International Association
for Cryptologic Research

The Fujisaki-Okamoto transform (FO) is the go-to method for achieving chosen-ciphertext (CCA) security for post-quantum key encapsulation mechanisms (KEMs). An important step in FO is augmenting the decryption/ decapsulation algorithm with a re-encryption step -- the decrypted message is re-encrypted to check whether the correct encryption randomness was used. While solving a security problem (ciphertext-malleability), re-encryption has turned out to introduce side-channel vulnerabilities and is computationally expensive, which has lead designers to searching for alternatives. In this work, we perform a comprehensive study of such alternatives. We formalize a central security property, computational rigidity, and show that it is sufficient for obtaining CCA security. We present a framework for analyzing algorithms that can replace re-encryption and still achieve rigidity, and analyze existing proposals in this framework. Along the way, we pick up a novel QROM security statement for explicitly rejecting KEMs based on deterministic PKE schemes, something that so far only was possible when requiring a hard-to-ensure quantum property for the base PKE scheme.

Lattice-based cryptography is in the process of being standardized. Several proposals to deal with side-channel information using lattice reduction exist. However, it has been shown that algorithms based on Bayesian updating are often more favorable in practice. In this work, we define \textit{distribution hints}; a type of hint that allows modelling probabilistic information. These hints generalize most previously defined hints and the information obtained in several attacks. We define two solvers for our hints; one is based on belief propagation and the other one uses a greedy approach. We prove that the latter is a computationally less expensive approximation of the former and that previous algorithms used for specific attacks may be seen as special cases of our solvers. Thereby, we provide a systematization of previously obtained information and used algorithms in real-world side-channel attacks. In contrast to lattice-based approaches, our framework is not limited to value leakage. For example, it can deal with noisy Hamming weight leakage or partially incorrect information. Moreover, it improves upon the recovery of the secret key from approximate hints in the form they arise in real-world attacks. Our framework has several practical applications: We exemplarily show that a recent attack can be improved; we reduce the number of traces and corresponding ciphertexts and increase the noise resistance. Further, we explain how distribution hints could be applied in the context of previous attacks and outline a potential new attack.

While in classical cryptography one-way functions (OWFs) are widely regarded as the “minimal assumption”, the situation in quantum cryptography is less clear. Recent works have put forward two concurrent candidates for the minimal assumption in quantum cryptography: One- way state generators (OWSGs), postulating the existence of a hard search problem with an efficient verification algorithm, and EFI pairs, postulating the existence of a hard distinguishing problem. Two recent papers [Khurana and Tomer STOC’24; Batra and Jain FOCS’24] showed that OWSGs imply EFI pairs, but the reverse direction remained open. In this work, we give strong evidence that the opposite direction does not hold: We show that there is a quantum unitary oracle relative to which EFI pairs exist but OWSGs do not. In fact, we show a slightly stronger statement that holds also for EFI pairs that output classical bits (QEFID). As a consequence, we separate, via our oracle, QEFID and one-way puzzles from OWSGs and several other Microcrypt primitives, including efficiently verifiable one-way puzzles and unclonable state generators. In particular, this solves a problem left open in [Chung, Goldin, and Gray Crypto’24]. Using similar techniques, we also establish a fully black-box separation (which is slightly weaker than an oracle separation) between private-key quantum money schemes and QEFID pairs. One conceptual implication of our work is that the existence of an efficient verification algorithm may lead to qualitatively stronger primitives in quantum cryptography.

In this article we present a non-uniform reduction from rank-2 module-LIP over Complex Multiplication fields, to a variant of the Principal Ideal Problem, in some fitting quaternion algebra. This reduction is classical deterministic polynomial-time in the size of the inputs. The quaternion algebra in which we need to solve the variant of the principal ideal problem depends on the parameters of the module-LIP problem, but not on the problem's instance. Our reduction requires the knowledge of some special elements of this quaternion algebras, which is why it is non-uniform. In some particular cases, these elements can be computed in polynomial time, making the reduction uniform. This is the case for the Hawk signature scheme: we show that breaking Hawk is no harder than solving a variant of the principal ideal problem in a fixed quaternion algebra (and this reduction is uniform).

Secure key leasing (a.k.a. key-revocable cryptography) enables us to lease a cryptographic key as a quantum state in such a way that the key can be later revoked in a verifiable manner. We propose a simple framework for constructing cryptographic primitives with secure key leasing via the certified deletion property of BB84 states. Based on our framework, we obtain the following schemes. - A public key encryption scheme with secure key leasing that has classical revocation based on any IND-CPA secure public key encryption scheme. Prior works rely on either quantum revocation or stronger assumptions such as the quantum hardness of the learning with errors (LWE) problem. - A pseudorandom function with secure key leasing that has classical revocation based on one-way functions. Prior works rely on stronger assumptions such as the quantum hardness of the LWE problem. - A digital signature scheme with secure key leasing that has classical revocation based on the quantum hardness of the short integer solution (SIS) problem. Our construction has static signing keys, i.e., the state of a signing key almost does not change before and after signing. Prior constructions either rely on non-static signing keys or indistinguishability obfuscation to achieve a stronger goal of copy-protection. In addition, all of our schemes remain secure even if a verification key for revocation is leaked after the adversary submits a valid certificate of deletion. To our knowledge, all prior constructions are totally broken in this setting. Moreover, in our view, our security proofs are much simpler than those for existing schemes.

We present almost-optimal lattice-based attribute-based encryption (ABE) and laconic function evaluation (LFE). For depth d circuits over L-bit inputs, we obtain * key-policy (KP) and ciphertext-policy (CP) ABE schemes with ciphertext, secret key and public key size O(1); * LFE with ciphertext size L + O(1) as well as CRS and digest size O(1); where O(·) hides poly(d, λ) factors. The parameter sizes are optimal, up to the poly(d) dependencies. The security of our schemes rely on succinct LWE (Wee, CRYPTO 2024). Our results constitute a substantial improvement over the state of the art; none of our results were known even under the stronger evasive LWE assumption.

