on the number of necessary random bits are known, we consider the AND function, for which some such bounds are known. We give a new protocol to 1-privately compute the n-player AND function, which uses a single random source and 6 random bits tossed by that source. This improves, upon the currently best known results (Kushilevitz et al., TCC 2019), at the same time the number of sources and the number of random bits ((Kushilevitz et al., TCC 2019) gives a 2-source, 8-bits protocol). This result gives maybe some evidence that for 1-privacy, using the minimum necessary number of sources one can also achieve the necessary minimum number of random bits. We believe however that our protocol is of independent interest for the study of randomness in private computation.
2022
ASIACRYPT
Recovering the tight security proof of SPHINCS+
In 2020, Kudinov, Kiktenko, and Fedorov pointed out a flaw in the tight security proof of the SPHINCS+ construction. This work gives a new tight security proof for SPHINCS+. The flaw can be traced back to the security proof for the Winternitz one-time signature scheme (WOTS) used within SPHINCS+. In this work, we give a stand-alone description of the WOTS variant used in SPHINCS+ that we call WOTS-TW. We provide a security proof for WOTS-TW and multi-instance WOTS-TW against non-adaptive chosen message attacks where the adversary only learns the public key after it made its signature query. Afterwards, we show that this is sufficient to give a tight security proof for SPHINCS+. We recover almost the same bound for the security of SPHINCS+, with only a factor w loss compared to the previously claimed bound, where w is the Winternitz parameter that is commonly set to 16. On a more technical level, we introduce new lower bounds on the quantum query complexity for generic attacks against properties of cryptographic hash functions and analyse the constructions of tweakable hash functions used in SPHINCS+ with regard to further security properties.
2022
ASIACRYPT
Revisiting Related-Key Boomerang attacks on AES using computer-aided tool
In recent years, several MILP models were introduced to search automatically for boomerang distinguishers and boomerang attacks on block ciphers. However, they can only be used when the key schedule is linear. Here, a new model is introduced to deal with nonlinear key schedules as it is the case for {\mbox{\tt AES}}. This model is more complex and actually it is too slow for exhaustive search. However, when some hints are added to the solver, it found the current best related-key boomerang attack on {\mbox{\tt AES-192}} with $2^{124}$ time, $2^{124}$ data, and $2^{79.8}$ memory complexities, which is better than the one presented by Biryukov and Khovratovich at ASIACRYPT 2009 with complexities $2^{176}/2^{123}/2^{152}$ respectively. This represents a huge improvement for the time and memory complexity, illustrating the power of MILP in cryptanalysis.
2022
ASIACRYPT
Rotatable Zero Knowledge Sets: Post Compromise Secure Auditable Dictionaries with application to Key Transparency
Recently, the area of Key Transparency (KT) has received a lot of attention, as it allows the service provider to provide auditable and verifiable proofs regarding authenticity of public keys used by various participants. Moreover, it is highly preferable to do it in a privacy-preserving ways, so that users and auditors do not learn anything beyond what is necessary to keep the service provider accountable. Abstractly, the problem of building such systems reduces to constructing so called append-only Zero-Knowledge Sets (aZKS). Unfortunately, none of the previous aZKS constructions adequately addressed the problem of key rotation, which would provide Post-Compromise Security (PCS) in case the server in compromised. In this work we address this concern, and refine an extension of aZKS called Rotatable ZKS (RZKS). In addition to addressing the PCS concern, our notion of RZKS has several other attractive features, such as stronger soundness notion (called extractability), and the ability for a stale communication party to quickly catch up with the current epoch, while ensuring the the server did not erase any of the past data. Of independent interest, we also introduce and build a new primitive called Rotatable Verifiable Random Function (VRF), and show how to build RZKS in a modular fashion from rotatable VRF, ordered accumulators and append-only vector commitment schemes.
