International Association
for Cryptologic Research

Updatable Encryption (UE) and Proxy Re-encryption (PRE) allow re-encrypting a ciphertext from one key to another in the symmetric-key and public-key settings, respectively, without decryption. A longstanding open question has been the following: do unidirectional UE and PRE schemes (where ciphertext re-encryption is permitted in only one direction) necessarily require stronger/more structured assumptions as compared to their bidirectional counterparts? Known constructions of UE and PRE seem to exemplify this "gap" -- while bidirectional schemes can be realized as relatively simple extensions of public-key encryption from standard assumptions such as DDH or LWE, unidirectional schemes typically rely on stronger assumptions such as FHE or indistinguishability obfuscation (iO), or highly structured cryptographic tools such as bilinear maps or lattice trapdoors. In this paper, we bridge this gap by showing the first feasibility results for realizing unidirectional UE and PRE from a new generic primitive that we call Key and Plaintext Homomorphic Encryption (KPHE) -- a public-key encryption scheme that supports additive homomorphisms on its plaintext and key spaces simultaneously. We show that KPHE can be instantiated from DDH. This yields the first constructions of unidirectional UE and PRE from DDH. Our constructions achieve the strongest notions of post-compromise security in the standard model. Our UE schemes also achieve "backwards-leak directionality" of key updates (a notion we discuss is equivalent, from a security perspective, to that of unidirectionality with no-key updates). Our results establish (somewhat surprisingly) that unidirectional UE and PRE schemes satisfying such strong security notions do not, in fact, require stronger/more structured cryptographic assumptions as compared to bidirectional schemes.

We present the first round-optimal and plausibly quantum-safe oblivious transfer (OT) and multi-party computation (MPC) protocols from the computational CSIDH assumption - the weakest and most widely studied assumption in the CSIDH family of isogeny-based assumptions. We obtain the following results: - The first round-optimal maliciously secure OT and MPC protocols in the plain model that achieve (black-box) simulation-based security while relying on the computational CSIDH assumption. - The first round-optimal maliciously secure OT and MPC protocols that achieves Universal Composability (UC) security in the presence of a trusted setup (common reference string plus random oracle) while relying on the computational CSIDH assumption. Prior plausibly quantum-safe isogeny-based OT protocols (with/without setup assumptions) are either not round-optimal, or rely on potentially stronger assumptions. We also build a 3-round maliciously-secure OT extension protocol where each base OT protocol requires only 4 isogeny computations. In comparison, the most efficient isogeny-based OT extension protocol till date due to Lai et al. [Eurocrypt 2021] requires 12 isogeny computations and 4 rounds of communication, while relying on the same assumption as our construction, namely the reciprocal CSIDH assumption.

Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a workaround, but several aspects remain unclear. In this work, we develop the tools necessary to practically run such a distributed trusted-setup ceremony. Our key contribution is the first statistically zero-knowledge proof of isogeny knowledge that is compatible with any base field. To prove statistical ZK, we introduce isogeny graphs with Borel level structure and prove they have the Ramanujan property. Then, we analyze the security of a distributed trusted-setup protocol based on our ZK proof in the simplified universal composability framework. Lastly, we develop an optimized implementation of the ZK proof, and we propose a strategy to concretely deploy the trusted-setup protocol.

The OCB mode of operation for block ciphers has three variants, OCB1, OCB2 and OCB3. OCB1 and OCB3 can be used as secure authenticated encryption schemes whereas OCB2 has been shown to be classically insecure (Inoue et al., Crypto 2019). Even further, in the presence of quantum queries to the encryption functionality, a series of works by Kaplan et al. (Crypto 2016), Bhaumik et al. (Asiacrypt 2021) and Bonnetain et al. (Asiacrypt 2021) have shown how to break the unforgeability of the OCB modes. However, these works did not consider the confidentiality of OCB in the presence of quantum queries.We fill this gap by presenting the first formal analysis of the IND-qCPA security of OCB. In particular, we show the first attacks breaking the IND-qCPA security of the OCB modes. Surprisingly, we are able to prove that OCB2 is IND-qCPA secure when used without associated data, while relying on the assumption that the underlying block cipher is a quantum-secure pseudorandom permutation. Additionally, we present new quantum attacks breaking the universal unforgeability of OCB. Our analysis of OCB has implications for the post-quantum security of XTS, a well-known disk encryption standard, that was considered but mostly left open by Anand et al. (PQCrypto 2016).

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.