We describe, formally model, and prove the security of Telegram's key exchange protocols for client-server communications. To achieve this, we develop a suitable multi-stage key exchange security model along with pseudocode descriptions of the Telegram protocols that are based on analysis of Telegram's specifications and client source code. We carefully document how our descriptions differ from reality and justify our modelling choices. Our security proofs reduce the security of the protocols to that of their cryptographic building blocks, but the subsequent analysis of those building blocks requires the introduction of a number of novel security assumptions, reflecting many design decisions made by Telegram that are suboptimal from the perspective of formal analysis. Along the way, we provide a proof of IND-CCA security for the variant of RSA-OEAP+ used in Telegram and identify a hypothetical attack exploiting current Telegram server behaviour (which is not captured in our protocol descriptions). Finally, we reflect on the broader lessons about protocol design that can be taken from our work.

We study error detection and correction in a computationally bounded world, where errors are introduced by an arbitrary polynomial-time adversarial channel. Our focus is on seeded codes, where the encoding and decoding procedures can share a public random seed, but are otherwise deterministic. We can ask for either selective or adaptive security, depending on whether the adversary can choose the message being encoded before or after seeing the seed. For large alphabets, a recent construction achieves essentially optimal rate versus error tolerance trade-offs under minimal assumptions, surpassing information-theoretic limits. However, for the binary alphabet, the only prior improvement over information theoretic codes relies on non-standard assumptions justified via the random oracle model. We show the following: – Selective Security under LWE: Under the learning with errors (LWE) assumption, we construct selectively secure codes over the binary alphabet. For error detection, our codes achieve essentially optimal rate R ≈ 1 and relative error tolerance p ≈ 1/2. For error correction, they can uniquely correct p < 1/4 relative errors with a rate R that essentially matches that of the best list-decodable codes with error tolerance p. Both cases provide significant improvements over information-theoretic counterparts. The construction relies on a novel form of 2-input correlation intractable hash functions that we construct from LWE. – Adaptive Security via Crypto Dark Matter: Assuming the exponential security of a natural collision-resistant hash function candidate based on the “crypto dark matter” approach of mixing linear functions over different moduli, we construct adaptively secure codes over the binary alphabet, for both error detection and correction. They achieve essentially the same trade-offs between error tolerance p and rate R as above, with the caveat that for error-correction they only do so for sufficiently small values of p.

We present BitGC, a garbling scheme for Boolean circuits with 1 bit per gate communication based on either ring learning with errors (RLWE) or NTRU assumption, with key-dependent message security. The garbling consists of 1) a homomorphically encrypted seed that can be expanded to encryption of many pseudo-random bits and 2) one-bit stitching information per gate to reconstruct garbled tables from the expanded ciphertexts. By using low-complexity PRGs, both the garbling and evaluation of each gate require only O(1) homomorphic addition/multiplication operations without bootstrapping.

We present a new approach for constructing non-interactive zero-knowledge (NIZK) proof systems from {\em vector trapdoor hashing} (VTDH) -- a generalization of trapdoor hashing [D\"ottling et al., Crypto'19]. Unlike prior applications of trapdoor hash to NIZKs, we use VTDH to realize the hidden bits model [Feige-Lapidot-Shamir, FOCS'90] leading to {\em black-box} constructions of NIZKs. This approach gives us the following new results: \begin{itemize} \item A {\em statistically-sound} NIZK proof system based on the hardness of decisional Diffie-Hellman (DDH) and learning parity with noise (LPN) over finite fields with inverse polynomial noise rate. This gives the first statistically sound NIZK proof system that is not based on either LWE, or bilinear maps, or factoring. \item A dual-mode NIZK satisfying statistical zero-knowledge in the common random string mode and statistical soundness in the common reference string mode assuming the hardness of learning with errors (LWE) with {\em polynomial} modulus-to-noise ratio. This gives the first {\it black-box} construction of such a dual-mode NIZK under LWE. This improves the recent work of Waters (STOC'24) which relied on LWE with super-polynomial modulus-to-noise ratio and required a setup phase with private coins. \end{itemize} The above constructions are black-box and satisfy single-theorem zero-knowledge property. Building on the works of Feige et al.(FOCS'90) and Fischlin and Rohrback (PKC'21), we upgrade these constructions (under the same assumptions) to satisfy multi-theorem zero-knowledge property at the expense of making non-black-box use of cryptography.

Garbled circuits, introduced in the seminal work of Yao (FOCS, 1986), have received considerable attention in the boolean setting due to their efficiency and application to round-efficient secure computation. In contrast, arithmetic garbling schemes have received much less scrutiny. The main efficiency measure of garbling schemes is their rate, defined as the bit size of each gate's output divided by the (amortized) garbled gate. Despite recent progress, state-of-the-art garbling schemes for arithmetic circuits suffer from important limitations: all existing schemes are either restricted to B-bounded integer arithmetic circuits (a computational model where the arithmetic is performed over Z and correctness is only guaranteed if no intermediate computation exceeds the bound B) and achieve constant rate only for very large bounds B = 2^Ω(λ^3), or have rate at most O(1/λ) otherwise, where λ denotes a security parameter. In this work, we improve this state of affairs in both settings. - As our main contribution, we introduce the first arithmetic garbling scheme over modular rings Z_B with rate O(log λ / λ), breaking for the first time the 1/λ-rate barrier for modular arithmetic garbling. Our construction relies on the power-DDH assumption. - As a secondary contribution, we introduce a new arithmetic garbling scheme for B-bounded integer arithmetic that achieves a constant rate for bounds B as low as 2^O(λ). Our construction relies on a new non-standard KDM-security assumption on Paillier encryption with small exponents.

We study the problem of embedded code encryption, i.e., encryption for binary software code for a secure microcontroller that is stored in an insecure external memory. As every single instruction must be decrypted before it can be executed, this scenario requires an extremely low latency decryption. We present a formal treatment of embedded code encryption security definitions, propose three constructions, namely ACE1, ACE2 and ACE3, and analyze their security. Further, we present ChiLow, a family of tweakable block ciphers and a related PRF specifically designed for embedded code encryption. At the core of ChiLow, there is ChiChi, a new family of non-linear layers of even dimension based on the well-known χ function. Our fully unrolled hardware implementation of ChiLow, using the Nangate 15nm Open Cell Library, achieves a decryption latency of less than 280 picoseconds.