2022
ASIACRYPT
Security of Truncated Permutation Without Initial Value
Indifferentiability is a powerful notion in cryptography. If a construction is proven to be indifferentiable from an ideal object, it can under certain assumptions instantiate that ideal object in higher-level constructions. Indifferentiability is a particularly useful model for cryptographic hash functions, and myriad results are known proving that a hash function behaves like a random oracle under the assumption that the underlying primitive (typically a compression function, a block cipher, or a permutation) is random. Recently, advances have been made in proving indifferentiability of one-way functions with fixed input length. One such example is truncation of a permutation. If one evaluates a random permutation on an input value concatenated with a fixed initial value, and truncates the output, one obtains a construction that is indifferentiable from a random function up to a certain bound (Dodis et al., FSE 2009; Choi et al., ASIACRYPT 2019). Security of this construction, however, is in part determined by the length of the initial value; omission of this fixed value yields an insecure construction. In this paper, we reconsider truncation of a permutation, and prove that the construction is indifferentiable from a random oracle, even if this fixed initial value is replaced by a randomized value. This randomized value may be the same for different evaluations of the construction, or freshly generated, up to the discretion of the adversary. The security level is the same as that of truncation with fixed initial value, up to collisions in the randomized value. We show that our construction has immediate implications in the context of parallel variable-length digest generation. In detail, we describe Cascade-MGF, that operates on top of any cryptographic hash function and uses the hash function output as randomized initial value in truncation. We demonstrate that Cascade-MGF compares favorably over earlier parallel variable-length digest generation constructions, namely Counter-MGF and Chained-MGF, in almost all settings.
2022
ASIACRYPT
Short-lived zero-knowledge proofs and signatures
We introduce the short-lived proof, a non-interactive proof of knowledge with a novel feature: after a specified period of time, the proof is no longer convincing. This time-delayed loss of soundness happens "naturally" without further involvement from the prover or any third party. We propose definitions for short-lived proofs as well as the special case of short-lived signatures. We show several practical constructions built using verifiable delay functions (VDFs). The key idea in our approach is to allow any party to forge any proof by executing a large sequential computation. Some constructions achieve a stronger property called reusable forgeability in which one sequential computation allows forging an arbitrary number of proofs of different statements. We also introduces two novel types of VDFs, re-randomizable VDFs and zero-knowledge VDFs, which may be of independent interest. Our constructions for short-lived Sigma-protocols and signatures are practically efficient for provers and verifiers, adding a few hundred bytes of overhead and tens to hundreds of milliseconds of proving/verification time.
2022
ASIACRYPT
SIDH Proof of Knowledge
We show that the soundness proof for the De Feo--Jao--Plût identification scheme (the basis for supersingular isogeny Diffie--Hellman (SIDH) signatures) contains an invalid assumption, and we provide a counterexample for this assumption---thus showing the proof of soundness is invalid. As this proof was repeated in a number of works by various authors, multiple pieces of literature are affected by this result. Due to the importance of being able to prove knowledge of an SIDH key (for example, to prevent adaptive attacks), soundness is a vital property. Surprisingly, the problem of proving knowledge of a specific isogeny turns out to be considerably more difficult than was perhaps anticipated. The main results of this paper are a sigma protocol to prove knowledge of a walk of specified length in a supersingular isogeny graph, and a second one to additionally prove that the isogeny maps some torsion points to some other torsion points (as seen in SIDH public keys). Our scheme also avoids the SIDH identification scheme soundness issue raised by Ghantous, Pintore and Veroni. In particular, our protocol provides a non-interactive way of verifying correctness of SIDH public keys, and related statements, as protection against adaptive attacks. Post-scriptum: Some months after this work was completed and made public, the SIDH assumption was broken in a series of papers by several authors. Hence, in the standard SIDH setting, some of the statements studied here now have trivial polynomial time non-interactive proofs. Nevertheless our first sigma protocol is unaffected by the attacks, and our second protocol may still be useful in present and future variants of SIDH that escape the attacks.
2022
ASIACRYPT
SNACKs: Leveraging Proofs of Sequential Work for Blockchain Light Clients
The success of blockchains has led to ever-growing ledgers that are stored by all participating full nodes. In contrast, light clients only store small amounts of blockchain-related data and rely on the mediation of full nodes when interacting with the ledger. A broader adoption of blockchains calls for protocols that make this interaction trustless. We revisit the design of light-client blockchain protocols from the perspective of classical proof-system theory, and explain the role that proofs of sequential work (PoSWs) can play in it. To this end, we define a new primitive called succinct non-interactive argument of chain knowledge (SNACK), a non-interactive proof system that provides clear security guarantees to a verifier (a light client) even when interacting only with a single dishonest prover (a full node). We show how augmenting any blockchain with any graph-labeling PoSW (GL-PoSW) enables SNACK proofs for this blockchain. We also provide a unified and extended definition of GL-PoSWs covering all existing constructions, and describe two new variants. We then show how SNACKs can be used to construct light-client protocols, and highlight some deficiencies of existing designs, along with mitigations. Finally, we introduce incremental SNACKs which could potentially provide a new approach to light mining.