We present a new framework for building round-optimal one-sided statistically secure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer (EOT) with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables the first instantiations of round-optimal one-sided statistically secure 2PC protocols from the CDH assumption and certain families of isogeny-based assumptions. As part of our compiler, we introduce the following new one-sided statistically secure primitives in the pre-processing model that might also be of independent interest: 1. Three round statistically sender private random-OT where only the last OT message depends on the receiver's choice bit and the sender receives random outputs generated by the protocol. 2. Four round delayed-input statistically sender private conditional disclosure of secrets where the first two rounds of the protocol are independent of the inputs of the parties. The above primitives are directly constructed from EOT and hence we obtain their instantiations from the same set of assumptions as our 2PC.

The task of achieving full security (with guaranteed output delivery) in secure multiparty computation (MPC) is a long-studied problem with known impossibility results that rule out constructions in the dishonest majority setting. In this work, we investigate the question of constructing fully-secure MPC protocols in the dishonest majority setting with the help of an external trusted party (TP). It is well-known that the existence of such a trusted party is sufficient to bypass the impossibility results. As our goal is to study the minimal requirements needed from this trusted party, we restrict ourselves to the extreme setting where the size of the TP is independent of the size of the functionality to be computed (called "small" TP) and this TP is invoked only once during the protocol execution. We present several positive and negative results for fully-secure MPC in this setting. - For a natural class of protocols, specifically, those with a universal output decoder, we show that the size of the TP must necessarily be exponential in the number of parties. This result holds irrespective of the computational assumptions used in the protocol. This class is broad enough to capture the prior results and indicates that the prior techniques necessitate the use of an exponential-sized TP. We additionally rule out the possibility of achieving information-theoretic full security (without the restriction of using a universal output decoder) using a "small" TP in the plain model (i.e., without any setup). - In order to get around the above negative result, we consider protocols without a universal output decoder. The main positive result in our work is a construction of such a fully-secure MPC protocol assuming the existence of a succinct Functional Encryption scheme. We also give evidence that such an assumption is likely to be necessary for fully-secure MPC in certain restricted settings. - We also explore the possibility of achieving full-security with a semi-honest TP that could collude with the other malicious parties in the protocol (which are in a dishonest majority). In this setting, we show that fairness is impossible to achieve even if we allow the size of the TP to grow with the circuit-size of the function to be computed.

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.

Algebraic structure lies at the heart of much of Cryptomania as we know it. An interesting question is the following: instead of building (Cryptomania) primitives from concrete assumptions, can we build them from simple Minicrypt primitives endowed with additional algebraic structure? In this work, we affirmatively answer this question by adding algebraic structure to the following Minicrypt primitives: One-Way Function (OWF) Weak Unpredictable Function (wUF) Weak Pseudorandom Function (wPRF) The algebraic structure that we consider is group homomorphism over the input/output spaces of these primitives. We also consider a “bounded” notion of homomorphism where the primitive only supports an a priori bounded number of homomorphic operations in order to capture lattice-based and other “noisy” assumptions. We show that these structured primitives can be used to construct many cryptographic protocols. In particular, we prove that: (Bounded) Homomorphic OWFs  (HOWFs) imply collision-resistant hash functions, Schnorr-style signatures and chameleon hash functions. (Bounded) Input-Homomorphic weak UFs  (IHwUFs) imply CPA-secure PKE, non-interactive key exchange, trapdoor functions, blind batch encryption (which implies anonymous IBE, KDM-secure and leakage-resilient PKE), CCA2 deterministic PKE, and hinting PRGs (which in turn imply transformation of CPA to CCA security for ABE/1-sided PE). (Bounded) Input-Homomorphic weak PRFs  (IHwPRFs) imply PIR, lossy trapdoor functions, OT and MPC (in the plain model). In addition, we show how to realize any CDH/DDH-based protocol with certain properties in a generic manner using IHwUFs/IHwPRFs, and how to instantiate such a protocol from many concrete assumptions. We also consider primitives with substantially richer structure, namely Ring IHwPRFs and L-composable IHwPRFs . In particular, we show the following: Ring IHwPRFs with certain properties imply FHE. 2-composable IHwPRFs imply (black-box) IBE, and L -composable IHwPRFs imply non-interactive $$(L+1)$$ ( L + 1 ) -party key exchange. Our framework allows us to categorize many cryptographic protocols based on which structured Minicrypt primitive implies them. In addition, it potentially makes showing the existence of many cryptosystems from novel assumptions substantially easier in the future.