We consider constructions that combine outputs of a single permutation $\pi:\{0,1\}^n \rightarrow \{0,1\}^n$ using a public function. These are popular constructions for achieving security beyond the birthday bound when implementing a pseudorandom function using a block cipher (i.e., a pseudorandom permutation). One of the best-known constructions (denoted SXoP$[2,n]$) XORs the outputs of 2 domain-separated calls to $\pi$. Modeling $\pi$ as a uniformly chosen permutation, several previous works proved a tight information-theoretic indistinguishability bound for SXoP$[2,n]$ of about $q/2^{n}$, where $q$ is the number of queries. However, tight bounds are unknown for the generalized variant (denoted SXoP$[r,n]$) which XORs the outputs of $r \geq 2$ domain-separated calls to a uniform permutation. In this paper, we obtain two results. Our first result improves the known bounds for SXoP$[r,n]$ for all (constant) $r \geq 3$ (assuming $q \leq O(2^n/r)$ is not too large) in both the single-user and multi-user settings. In particular, for $r=3$, our bound is about $\sqrt{u}q_{\max}/2^{2.5n}$ (where $u$ is the number of users and $q_{\max}$ is the maximal number of queries per user), improving the best-known previous result by a factor of at least $2^n$. For odd $r$, our bounds are tight for $q > 2^{n/2}$, as they match known attacks. For even $r$, we prove that our single-user bounds are tight by providing matching attacks. Our second and main result is divided into two parts. First, we devise a family of constructions that output $n$ bits by efficiently combining outputs of 2 calls to a permutation on $\{0,1\}^n$, and achieve multi-user security of about $\sqrt{u} q_{\max}/2^{1.5n}$. Then, inspired by the CENC construction of Iwata~[FSE'06], we further extend this family to output $2n$ bits by efficiently combining outputs of 3 calls to a permutation on $\{0,1\}^n$. The extended construction has similar multi-user security of $\sqrt{u} q_{\max}/2^{1.5n}$. The new single-user ($u=1$) bounds of $q/2^{1.5n}$ for both families should be contrasted with the previously best-known bounds of $q/2^n$, obtained by the comparable constructions of SXoP$[2,n]$ and CENC. All of our bounds are proved by Fourier analysis, extending the provable security toolkit in this domain in multiple ways.

With the rapid development of quantum computers, optimizing the quantum implementations of symmetric-key ciphers, which constitute the primary components of the quantum oracles used in quantum attacks based on Grover and Simon's algorithms, has become an active topic in the cryptography community. In this field, a challenge is to construct quantum circuits that require the least amount of quantum resources. In this work, we aim to address the problem of constructing quantum circuits with the minimal T-depth or width (number of qubits) for nonlinear components, thereby enabling implementations of symmetric-key ciphers with the minimal T-depth or width. Specifically, we propose several general methods for obtaining quantum implementation of generic vectorial Boolean functions and multiplicative inversions in GF(2^n), achieving the minimal T-depth and low costs across other metrics. As an application, we present a highly compact T-depth-3 Clifford+T circuit for the AES S-box. Compared to the T-depth-3 circuits presented in previous works (ASIACRYPT 2022, IEEE TC 2024), our circuit has significant reductions in T-count, full depth and Clifford gate count. Compared to the state-of-the-art T-depth-4 circuits, our circuit not only achieves the minimal T-depth but also exhibits reduced full depth and closely comparable width. This leads to lower costs for the DW-cost and T-DW-cost. Additionally, we propose two methods for constructing minimal-width implementations of vectorial Boolean functions. As applications, for the first time, we present a 9-qubit Clifford+T circuit for the AES S-box, a 16-qubit Clifford+T circuit for a pair of AES S-boxes, and a 5-qubit Clifford+T circuit for the chi function of SHA3. These circuits can be used to derive quantum circuits that implement AES or SHA3 without ancilla qubits.

The rank-2 module-LIP problem was introduced in cryptography by (Ducas, Postlethwaite, Pulles, van Woerden, Asiacrypt 2022), to construct the highly performant HAWK scheme. A first cryptanalytic work by (Mureau, Pellet--Mary, Pliatsok, Wallet, Eurocrypt 2024) showed a heuristic polynomial time attack against the rank-2 module-LIP problem over totally real number fields. While mathematically interesting, this attack focuses on number fields that are not relevant for cryptography. The main families of fields used in cryptography are the highly predominant cyclotomic fields (used for instance in the HAWK scheme), as well as the NTRU Prime fields, used for instance in the eponymous NTRU Prime scheme (Bernstein, Chuengsatiansup, Lange, van Vredendaal, SAC 2017). In this work, we generalize the attack of Mureau et al. against rank-2 module-LIP to the family of all number fields with at least one real embedding, which contains the NTRU Prime fields. We present three variants of our attack, firstly a heuristic one that runs in quantum polynomial time. Secondly, under the extra assumption that the defining polynomial of K has a 2-transitive Galois group (which is the case for the NTRU Prime fields), we give a provable attack that runs in quantum polynomial time. And thirdly, with the same 2-transitivity assumption we give a heuristic attack that runs in classical polynomial time. For the latter we use a generalization of the Gentry--Szydlo algorithm to any number field which might be of independent interest.