2022
ASIACRYPT
State Machine Replication under Changing Network Conditions
Protocols for state machine replication (SMR) are typically designed for synchronous or asynchronous networks, with a lower corruption threshold in the latter case. Recent network-agnostic protocols are secure when run in either a synchronous or an asynchronous network. We propose two new constructions of network-agnostic SMR protocols that improve on existing protocols in terms of either the adversarial model or communication complexity: 1. an adaptively secure protocol with optimal corruption thresholds and quadratic amortized communication complexity per transaction; 2. a statically secure protocol with near-optimal corruption thresholds and linear amortized communication complexity per transaction. We further explore SMR protocols run in a network that may change between synchronous and asynchronous arbitrarily often; parties can be uncorrupted (as in the proactive model), and the protocol should remain secure as long as the appropriate corruption thresholds are maintained. We show that purely asynchronous proactive secret sharing is impossible without some form of synchronization between the parties, ruling out a natural approach to proactively secure network-agnostic SMR protocols. Motivated by this negative result, we consider a model where the adversary is limited in the total number of parties it can corrupt over the duration of the protocol and show, in this setting, that our SMR protocols remain secure even under arbitrarily changing network conditions.
2022
ASIACRYPT
Statistical Decoding 2.0: Reducing Decoding to LPN
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decodings at code rates smaller than 0.3. It gives for the first time after 60 years, a better decoding algorithm for a significant range which does not belong to the ISD family.
2022
ASIACRYPT
Stretching Cube Attacks: Improved Methods to Recover Massive Superpolies
Cube attacks exploit the algebraic properties of symmetric ciphers by recovering a special polynomial, the superpoly, and subsequently the secret key. When the algebraic normal forms of the corresponding Boolean functions are not available, the division property based approach allows to recover the exact superpoly in a clever way. However, the computational cost to recover the superpoly becomes prohibitive as the number of rounds of the cipher increases. For example, the nested monomial predictions (NMP) proposed at ASIACRYPT 2021 stuck at round 845 for \trivium. To alleviate the bottleneck of the NMP technique, i.e., the unsolvable model due to the excessive number of monomial trails, we shift our focus to the so-called valuable terms of a specific middle round that contribute to the superpoly. Two new techniques are introduced, namely, Non-zero Bit-based Division Property (NBDP) and Core Monomial Prediction (CMP), both of which result in a simpler MILP model compared to the MILP model of MP. It can be shown that the CMP technique offers a substantial improvement over the monomial prediction technique in terms of computational complexity of recovering valuable terms. Combining the divide-and-conquer strategy with these two new techniques, we catch the valuable terms more effectively and thus avoid wasting computational resources on intermediate terms contributing nothing to the superpoly. As an illustration of the power of our techniques, we apply our framework to \trivium, \grain, \kreyvium and \acorn. As a result, the computational cost of earlier attacks can be significantly reduced and the exact ANFs of the superpolies for 846-, 847- and 848-round \trivium, 192-round \grain, 895-round \kreyvium and 776-round \acorn can be recovered in practical time, even though the superpoly of 848-round \trivium contains over 500 million terms; this corresponds to respectively 3, 1, 1 and 1 rounds more than the previous best results. Moreover, by investigating the internal properties of M\"obius transformation, we show how to perform key recovery using superpolies involving full key bits, which leads to the best key recovery attacks on the targeted ciphers.