Microarchitectural attacks on computing systems often stem from simple artefacts in the underlying architecture. In this paper, we focus on the Return Address Stack (RAS), a small hardware stack present in modern processors to reduce the branch miss penalty by storing the return addresses of each function call. The RAS is useful to handle specifically the branch predictions for the RET instructions which are not accurately predicted by the typical branch prediction units. In particular, we envisage a spy process who crafts an overflow condition in the RAS by filling it with arbitrary return addresses, and wrestles with a concurrent process to establish a timing side channel between them. We call this attack principle, RASSLE 1 (Return Address Stack based Side-channel Leakage), which an adversary can launch on modern processors by first reverse engineering the RAS using a generic methodology exploiting the established timing channel. Subsequently, we show three concrete attack scenarios: i) How a spy can establish a covert channel with another co-residing process? ii) How RASSLE can be utilized to determine the secret key of the P-384 curves in OpenSSL (v1.1.1 library)? iii) How an Elliptic Curve Digital Signature Algorithm (ECDSA) secret key on P-256 curve of OpenSSL can be revealed using Lattice Attack on partially leaked nonces with the aid of RASSLE? In this attack, we show that the OpenSSL implementation of scalar multiplication on this curve has varying number of add-and-sub function calls, which depends on the secret scalar bits. We demonstrate through several experiments that the number of add-and-sub function calls can be used to template the secret bit, which can be picked up by the spy using the principles of RASSLE. Finally, we demonstrate a full end-to-end attack on OpenSSL ECDSA using curve parameters of curve P-256. In this part of our experiments with RASSLE, we abuse the deadline scheduler policy to attain perfect synchronization between the spy and victim, without any aid of induced synchronization from the victim code. This synchronization and timing leakage through RASSLE is sufficient to retrieve the Most Significant Bits (MSB) of the ephemeral nonces used while signature generation, from which we subsequently retrieve the secret signing key of the sender applying the Hidden Number Problem. 1RASSLE is a non-standard spelling for wrestle.

In the past decades, user authentication has been dominated by server-side password-based solutions that rely on ``what users know". This approach is susceptible to breaches and phishing attacks, and poses usability challenges. As a result, the industry is gradually moving to biometric-based client-side solutions that do not store any secret information on servers. This shift necessitates the safe storage of biometric templates and private keys, which are used to generate tokens, on user devices. We propose a new generic framework called Biometric Enabled Threshold Authentication (BETA) to protect sensitive client-side information like biometric templates and cryptographic keys. Towards this, we formally introduce the notion of Fuzzy Threshold Tokenizer (FTT) where an initiator can use a ``close'' biometric measurement to generate an authentication token if at least t (the threshold) devices participate. We require that the devices only talk to the initiator, and not to each other, to capture the way user devices are connected in the real world. We use the universal composability (UC) framework to model the security properties of FTT, including the unforgeability of tokens and the privacy of the biometric values (template and measurement), under a malicious adversary. We construct three protocols that meet our definition. Our first two protocols are general feasibility results that work for any distance function, any threshold t and tolerate the maximal (i.e. t-1) amount of corruption. They are based on any two round UC-secure multi-party computation protocol in the standard model (with a CRS) and threshold fully homomorphic encryption, respectively. We show how to effectively use these primitives to build protocols in a constrained communication model with just four rounds of communication. For the third protocol, we consider inner-product based distance metrics (cosine similarity, Euclidean distance, etc.) specifically, motivated by the recent interest in its use for face recognition. We use Paillier encryption, efficient NIZKs for specific languages, and a simple garbled circuit to build an efficient protocol for the common case of n=3 devices with one compromised.

We present a new framework for building round-optimal (two-round) adaptively secure MPC. We show that a relatively weak notion of OT that we call indistinguishability OT with receiver oblivious sampleability (r-iOT) is enough to build two-round, adaptively secure MPC against malicious adversaries in the CRS model. We then show how to construct r-iOT from CDH, LPN, or isogeny-based assumptions that can be viewed as group actions (such as CSIDH and CSI-FiSh). This yields the first concrete constructions of two-round adaptively secure MPC against malicious adversaries from CDH, LPN, or isogeny-based assumptions. We further extend our non-isogeny results to the plain model, achieving (to the best of our knowledge) the first construction of two-round adaptively secure MPC against semi-honest adversaries in the plain model from LPN. Our results allow us to build two-round adaptively secure MPC against malicious adversaries from essentially all of the well-studied assumptions in cryptography. In addition, our constructions from isogenies or LPN provide the first post-quantum alternatives to LWE-based constructions for round-optimal adaptively secure MPC. Along the way, we show that r-iOT also implies non-committing encryption (NCE), thereby yielding the first constructions of NCE from isogenies or LPN.