Falcon is one of the three postquantum signature schemes already selected by NIST for standardization. It is the most compact among them, and offers excellent efficiency and security. However, it is based on a complex algorithm for lattice discrete Gaussian sampling which presents a number of implementation challenges. In particular, it relies on (possibly emulated) floating-point arithmetic, which is often regarded as a cause for concern, and has been leveraged in, e.g., side-channel analysis. The extent to which Falcon's use of floating point arithmetic can cause security issues has yet to be thoroughly explored in the literature. In this paper, we contribute to filling this gap by identifying a way in which Falcon's lattice discrete Gaussian sampler, due to specific design choices, is singularly sensitive to floating-point errors. In the presence of small floating-point discrepancies (which can occur in various ways, including the use of the two almost but not quite equivalent signing procedures ``dynamic'' and ``tree'' exposed by the Falcon API), we find that, when called twice on the same input, the Falcon sampler has a small but significant chance (on the order of once in a few thousand calls) of outputting two different lattice points with a very structured difference, that immediately reveals the secret key. This is in contrast to other lattice Gaussian sampling algorithms like Peikert's sampler and Prest's hybrid sampler, that are stable with respect to small floating-point errors. Correctly generated Falcon signatures include a salt that should in principle prevent the sampler to ever be called on the same input twice. In that sense, our observation has little impact on the security of Falcon signatures per se (beyond echoing warnings about the dangers of repeated randomness). On the other hand, it is critical for derandomized variants of Falcon, which have been proposed for use in numerous settings. One can mention in particular identity-based encryption, SNARK-friendly signatures, and sublinear signature aggregation. For all these settings, small floating point discrepancies have a chance of resulting in full private key exposure, even when using the slower, integer-based emulated floating-point arithmetic of Falcon's reference implementation.

There are two security notions for FHE schemes the traditional notion of IND-CPA, and a more stringent notion of IND-CPA^D. The notions are equivalent if the FHE schemes are perfectly correct, however for schemes with negligible failure probability the FHE parameters needed to obtain IND-CPA^D security can be much larger than those needed to obtain IND-CPA security. This paper uses the notion of ciphertext drift in order to understand the practical difference between IND-CPA and IND-CPA^D security in schemes such as FHEW, TFHE and FINAL. This notion allows us to define a modulus switching operation (the main culprit for the difference in parameters) such that one does not require adapting IND-CPA cryptographic parameters to meet the IND-CPA^D security level. Further, the extra cost incurred by the new techniques has no noticeable performance impact in practical applications. The paper also formally defines a stronger version for IND-CPA^D security called sIND-CPA^D, which is proved to be strictly separated from the IND-CPA^D notion. Criterion for turning an IND-CPA^D secure public-key encryption into an sIND-CPA^D one is also provided.

A tweakable wide blockcipher is a construction which behaves in the same way as a tweakable blockcipher, with the difference that the actual block size is flexible. Due to this feature, a tweakable wide blockcipher can be directly used as a strong encryption scheme that provides full diffusion when encrypting plaintexts to ciphertexts and vice versa. Furthermore, it can be the basis of authenticated encryption schemes fulfilling the strongest security notions. In this paper, we present three instantiations of the docked double decker tweakable wide blockcipher: ddd-AES, ddd-AES^+, and bbb-ddd-AES. These instances exclusively use similar building blocks as AES-GCM (AES and finite field multiplication), are designed for maximal parallelism, and hence, can make efficient use of existing hardware accelerators. ddd-AES is a birthday bound secure scheme, and ddd-AES^+ is an immediate generalization to allow for variable length tweaks. bbb-ddd-AES achieves security beyond the birthday bound provided that the same tweak is not used too often. Moreover, bbb-ddd-AES builds upon a novel conditionally beyond birthday bound secure pseudorandom function, a tweakable variant of the XOR of permutations, facilitating in the need to include a tweak in the AES evaluations without sacrificing flexibility in docked double decker. We furthermore introduce an authenticated encryption mode aaa specifically tailored to be instantiated with ddd-AES and bbb-ddd-AES, where special attention is given to how the nonce and associated data can be processed. We prove that this mode is secure in the nonce-respecting setting, in the nonce-misuse setting, as well as in the setting where random nonces are used. We finally present a comparison with other tweakable wide blockciphers, give a high-level idea of the efficiency potential of our schemes, and provide benchmarks that confirm this idea.

We present new techniques for garbling mixed arithmetic and boolean circuits, utilizing the homomorphic secret sharing scheme introduced by Roy \& Singh (Crypto 2021), along with the half-tree protocol developed by Guo et al. (Eurocrypt 2023). Compared to some two-party interactive protocols, our mixed garbling only requires several times $(<10)$ more communication cost. We construct the bit decomposition/composition gadgets with communication cost $O((\lambda+\lambda_{\text{DCR}}/k)b)$ for integers in the range $(-2^{b-1}, 2^{b-1})$, requiring $O(2^k)$ computations for the GGM-tree. Our approach is compatible with constant-rate multiplication protocols, and the cost decreases as $k$ increases. Even for a small $k=8$, the concrete efficiency ranges from $6\lambda b$ ($b \geq 1000$ bits) to $9\lambda b$ ($b \sim 100$ bits) per decomposition/composition. In addition, we develop the efficient gadgets for mod $q$ and unsigned truncation based on bit decomposition and composition. We construct efficient arithmetic gadgets over various domains. For bounded integers, we improve the multiplication rate in the work of Meyer et al. (TCC 2024) from $\textstyle\frac{\zeta-2}{\zeta+1}$ to $\frac{\zeta-2}{\zeta}$. We propose new garbling schemes over other domains through bounded integers with our modular and truncation gadgets, which is more efficient than previous constructions. For $\mathbb{Z}_{2^b}$, additions and multiplication can be garbled with a communication cost comparable to our bit decomposition. For general finite field $\mathbb{F}_{p^n}$, particularly for large values of $p$ and $n$, we garble the addition and multiplication at the cost of $O((\lambda+\lambda_{\text{DCR}}/k)b)$, where $b = n\lceil \log p \rceil$. For applications to real numbers, we introduce an ``error-based'' truncation that makes the cost of multiplication dependent solely on the desired precision. \keywords{Garbled circuit \and Mixed circuits \and Secure computation}

A Private Simultaneous Messages (PSM) protocol is a secure multiparty computation protocol with a minimal interaction pattern, which allows input parties sharing common randomness to securely reveal the output of a function by sending messages only once to an external party. Since existing PSM protocols for arbitrary functions have exponentially large communication complexity in the number $n$ of parties, it is important to explore efficient protocols by focusing on special functions of practical use. In this paper, we study the communication efficiency of PSM protocols for symmetric functions, which provide many useful functionalities for real-world applications. We present a new $n$-party PSM protocol for symmetric functions with communication complexity $n^{2d/3+O(1)}$, where $d$ is the size of the input domain of each party. Our protocol improves the currently best known communication complexity of $n^{d+O(1)}$. As applications to other related models, we show that our novel protocol implies improved communication complexity of ad-hoc PSM, where only a subset of parties actually send messages, and also leads to a more communication-efficient robust PSM protocol, which is secure against collusion of the external party and input parties. The extension to ad-hoc PSM is not a straightforward application of the previous transformation but includes an optimization technique based on the symmetry of functions.