2022
ASIACRYPT
Strongly Anonymous Ratcheted Key Exchange
Anonymity is an (abstract) security goal that is especially important to threatened user groups. Therefore, widely deployed communication protocols implement various measures to hide different types of information (i.e., metadata) about their users. Before actually defining anonymity, we consider an attack vector about which targeted user groups can feel concerned: continuous, temporary exposure of their secrets. Examples for this attack vector include intentionally planted viruses on victims' devices, as well as physical access when their users are detained. Ratcheted (or Continuous) Key Exchange (RKE) is a novel class of protocols that increase confidentiality and authenticity guarantees against temporary exposure of user secrets. For this, an RKE regularly renews user secrets such that the damage due to past and future exposures is minimized; this is called Post-Compromise Security and Forward-Secrecy, respectively. With this work, we are the first to leverage the strength of RKE for achieving strong anonymity guarantees under temporary exposure of user secrets. We extend existing definitions for RKE to capture attacks that interrelate ciphertexts, seen on the network, with secrets, exposed from users' devices. Although, at first glance, strong authenticity (and confidentiality) conflicts with strong anonymity, our anonymity definition is as strong as possible without diminishing other goals. We build strongly anonymity-, authenticity-, and confidentiality-preserving RKE and, along the way, develop new tools with applicability beyond our specific use-case: Updatable and Randomizable Signatures as well as Updatable and Randomizable Public Key Encryption. For both new primitives, we build efficient constructions.
2022
ASIACRYPT
SwiftEC: Shallue--van de Woestijne Indifferentiable Function to Elliptic Curves
Hashing arbitrary values to points on an elliptic curve is a required step in many cryptographic constructions, and a number of techniques have been proposed to do so over the years. One of the first ones was due to Shallue and van de Woestijne (ANTS-VII), and it had the interesting property of applying to essentially all elliptic curves over finite fields. It did not, however, have the desirable property of being *indifferentiable from a random oracle* when composed with a random oracle to the base field. Various approaches have since been considered to overcome this limitation, starting with the foundational work of Brier et al. (CRYPTO 2011). For example, if f: F_q→E(F_q) is the Shallue--van de Woestijne (SW) map and H, H' are *two* independent random oracles, we now know that m↦f(H(m))+f(H'(m)) is indifferentiable from a random oracle. Unfortunately, this approach has the drawback of being twice as expensive to compute than the straightforward, but not indifferentiable, m↦f(H(m)). Most other solutions so far have had the same issue: they are at least as costly as two base field exponentiations, whereas plain encoding maps like f cost only one exponentiation. Recently, Koshelev (DCC 2022) provided the first construction of indifferentiable hashing at the cost of one exponentiation, but only for a very specific class of curves (some of those with j-invariant 0), and using techniques that are unlikely to apply more broadly. In this work, we revisit this long-standing open problem, and observe that the SW map actually fits in a one-parameter family (f_u)_{u∈F_q} of encodings, such that for independent random oracles H, H', F: m↦f_{H'(m)}(H(m)) is indifferentiable. Moreover, on a very large class of curves (essentially those that are either of odd order or of order divisible by 4), the one-parameter family admits a rational parametrization, which lets us compute F at almost the same cost as small f, and finally achieve indifferentiable hashing to most curves with a single exponentiation. Our new approach also yields an improved variant of the Elligator Squared technique of Tibouchi (FC 2014) that represents points of arbitrary elliptic curves as close-to-uniform random strings.
2022
ASIACRYPT
Synthesizing Quantum Circuits of AES with Lower T-depth and Less Qubits
The significant progress in the development of quantum computers has made the study of cryptanalysis based on quantum computing an active topic. To accurately estimate the resources required to carry out quantum attacks, the involved quantum algorithms have to be synthesized into quantum circuits with basic quantum gates. In this work, we present several generic synthesis and optimization techniques for circuits implementing the quantum oracles of iterative symmetric-key ciphers that are commonly employed in quantum attacks based on Grover and Simon's algorithms. Firstly, a general structure for implementing the round functions of block ciphers in-place is proposed. Then, we present some novel techniques for synthesizing efficient quantum circuits of linear and non-linear cryptographic building blocks. We apply these techniques to AES and systematically investigate the strategies for depth-width trade-offs. Along the way, we derive a quantum circuit for the AES S-box with provably minimal T-depth based on some new observations on its classical circuit. As a result, the T-depth and width (number of qubits) required for implementing the quantum circuits of AES are significantly reduced. Compared with the circuit proposed in EUROCRYPT 2020, the T-depth is reduced from 60 to 40 without increasing the width or 30 with a slight increase in width. These circuits are fully implemented in Microsoft Q# and the source code is publicly available. Compared with the circuit proposed in ASIACRYPT 2020, the width of one of our circuits is reduced from 512 to 371, and the Toffoli-depth is reduced from 2016 to 1558 at the same time. Actually, we can reduce the width to 270 at the cost of increased depth. Moreover, a full spectrum of depth-width trade-offs is provided, setting new records for the synthesis and optimization of quantum circuits of AES.