Fault attacks (FA) are one of the potent practical threats to modern cryptographic implementations. Over the years the FA techniques have evolved, gradually moving towards the exploitation of device-centric properties of the faults. In this paper, we exploit the fact that activation and propagation of a fault through a given combinational circuit (i.e., observability of a fault) is data-dependent. Next, we show that this property of combinational circuits leads to powerful Fault Template Attacks (FTA), even for implementations having dedicated protections against both power and fault-based vulnerabilities. The attacks found in this work are applicable even if the fault injection is made at the middle rounds of a block cipher, which are out of reach for most of the other existing fault analysis strategies. Quite evidently, they also work for a known-plaintext scenario. Moreover, the middle round attacks are entirely blind in the sense that no access to the ciphertexts (correct/faulty) or plaintexts are required. The adversary is only assumed to have the power of repeating an unknown plaintext several times. Practical validation over a hardware implementation of SCA-FA protected PRESENT, and simulated evaluation on a public software implementation of protected AES prove the efficacy of the proposed attacks.

Isogeny-based assumptions have emerged as a viable option for quantum-secure cryptography. Recent works have shown how to build efficient (public-key) primitives from isogeny-based assumptions such as CSIDH and CSI-FiSh. However, in its present form, the landscape of isogenies does not seem very amenable to realizing new cryptographic applications. Isogeny-based assumptions often have unique efficiency and security properties, which makes building new cryptographic applications from them a potentially tedious and time-consuming task. In this work, we propose a new framework based on group actions that enables the easy usage of a variety of isogeny-based assumptions. Our framework generalizes the works of Brassard and Yung (Crypto'90) and Couveignes (Eprint'06). We provide new definitions for group actions endowed with natural hardness assumptions that model isogeny-based constructions amenable to group actions such as CSIDH and CSI-FiSh. We demonstrate the utility of our new framework by leveraging it to construct several primitives that were not previously known from isogeny-based assumptions. These include smooth projective hashing, dual-mode PKE, two-message statistically sender-private OT, and Naor-Reingold style PRF. These primitives are useful building blocks for a wide range of cryptographic applications. We introduce a new assumption over group actions called Linear Hidden Shift (LHS) assumption. We then present some discussions on the security of the LHS assumption and we show that it implies symmetric KDM-secure encryption, which in turn enables many other primitives that were not previously known from isogeny-based assumptions.

In this work, we propose new constructions for zero inner-product encryption (ZIPE) and non-zero inner-product encryption (NIPE) from prime-order bilinear pairings, which are both attribute and function private in the public-key setting. Our ZIPE scheme is adaptively attribute private under the standard Matrix DDH assumption for unbounded collusions. It is additionally computationally function private under a min-entropy variant of the Matrix DDH assumption for predicates sampled from distributions with super-logarithmic min-entropy. Existing (statistically) function private ZIPE schemes due to Boneh et al. [Crypto’13, Asiacrypt’13] necessarily require predicate distributions with significantly larger min-entropy in the public-key setting.Our NIPE scheme is adaptively attribute private under the standard Matrix DDH assumption, albeit for bounded collusions. In addition, it achieves computational function privacy under a min-entropy variant of the Matrix DDH assumption for predicates sampled from distributions with super-logarithmic min-entropy. To the best of our knowledge, existing NIPE schemes from bilinear pairings were neither attribute private nor function private. Our constructions are inspired by the linear FE constructions of Agrawal et al. [Crypto’16] and the simulation secure ZIPE of Wee [TCC’17]. In our ZIPE scheme, we show a novel way of embedding two different hard problem instances in a single secret key - one for unbounded collusion-resistance and the other for function privacy. For NIPE, we introduce new techniques for simultaneously achieving attribute and function privacy. We further show that the two constructions naturally generalize to a wider class of predicate encryption schemes such as subspace membership, subspace non-membership and hidden-vector encryption.