Correlated randomness lies at the core of efficient modern secure multi-party computation (MPC) protocols. Costs of generating such correlated randomness required for the MPC online phase protocol often constitute a bottleneck in the overall protocol. A recent paradigm of {\em pseudorandom correlation generator} (PCG) initiated by Boyle et al. (CCS'18, Crypto'19) offers an appealing solution to this issue. In sketch, each party is given a short PCG seed, which can be locally expanded into long correlated strings, satisfying the target correlation. Among various types of correlations, there is oblivious linear evaluation (OLE), a fundamental and useful primitive for typical MPC protocols on arithmetic circuits. Towards efficient generating a great amount of OLE, and applications to MPC protocols, we establish the following results: (i) We propose a novel {\em programmable} PCG construction for OLE over any field $\Fp$. For $kN$ OLE correlations, we require $O(k\log{N})$ communication and $O(k^2N\log{N})$ computation, where $k$ is an arbitrary integer $\geq 2$. Previous works either have quadratic computation (Boyle et al. Crypto'19), or can only support fields of size larger than $2$ (Bombar et al. Crypto'23). (ii) We extend the above OLE construction to provide various types of correlations for any finite field. One of the fascinating applications is an efficient PCG for two-party {\em authenticated Boolean multiplication triples}. For $kN$ authenticated triples, we offer PCGs with seed size of $O(k^2\log{N})$ bits. To our best knowledge, such correlation has not been efficiently realized with sublinear communication ever before. (iii) In addition, the {\em programmability} admits efficient PCGs for multi-party Boolean triples, and thus the first efficient MPC protocol for Boolean circuits with {\em silent} preprocessing. In particular, we show $kN$ $m$-party Boolean multiplication triples can be generated in $O(m^2k\log{N})$-bit communication, while the state-of-the-art FOLEAGE (Asiacrypt'24) requires a broadcast channel and takes $mkN+O(m^2\log{kN})$ bits communication. (iv) Finally, we present efficient PCGs for circuit-dependent preprocessing, matrix multiplications triples, and string OTs etc. Compared to previous works, each has its own right.

Verifiable random functions (VRFs) are pseudorandom functions where the function owner can prove that a generated output is correct relative to a committed key. In this paper we introduce the notion of an exponent-VRF (eVRF): a VRF that does not provide its output y explicitly, but instead provides Y = y*G, where G is a generator of some finite cyclic group (or Y=g^y in multiplicative notation). We construct eVRFs from the Paillier encryption scheme and from DDH (both in the random-oracle model). We then show that an eVRF is a powerful tool that has many important applications in threshold cryptography. In particular, we construct (1) a one-round fully simulatable distributed key-generation protocol (after a single two-round initialization phase), (2) a two-round fully simulatable signing protocol for multiparty Schnorr with a deterministic variant, (3) a two-party ECDSA protocol that has a deterministic variant, (4) a threshold Schnorr signing protocol where the parties can later prove that they signed without being able to frame another group, and (5) an MPC-friendly and verifiable HD-derivation. All these applications are derived from this single new eVRF abstraction. The resulting protocols are concretely efficient.

The notion of Anamorphic Encryption (Persiano {\em et al.} Eurocrypt 2022) aims at establishing private communication against an adversary who can access secret decryption keys and influence the chosen messages. Persiano {\em et al.} gave a simple, black-box, rejection sampling-based technique to send anamorphic {\em bits} using any $ \indcpa $ secure scheme as underlying PKE. In this paper however we provide evidence that their solution is not as general as claimed: indeed there exists a (contrived yet secure) PKE which lead to insecure anamorphic instantiations. Actually, our result implies that such stateless black-box realizations of AE are impossible to achieve, unless weaker notions are targeted or extra assumptions are made on the PKE. Even worse, this holds true even if one resort to powerful non-black-box techniques, such as NIZKs, $ \iO $ or garbling. From a constructive perspective, we shed light on those required assumptions. Specifically, we show that one could bypass (to some extent) our impossibility by either considering a weaker (but meaningful) notion of AE or by assuming the underlying PKE to (always) produce high min-entropy ciphertexts. Finally, we prove that, for the case of {\em Fully-Asymmetric} AE, $ \iO $ {\em can} actually be used to overcome existing impossibility barriers. We show how to use $ \iO $ to build Fully-Asymmetric AE (with small anamorphic message space) generically from any $ \indcpa $ secure PKE with sufficiently high min-entropy ciphertexts. Put together our results provide a clearer picture of what black-box constructions can and cannot achieve.

We study differential additions formulas on Kummer lines that factorize through a degree~$2$ isogeny $\phi$. We call the resulting formulas half differential additions: from the knowledge of $\phi(P), \phi(Q)$ and $P-Q$, the half differential addition allows to recover $P+Q$. We explain how Mumford's theta group theory allows, in any model of Kummer lines, to find a basis of the half differential relations. This involves studying the dimension~$2$ isogeny $(P, Q) \mapsto (P+Q, P-Q)$. We then use the half differential addition formulas to build a new type of Montgomery ladder, called the half-ladder, using a time-memory trade-off. On a Montgomery curve with full rational $2$-torsion, our half ladder first build a succession of isogeny images $P_i=\phi_i(P_{i-1})$, which only depends on the base point $P$ and not the scalar $n$, for a pre-computation cost of $2S+1m_0$ by bit. Then we use half doublings and half differential additions to compute any scalar multiplication $n \cdot P$, for a cost of $4M+2S+1m_0$ by bit. The total cost is then $4M + 4S + 2m_0$, even when the base point $P$ is not normalized. By contrast, the usual Montgomery ladder costs $4M + 4S + 1m + 1m_0$ by bit, for a normalized point. In the long version of the paper, we extend our approach to higher dimensional ladders in theta coordinates or twisted theta coordinates. In dimension~$2$, after a precomputation step which depends on the base point~$P$, our half ladder only costs $7\cM + 4\cS+3\cm_0$, compared to $10\cM+9\cS+6\cm_0$ for the standard ladder.