2022
ASIACRYPT
The Abe-Okamoto Partially Blind Signature Scheme Revisited
Partially blind signatures, an extension of ordinary blind signatures, are a primitive with wide applications in e-cash and electronic voting. One of the most efficient schemes to date is the one by Abe and Okamoto (CRYPTO 2000), whose underlying idea - the OR-proof technique - has served as the basis for several works. We point out several subtle flaws in the original proof of security, and provide a new detailed and rigorous proof, achieving similar bounds as the original work. We believe our insights on the proof strategy will find useful in the security analyses of other OR-proof-based schemes.
2022
ASIACRYPT
Threshold Linearly Homomorphic Encryption on Z/2^kZ
A threshold public key encryption protocol is a public key system where the private key is distributed among n different servers. It offers high security since no single server is entrusted to perform the decryption in its entirety. It is the core component of many multiparty computation protocols which involves mutually distrusting parties with common goals. It is even more useful when it is homomorphic, which means that public operations on ciphertexts translates on operations on the underlying plaintexts. In particular, Cramer, Damgård and Nielsen at Eurocrypt 2001 provide a new approach to multiparty computation from linearly homomorphic threshold encryption schemes. On the other hand, there has been recent interest in developing multiparty computations modulo 2^k for a certain integer k, that closely match data manipulated by a CPU. Multiparty computation would therefore benefit from an encryption scheme with such a message space that would support a distributed decryption. In this work, we provide the first threshold linearly homomorphic encryption whose message space is Z/2^kZ for any k. It is inspired by Castagnos and Laguillaumie’s encryption scheme from RSA 2015, but works with a class group of discriminant whose factorisation is unknown. Its natural structure à la Elgamal makes it possible to distribute the decryption among servers using linear integer secret sharing, allowing any access structure for the decryption policy. Furthermore its efficiency and its flexibility on the choice of the message space make it a good candidate for applications to multiparty computation.
2022
ASIACRYPT
Towards Case-Optimized Hybrid Homomorphic Encryption -Featuring the Elisabeth Stream Cipher-
Hybrid Homomorphic Encryption (HHE) reduces the amount of computation client-side and bandwidth usage in a Fully Homomorphic Encryption (FHE) framework. HHE requires the usage of specific symmetric schemes that can be evaluated homomorphically efficiently. In this paper, we introduce the paradigm of Group Filter Permutator (GFP) as a generalization of the Improved Filter Permutator paradigm introduced by M ́eaux et al. From this paradigm, we specify Elisabeth , a family of stream cipher and give an instance: Elisabeth-4. After proving the security of this scheme, we provide a Rust implementation of it and ensure its performance is comparable to state-of-the-art HHE. The true strength of Elisabeth lies in the available operations server-side: while the best HHE applications were limited to a few multiplications server-side, we used data sent through Elisabeth-4 to homomorphically evaluate a neural network inference. Finally, we discuss the improvement and loss between the HHE and the FHE framework and give ideas to build more efficient schemes from the Elisabeth family.
2022
ASIACRYPT
Towards Practical Topology-Hiding Computation
\par Topology-hiding computation (THC) enables $n$ parties to perform a secure multiparty computation (MPC) protocol in an incomplete communication graph while keeping the communication graph hidden. The work of Akavia et al. (CRYPTO 2017 and JoC 2020) shown that THC is feasible for any graph. In this work, we focus on the efficiency of THC and give improvements for various tasks including broadcast, sum and general computation. We mainly consider THC on undirected cycles, but we also give two results for THC on general graphs. All of our results are derived in the presence of a passive adversary statically corrupting any number of parties. \par In the undirected cycles, the state-of-the-art topology-hiding broadcast (THB) protocol is the Akavia-Moran (AM) protocol of Akavia et al. (EUROCRYPT 2017). We give an optimization for the AM protocol such that the communication cost of broadcasting $O(\kappa)$ bits is reduced from $O(n^2\kappa^2)$ bits to $O(n^2\kappa)$ bits. We also consider the sum and general computation functionalities. Previous to our work, the only THC protocols realizing the sum and general computation functionalities are constructed by using THB to simulate point-to-point channels in an MPC protocol realizing the sum and general computation functionalities, respectively. By allowing the parties to know the exact value of the number of the parties (the AM protocol and our optimization only assume the parties know an upper bound of the number of the parties), we can derive more efficient THC protocols realizing these two functionalities. As a result, comparing with previous works, we reduce the communication cost by a factor of $O(n\kappa)$ for both the sum and general computation functionalities. \par As we have mentioned, we also get two results for THC on general graphs. The state-of-the-art THB protocol for general graphs is the Akavia-LaVigne-Moran (ALM) protocol of Akavia et al. (CRYPTO 2017 and JoC 2020). Our result is that our optimization for the AM protocol also applies to the ALM protocol and can reduce its communication cost by a factor of $O(\kappa)$. Moreover, we optimize the fully-homomorphic encryption (FHE) based GTHC protocol of LaVigne et al. (TCC 2018) and reduce its communication cost from $O(n^8\kappa^2)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys to $O(n^6\kappa)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys.