Algebraic structure lies at the heart of Cryptomania as we know it. An interesting question is the following: instead of building (Cryptomania) primitives from concrete assumptions, can we build them from simple Minicrypt primitives endowed with some additional algebraic structure? In this work, we affirmatively answer this question by adding algebraic structure to the following Minicrypt primitives:One-Way Function (OWF)Weak Unpredictable Function (wUF)Weak Pseudorandom Function (wPRF) The algebraic structure that we consider is group homomorphism over the input/output spaces of these primitives. We also consider a “bounded” notion of homomorphism where the primitive only supports an a priori bounded number of homomorphic operations in order to capture lattice-based and other “noisy” assumptions. We show that these structured primitives can be used to construct many cryptographic protocols. In particular, we prove that: (Bounded) Homomorphic OWFs (HOWFs) imply collision-resistant hash functions, Schnorr-style signatures and chameleon hash functions.(Bounded) Input-Homomorphic weak UFs (IHwUFs) imply CPA-secure PKE, non-interactive key exchange, trapdoor functions, blind batch encryption (which implies anonymous IBE, KDM-secure and leakage-resilient PKE), CCA2 deterministic PKE, and hinting PRGs (which in turn imply transformation of CPA to CCA security for ABE/1-sided PE).(Bounded) Input-Homomorphic weak PRFs (IHwPRFs) imply PIR, lossy trapdoor functions, OT and MPC (in the plain model). In addition, we show how to realize any CDH/DDH-based protocol with certain properties in a generic manner using IHwUFs/IHwPRFs, and how to instantiate such a protocol from many concrete assumptions.We also consider primitives with substantially richer structure, namely Ring IHwPRFs and L-composable IHwPRFs. In particular, we show the following: Ring IHwPRFs with certain properties imply FHE.2-composable IHwPRFs imply (black-box) IBE, and L-composable IHwPRFs imply non-interactive $$(L+1)$$ (L+1)-party key exchange. Our framework allows us to categorize many cryptographic protocols based on which structured Minicrypt primitive implies them. In addition, it potentially makes showing the existence of many cryptosystems from novel assumptions substantially easier in the future.

Securely managing encrypted data on an untrusted party is a challenging problem that has motivated the study of a wide variety of cryptographic primitives. A special class of such primitives allows an untrusted party to transform a ciphertext encrypted under one key to a ciphertext under another key, using some auxiliary information that does not leak the underlying data. Prominent examples of such primitives in the symmetric setting are key-homomorphic (weak) PRFs, updatable encryption, and proxy re-encryption. Although these primitives differ significantly in terms of their constructions and security requirements, they share two important properties: (a) they have secrets with structure or extra functionality, and (b) all known constructions of these primitives satisfying reasonably strong definitions of security are based on concrete public-key assumptions, e.g., DDH and LWE. This raises the question of whether these objects inherently belong to the world of public-key primitives, or they can potentially be built from simple symmetric-key objects such as pseudorandom functions. In this work, we show that the latter possibility is unlikely. More specifically, we show that:Any (bounded) key-homomorphic weak PRF with an abelian output group implies a (bounded) input-homomorphic weak PRF, which has recently been shown to imply not only public-key encryption  but also a variety of primitives such as PIR, lossy TDFs, and even IBE.Any ciphertext-independent updatable encryption scheme that is forward and post-compromise secure implies PKE. Moreover, any symmetric-key proxy re-encryption scheme with reasonably strong security guarantees implies a forward and post-compromise secure ciphertext-independent updatable encryption, and hence PKE. In addition, we show that unbounded (or exact) key-homomorphic weak PRFs over abelian groups are impossible in the quantum world. In other words, over abelian groups, bounded key-homomorphism is the best that we can hope for in terms of post-quantum security. Our attack also works over other structured primitives with abelian groups and exact homomorphisms, including homomorphic one-way functions and input-homomorphic weak PRFs.

This work focuses on side-channel resilient design strategies for symmetrickey cryptographic primitives targeting lightweight applications. In light of NIST’s lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make them amenable to low-cost threshold implementations (TI) - a provably secure strategy against side-channel attacks. The core building blocks for our strategy are cryptographically optimal 4×4 S-Boxes, implemented via repeated iterations of simple cellular automata (CA) rules. We present highly optimized TI circuits for such S-Boxes, that consume nearly 40% less area and power as compared to popular lightweight S-Boxes such as PRESENT and GIFT. We validate our claims via implementation results on ASIC using 180nm technology. We also present a comparison of TI circuits for two popular lightweight linear diffusion layer choices - bit permutations and MixColumns using almost-maximum-distance-separable (almost-MDS) matrices. We finally illustrate design paradigms that combine the aforementioned TI circuits for S-Boxes and diffusion layers to obtain fully side-channel secure SPN block cipher implementations with low area and power requirements.