Updatable public-key encryption (UPKE) allows anyone to update a public key while simultaneously producing an update token, given which the secret key holder could consistently update the secret key. Furthermore, ciphertexts encrypted under the old public key remain secure even if the updated secret key is leaked -- a property much desired in secure messaging. All existing lattice-based constructions of UPKE update keys by a noisy linear shift. As the noise accumulates, these schemes either require super-polynomial-size moduli or an a priori bounded number of updates to maintain decryption correctness. Inspired by recent works on cryptography based on the lattice isomorphism problem, we propose an alternative way to update keys in lattice-based UPKE. Instead of shifting, we rotate them. As rotations do not induce norm growth, our construction supports an unbounded number of updates with a polynomial-size modulus. The security of our scheme is based on the LWE assumption over hollow matrices -- matrices which generate linear codes with non-trivial hull -- and the hardness of permutation code equivalence. Along the way, we also show that LWE over hollow matrices is as hard as LWE over uniform matrices, and that a leftover hash lemma holds for hollow matrices.

In this work, we consider the communication complexity of MPC protocol in honest majority setting achieving malicious security in both information-theoretic setting and computational setting. On the one hand, we study the possibility of basing honest majority MPC protocols on oblivious linear evaluation (OLE)-hybrid model efficiently. More precisely, we instantiate preprocessing phase of the recent work Sharing Transformation (Goyal, Polychroniadou and Song, CRYPTO 2022) assuming random OLE correlations. Notably, we are able to prepare packed Beaver triples with malicious security achieving amortized communication $O(n)$ field elements plus $O(n)$ number of OLE correlations per packed Beaver triple, which is the best known result. To further efficiently prepare random OLE correlations, we resort to IKNP-style OT extension protocols (CRYPTO 2003) in random oracle model. On the other hand, we derive a communication lower bound for preparing OLE correlations in the information-theoretic setting based on negative results due to Damg{\aa}rd, Larsen, and Nielsen (CRYPTO 2019). Combining our positive result with the work of Goyal, Polychroniadou and Song (CRYPTO 2022), we derive an MPC protocol with amortized communication of $O(\ell+\kappa)$ elements per gate in random oracle model achieving malicious security, where $\ell$ denotes the length of a field element and $\kappa$ is the security parameter.

A hybrid cryptosystem combines two systems that fulfill the same cryptographic functionality, and its security enjoys the security of the harder one. There are many proposals for hybrid public-key encryption (hybrid PKE), hybrid signature (hybrid SIG) and hybrid authenticated key exchange (hybrid AKE). In this paper, we fill the blank of Hybrid Password Authentication Key Exchange (hybrid PAKE). For constructing hybrid PAKE, we first define an important class of PAKE -- full DH-type PAKE, from which we abstract sufficient properties to achieve UC security. Our full DH-type PAKE framework unifies lots of PAKE schemes like SPAKE2, TBPEKE, (Crs)X-GA-PAKE, and summarizes their common features for UC security. Stepping from full DH-type PAKE, we propose two generic approaches to hybrid PAKE, parallel composition and serial composition. -- We propose a generic construction of hybrid PAKE via parallel composition and prove that the hybrid PAKE by composing DH-type PAKEs in parallel is a full DH-type PAKE and hence achieves UC security, as long as one underlying DH-type PAKE is a full DH-type. -- We propose a generic construction of hybrid PAKE via serial composition, and prove that the hybrid PAKE by composing a DH-type PAKE and another PAKE in serial achieves UC security, if either the DH-type PAKE is a full DH-type or the other PAKE has UC security and the DH-type PAKE only has some statistical properties. Our generic constructions of hybrid PAKE result in a variety of hybrid PAKE schemes enjoying different nice features, like round-optimal, high efficiency, or UC security in quantum random oracle model (QROM).

ChaCha is a widely deployed stream cipher and one of the most important symmetric primitives. Due to this practical importance, many cryptanalysis have been proposed. Until now, Probabilistic Neutral Bits (PNBs) have been the most successful. Given differential-linear distinguishers, PNBs are the technique for key recovery relying on an experimental backward correlation obtained through blackbox analysis. A careful theoretical analysis exploiting the round function design may find a better attack and improve our understanding, but the complicated nature of the ARX structure makes such analysis difficult. We propose a theoretical methodology inspired by bit puncturing, which was recently proposed at Eurocrypt 2024. Our method has a theoretical foundation and is thus fundamentally different from PNBs, to which it is the first effective alternative. As a result, we significantly improved the attack complexity for 6, 7, and 7.5-round ChaCha. The 7-round attack is about $2^{40}$ times faster than the previous best. Furthermore, we propose the first 7.5-round attack with a non-negligible advantage over an exhaustive search.

Collision-resistant hashing (CRH) is a cornerstone of cryptographic protocols. However, despite decades of research, no construction of a CRH based solely on one-way functions has been found. Moreover, there are black-box limitations that separate these two primitives. Harnik and Naor [HarnikN10] overcame this black-box barrier by introducing the notion of instance compression. Instance compression reduces large NP instances to a size that depends on their witness size while preserving the ``correctness'' of the instance relative to the language. Shortly thereafter, Fortnow and Santhanam showed that efficient instance compression algorithms are unlikely to exist (as the polynomial hierarchy would collapse). Bronfman and Rothblum defined a computational analog of instance compression, which they called computational instance compression (CIC), and gave a construction of CIC under standard assumptions. Unfortunately, this notion is not strong enough to replace instance compression in Harnik and Naor's CRH construction. In this work, we revisit the notion of computational instance compression and ask what the ``correct'' notion for CIC is, in the sense that it is sufficiently strong to achieve useful cryptographic primitives while remaining consistent with common assumptions. First, we give a natural strengthening of the CIC definition that serves as a direct substitute for the instance compression scheme in the Harnik-Naor construction. However, we show that even this notion is unlikely to exist. We then identify a notion of CIC that gives new hope for constructing CRH from one-way functions via instance compression. We observe that this notion is achievable under standard assumptions and, by revisiting the Harnik-Naor proof, demonstrate that it is sufficiently strong to achieve CRH. In fact, we show that our CIC notion is existentially equivalent to CRH. Beyond Minicrypt, Harnik and Naor showed that a strengthening of instance compression can be used to construct OT and public-key encryption. We rule out the computational analog of this stronger notion by showing that it contradicts the existence of incompressible public-key encryption, which was recently constructed under standard assumptions.