2022
ASIACRYPT
Towards Tight Security Bounds for OMAC, XCBC and TMAC
OMAC --- a single-keyed variant of CBC-MAC by Iwata and Kurosawa --- is a widely used and standardized (NIST FIPS 800-38B, ISO/IEC 29167-10:2017) message authentication code (MAC) algorithm. The best security bound for OMAC is due to Nandi who proved that OMAC's pseudorandom function (PRF) advantage is upper bounded by $ O(q^2\ell/2^n) $, where $ q $, $ \ell $, and $ n $, denote the number of queries, maximum permissible query length (in terms of $ n $-bit blocks), and block size of the underlying block cipher, respectively. In contrast, there is no attack with matching lower bound. Indeed, the best known attack on OMAC is the folklore birthday attack achieving a lower bound of $ \Omega(q^2/2^n) $. In this work, we close this gap for a large range of message lengths. Specifically, we show that OMAC's PRF security is upper bounded by $ O(q^2/2^n + q\ell^2/2^n)$. In practical terms, this means that for a $ 128 $-bit block cipher, and message lengths up to $ 64 $ Gigabyte, OMAC can process up to $ 2^{64} $ messages before rekeying (same as the birthday bound). In comparison, the previous bound only allows $ 2^{48} $ messages. As a side-effect of our proof technique, we also derive similar tight security bounds for XCBC (by Black and Rogaway) and TMAC (by Kurosawa and Iwata). As a direct consequence of this work, we have established tight security bounds (in a wide range of $\ell$) for all the CBC-MAC variants, except for the original CBC-MAC.
2022
ASIACRYPT
Traceable Receipt-Free Encryption
CCA-like game-based security definitions capture confidentiality by asking an adversary to distinguish between honestly computed encryptions of chosen plaintexts. In the context of voting systems, such guarantees have been shown to be sufficient to prove ballot privacy (Asiacrypt'12). In this paper, we observe that they fall short when one seeks to obtain receipt-freeness, that is, when corrupted voters who submit chosen ciphertexts encrypting their vote must be prevented from proving how they voted to a third party. Since no known encryption security notion can lead to a receipt-free ballot submission process, we address this challenge by proposing a novel publicly verifiable encryption primitive coined Traceable Receipt-free Encryption (TREnc) and a new notion of traceable CCA security filling the definitional gap underlined above. We propose two TREnc instances, one generic achieving stronger guarantees for the purpose of relating it to existing building blocks, and a dedicated one based on SXDH. Both support the encryption of group elements in the standard model, while previously proposed encryption schemes aiming at offering receipt-freeness only support a polynomial-size message space, or security in the generic group model. Eventually, we demonstrate how a TREnc can be used to build receipt-free protocols, by following a standard blueprint.