It is well known that a trusted setup allows one to solve the Byzantine agreement problem in the presence of t < n/2 corruptions, bypassing the setup-free t < n/3 barrier. Alas, the overwhelming majority of protocols in the literature have the caveat that their security crucially hinges on the security of the cryptography and setup, to the point where if the cryptography is broken, even a single corrupted party can violate the security of the protocol. Thus these protocols provide higher corruption resilience (n/2 instead of n/3) for the price of increased assumptions. Is this trade-off necessary? We further the study of _crypto-agnostic_ Byzantine agreement among n parties that answers this question in the negative. Specifically, let t_s and t_i denote two parameters such that (1) 2t_i + t_s < n, and (2) t_i <= t_s < n/2. Crypto-agnostic Byzantine agreement ensures agreement among honest parties if (1) the adversary is computationally bounded and corrupts up to t_s parties, or (2) the adversary is computationally unbounded and corrupts up to t_i parties, and is moreover given all secrets of all parties established during the setup. We propose a compiler that transforms any pair of resilience-optimal Byzantine agreement protocols in the authenticated and information-theoretic setting into one that is crypto-agnostic. Our compiler has several attractive qualities, including using only O(lambda n^2) bits over the two underlying Byzantine agreement protocols, and preserving round and communication complexity in the authenticated setting. In particular, our results improve the state-of-the-art bit complexity by at least two factors of n and provide either early stopping (deterministic) or expected constant round complexity (randomized). We therefore provide fallback security for authenticated Byzantine agreement _for free_ for t_i <= n/4.

Key derivation functions (KDFs) are integral to many cryp- tographic protocols. Their functionality is to turn raw key material, such as a Diffie–Hellman secret, into a strong cryptographic key that is indis- tinguishable from random. This guarantee was formalized by Krawczyk together with the seminal introduction of HKDF (CRYPTO 2010), in a model where the KDF only takes a single key material input. Modern protocol designs, however, regularly need to combine multiple secrets, possibly even from different sources, with the guarantee that the derived key is secure as long as at least one of the inputs is good. This is par- ticularly relevant in settings like hybrid key exchange for quantum-safe migration. Krawczyk’s KDF formalism does not capture this goal, and there has been surprisingly little work on the security considerations for KDFs since then. In this work, we thus revisit the syntax and security model for KDFs to treat multiple, possibly correlated inputs. Our syntax is assertive: We do away with salts, which are needed in theory to extract from arbitrary sources in the standard model, but in practice, they are almost never used (or even available) and sometimes even misused, as we argue. We use our new model to analyze real-world multi-input KDFs—in Signal’s X3DH protocol, ETSI’s TS 103-744 standard, and MLS’ combiner for pre-shared keys—as well as new constructions we introduce for specialized settings— e.g., a purely blockcipher-based one. We further discuss the importance of collision resistance for KDFs and finally apply our multi-input KDF model to show how hybrid KEM key exchange can be analyzed from a KDF perspective.

We show that the smallness of message spaces can be used as a checksum allowing to hedge against CCA1 attacks in additively homomorphic encryption schemes. We first show that the additively homomorphic variant of Damg{\aa}rd's Elgamal provides IND-CCA1 security under the standard DDH assumption. Earlier proofs either required non-standard assumptions or only applied to hybrid versions of Damg{\aa}rd's Elgamal, which are not additively homomorphic. Our security proof builds on hash proof systems and exploits the fact that encrypted messages must be contained in a polynomial-size interval in order to enable decryption. With $3$ group elements per ciphertext, this positions Damg{\aa}rd's Elgamal as the most efficient/compact DDH-based additively homomorphic CCA1 cryptosystem. Under the same assumption, the best candidate so far was the lite Cramer-Shoup cryptosystem, where ciphertexts consist of $4$ group elements. We extend this observation to build an IND-CCA1 variant of the Boneh-Goh-Nissim encryption scheme, which allows evaluating $2$-DNF formulas on encrypted data. By computing tensor products of Damg{\aa}rd's Elgamal ciphertexts, we obtain product ciphertexts consisting of $9$ elements (instead of $16$ elements if we were tensoring lite Cramer-Shoup ciphertexts) in the target group of a bilinear map. Using similar ideas, we also obtain a CCA1 variant of the Elgamal-Paillier cryptosystem by forcing $\lambda$ plaintext bits to be zeroes, which yields CCA1 security almost for free. In particular, the message space remains exponentially large and ciphertexts are as short as in the IND-CPA scheme. We finally adapt the technique to the Castagnos-Laguillaumie system.

We give a new protocol for reliable broadcast with improved communication complexity for long messages. Namely, to reliably broadcast a message a message $m$ over an asynchronous network to a set of $n$ parties, of which fewer than $n/3$ may be corrupt, our protocol achieves a communication complexity of $1.5 |m| n + O( \kappa n^2 \log(n) )$, where $\kappa$ is the output length of a collision-resistant hash function. This result improves on the previously best known bound for long messages of $2 |m| n + O(\kappa n^2 \log(n))$.

Publicly identifiable abort is a critical feature for ensuring accountability in outsourced computations using secure multiparty computation (MPC). Despite its importance, no prior work has specifically addressed identifiable abort in the context of outsourced computations. In this paper, we present the first MPC protocol that supports publicly identifiable abort with minimal overhead for external clients. Our approach minimizes client-side computation by requiring only a few pseudorandom function evaluations per input. On the server side, the verification process involves lightweight linear function evaluations using homomorphic encryption. This results in verification times of a few nanoseconds per operation for servers, with client overhead being approximately two orders of magnitude lower. Additionally, the public verifiability of our protocol reduces client input/output costs compared to SPDZ-based protocols, on which we base our protocol. For example, in secure aggregation use cases, our protocol achieves over twice the efficiency during the offline phase and up to an 18 % speedup in the online phase, significantly outperforming SPDZ.