2022
ASIACRYPT
Triply Adaptive UC NIZK
Non-interactive zero knowledge (NIZK) enables a prover, to prove that a statement in an NP language is valid, given an accepting witness, without leaking any information about the witness. We study universally composable (UC) NIZKs which are secure against adaptive corruption of parties and provides adaptive soundness, i.e. the statement is adaptively chosen by a malicious prover based on the setup string distribution. The only known adaptively secure NIZK protocols either fail to achieve full adaptive soundness or rely on non-falsifiable knowledge assumptions. We construct the first NIZK protocols which are triply adaptive - secure against adaptive corruptions, guarantees adaptive soundness and satisfies adaptive zero knowledge, from falsifiable assumptions. We do so using the following methodology: - We define a new ideal functionality, denoted as F_NICOM, for non-interactive commitment schemes in the UC framework. - We define and construct Sigma protocols which satisfy triply adaptive security in the F_NICOM model. - By relying on correlation intractable (CI) hash functions, we compile a triply adaptively secure Sigma protocol (in F_NICOM model) into a triply adaptive UC-NIZK argument in the F_NICOM+common reference string (crs) model. In addition to CI hash functions, our compiler requires standard cryptographic primitives - non-interactive equivocal commitments and public key encryption with obliviously samplable ciphertexts, for implementing F_NICOM in the crs model. We instantiate our framework by demonstrating that most statically secure Sigma protocols can be proven to be triply adaptively secure in the F_NICOM model, hence, bridging the gap between static and adaptive security for NIZKs. Our NIZK arguments can be concretely based on assumptions, like LWE, or LPN and DDH.
2022
ASIACRYPT
Unconditionally Secure NIZK in the Fine-Grained Setting
Non-interactive zero-knowledge (NIZK) proof systems are often constructed based on cryptographic assumptions. In this paper, we propose the first unconditionally secure NIZK system in the AC0-fine-grained setting. More precisely, our NIZK system has perfect soundness for all adversaries and unconditional zero-knowledge for AC0 adversaries, namely, an AC0 adversary can only break the zero-knowledge property with negligible probability unconditionally. At the core of our construction is an OR-proof system for satisfiability of 1 out of polynomial many statements.
2022
ASIACRYPT
Universal Ring Signatures in the Standard Model
Ring signatures allow a user to sign messages on behalf of an \emph{ad hoc} set of users - a ring - while hiding her identity. The original motivation for ring signatures was whistleblowing [Rivest et al. ASIACRYPT'01]: a high government employee can anonymously leak sensitive information while certifying that it comes from a reliable source, namely by signing the leak. However, essentially all known ring signature schemes require the members of the ring to publish a structured verification key that is compatible with the scheme. This creates somewhat of a paradox since, if a user does not want to be framed for whistleblowing, they will stay clear of signature schemes that support ring signatures. In this work, we formalize the concept of universal ring signatures (URS). A URS enables a user to issue a ring signature with respect to a ring of users, independently of the signature schemes they are using. In particular, none of the verification keys in the ring need to come from the same scheme. Thus, in principle, URS presents an effective solution for whistleblowing. The main goal of this work is to study the feasibility of URS, especially in the standard model (i.e. no random oracles or common reference strings). We present several constructions of URS, offering different trade-offs between assumptions required, the level of security achieved, and the size of signatures: \begin{itemize} \item Our first construction is based on superpolynomial hardness assumptions of standard primitives. It achieves compact signatures. That means the size of a signature depends only logarithmically on the size of the ring and on the number of signature schemes involved. \item We then proceed to study the feasibility of constructing URS from standard polynomially-hard assumptions only. We construct a non-compact URS from witness encryption and additional standard assumptions. \item Finally, we show how to modify the non-compact construction into a compact one by relying on indistinguishability obfuscation. \end{itemize}
2022
ASIACRYPT
Witness Encryption and Null-IO from Evasive LWE
Witness encryption (WE) allows us to use an arbitrary NP statement $x$ as a public key to encrypt a message, and the witness $w$ serves as a decryption key. Security ensures that, when the statement $x$ is false, the encrypted message remains computationally hidden. WE appears to be significantly weaker than indistinguishability obfuscation (iO). Indeed, WE is closely related to a highly restricted form of iO that only guarantees security for null circuits (null iO). However, all current approaches towards constructing WE under nice assumptions go through iO. Such constructions are quite complex and are unlikely to lead to practically instantiable schemes. In this work, we revisit a very simple WE and null iO candidate of Chen, Vaikuntanathan and Wee (CRYPTO 2018). We show how to prove its security under a nice and easy-to-state assumption that we refer to as {\em evasive LWE} following Wee (EUROCRYPT 2022). Roughly speaking, the evasive LWE assumption says the following: assume we have some joint distributions over matrices $\mathbf{P}$, $\mathbf{S}$ and auxiliary information $\aux$ such that $$({\bS\bB + \bE},{\bS \bP + \bE'}, \aux) \approx_c ({\bU},{\bU'}, \aux),$$ for a uniformly random (and secret) matrix $\mathbf{B}$, where $\mathbf{U}, \mathbf{U}'$ are uniformly random matrices, and $\mathbf{E},\mathbf{E}'$ are chosen from the LWE error distribution with appropriate parameters. Then it must also be the case that: $$({\bS\bB + \bE}, \bB^{-1}(\bP),\aux) \approx_c (\bU, \bB^{-1}(\bP),\aux).$$ Essentially the above says that given ${\bS\bB + \bE}$, getting the additional component $\bB^{-1}(\bP)$ is no more useful than just getting the product $({\bS\bB + \bE})\cdot \bB^{-1}(\bP) \approx \bS \bP + \bE'$.
2022
ASIACRYPT
YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model
Achieving adaptive (or proactive) security in cryptographic protocols is notoriously difficult due to the adversary's power to dynamically corrupt parties as the execution progresses. Inspired by the work of Benhamouda \textit{et al.} in TCC 2020, Gentry \textit{et al.} in CRYPTO 2021 introduced the YOSO (You Only Speak Once) model for constructing adaptively (or proactively) secure protocols in massively distributed settings (\textit{e.g.} blockchains). In this model, instead of having all parties execute an entire protocol, smaller \emph{anonymous committees} are randomly chosen to execute each individual round of the protocol. After playing their role, parties encrypt protocol messages towards the the next anonymous committee and erase their internal state before publishing their ciphertexts. However, a big challenge remains in realizing YOSO protocols: \emph{efficiently} encrypting messages towards anonymous parties selected at random without learning their identities, while proving the encrypted messages are valid with respect to the protocol. In particular, the protocols of Benhamouda \textit{et al.} and of Gentry \textit{et al.} require showing ciphertexts contain valid shares of secret states. We propose concretely efficient methods for encrypting a protocol's secret state towards a random anonymous committee. We start by proposing a very simple and efficient scheme for encrypting messages towards randomly and anonymously selected parties. We then show constructions of publicly verifiable secret (re-)sharing (PVSS) schemes with concretely efficient proofs of (re-)share validity that can be generically instantiated from encryption schemes with certain linear homomorphic properties. In addition, we introduce a new PVSS with proof of sharing consisting of just two field elements, which as far as we know is the first achieving this, and may be of independent interest. Finally, we show that our PVSS schemes can be efficiently realized from our encyption scheme.
2022
ASIACRYPT
Zero-Knowledge Protocols for the Subset Sum Problem from MPC-in-the-Head with Rejection
We propose (honest verifier) zero-knowledge arguments for the modular subset sum problem. Previous combinatorial approaches, notably one due to Shamir, yield arguments with cubic communication complexity (in the security parameter). More recent methods, based on the MPC-in-the-head technique, also produce arguments with cubic communication complexity. We improve this approach by using a secret-sharing over small integers (rather than modulo q) to reduce the size of the arguments and remove the prime modulus restriction. Since this sharing may reveal information on the secret subset, we introduce the idea of rejection to the MPC-in-the-head paradigm. Special care has to be taken to balance completeness and soundness and preserve zero-knowledge of our arguments. We combine this idea with two techniques to prove that the secret vector (which selects the subset) is well made of binary coordinates. Our new protocols achieve an asymptotic improvement by producing arguments of quadratic size. This improvement is also practical: for a 256-bit modulus q, the best variant of our protocols yields 13KB arguments while previous proposals gave 1180KB arguments, for the best general protocol, and 122KB, for the best protocol restricted to prime modulus. Our techniques can also be applied to vectorial variants of the subset sum problem and in particular the inhomogeneous short integer solution (ISIS) problem for which they provide an efficient alternative to state-of-the-art protocols when the underlying ring is not small and NTT-friendly. We also show the application of our protocol to build efficient zero-knowledge arguments of plaintext and/or key knowledge in the context of fully-homomorphic encryption. When applied to the TFHE scheme, the obtained arguments are more than 20 times smaller than those obtained with previous protocols. Eventually, we use our technique to construct an efficient digital signature scheme based on a pseudo-random function due to Boneh, Halevi, and Howgrave-Graham.