Homomorphic secret sharing (HSS) is a distributed analogue of fully homomorphic encryption (FHE) where following an input-sharing phase, two or more parties can locally compute a function over their private inputs to obtain shares of the function output. Over the last decade, HSS schemes have been constructed from an array of different assumptions. However, all existing HSS schemes, except ones based on assumptions known to imply multi-key FHE, require a public-key infrastructure (PKI) or a correlated setup between parties. This limitation carries over to many applications of HSS. In this work, we construct *multi-key* homomorphic secret sharing (MKHSS), where given only a common reference string (CRS), two parties can secret share their inputs to each other and then perform local computations as in HSS, eliminating the need for PKI or a correlated setup. Specifically, we present the first MKHSS schemes supporting all NC1 computations from either the decisional Diffie--Hellman (DDH) assumption, the decisional composite residuosity (DCR) assumption, or DDH-like assumptions in class group. Our constructions imply the following applications in the CRS model: - Succinct two-round secure computation. Under the same assumptions as our MKHSS schemes, we construct a succinct, two-round, two-party secure computation protocol for NC1 circuits. Previously, such a result was only known from the learning with errors assumption. - Attribute-based NIKE. Under DCR or class group assumptions, we construct non-interactive key exchange (NIKE) protocols where two parties agree on a key if and only if their secret attributes satisfy a public NC1 predicate. This significantly generalizes the existing notion of password-based NIKE. - Public-key PCFs. Under DCR or class group assumptions, we construct public-key pseudorandom correlation functions (PCFs) for any NC1 correlation. This yields the first public-key PCFs for Beaver triples (and more) from non-lattice assumptions. - Silent MPC. Under DCR or class group assumptions, we construct a p-party secure computation protocol in the silent preprocessing model where the preprocessing phase has communication O(p), ignoring polynomial factors. All prior protocols that do not rely on multi-key FHE techniques require ω(p²) communication.

Recent constructions of vector commitments and non-interactive zero-knowledge (NIZK) proofs from LWE implicitly solve the following shifted multi-preimage sampling problem: given matrices $\mathbf{A}_1, \ldots, \mathbf{A}_\ell \in \mathbb{Z}_q^{n \times m}$ and targets $\mathbf{t}_1, \ldots, \mathbf{t}_\ell \in \mathbb{Z}_q^n$, sample a shift $\mathbf{c} \in \mathbb{Z}_q^n$ and short preimages $\boldsymbol{\pi}_1, \ldots, \boldsymbol{\pi}_\ell \in \mathbb{Z}_q^m$ such that $\mathbf{A}_i \boldsymbol{\pi}_i = \mathbf{t}_i + \mathbf{c}$ for all $i \in [\ell]$. In this work, we introduce a new technique for sampling $\mathbf{A}_1, \ldots, \mathbf{A}_\ell$ together with a succinct public trapdoor for solving the multi-preimage sampling problem with respect to $\mathbf{A}_1, \ldots, \mathbf{A}_\ell$. This enables the following applications: * We provide a dual-mode instantiation of the hidden-bits model (and by correspondence, a dual-mode NIZK proof for $\mathsf{NP}$) with (1) a linear-size common reference string (CRS); (2) a transparent setup in hiding mode (which yields statistical NIZK arguments); and (3) hardness from LWE with a polynomial modulus-to-noise ratio. This improves upon the work of Waters (STOC 2024) which required a quadratic-size structured reference string (in both modes) and LWE with a super-polynomial modulus-to-noise ratio. * We give a statistically-hiding vector commitment with transparent setup and polylogarithmic-size CRS, commitments, and openings from SIS. This simultaneously improves upon the vector commitment schemes of de Castro and Peikert (EUROCRYPT 2023) as well as Wee and Wu (EUROCRYPT 2023). At a conceptual level, our work provides a unified view of recent lattice-based vector commitments and hidden-bits model NIZKs through the lens of the shifted multi-preimage sampling problem.

The random probing model formalizes a leakage scenario where each wire in a circuit leaks with probability $p$. This model holds practical relevance due to its reduction to the noisy leakage model, which is widely regarded as the appropriate formalization for power and electromagnetic side-channel attacks. In this paper, we present new techniques for designing efficient masking schemes that achieve tighter random probing security with lower complexity. First, we introduce the notion of cardinal random probing composability (Cardinal-RPC), offering a new trade-off between complexity and security for composing masking gadgets. Next, we propose a novel refresh technique based on a simple iterative process: randomly selecting and updating two shares with fresh randomness. While not perfectly secure in the standard probing model, this method achieves arbitrary cardinal-RPC security, making it a versatile tool for constructing random-probing secure circuits. Using this refresh, we develop additional basic gadgets (e.g., linear multiplication, addition, and copy) that satisfy the cardinal-RPC notion. Despite the increased complexity, the gains in security significantly outweigh the overhead, with the number of iterations offering useful flexibility. To showcase our techniques, we apply them to lattice-based signatures. Specifically, we introduce a new random-probing composable gadget for sampling small noise, a key component in various post-quantum algorithms. To assess security in this context, we generalize the random probing security model to address auxiliary inputs and public outputs. We apply our findings to Raccoon, a masking-friendly signature scheme originally designed for standard probing security. We prove the secure composition of our new gadgets for key generation and signature computation, and show that our masking scheme achieves a superior security-performance tradeoff compared to previous approaches based on random probing expansion. To our knowledge, this is the first fully secure instantiation of a post-quantum algorithm in the random probing model.

The Doubly-Efficient Private Information Retrieval (DEPIR) protocol of Lin, Mook, and Wichs (STOC'23) relies on a Homomorphic Encryption (HE) scheme that is algebraic, i.e., whose ciphertext space has a ring structure that matches the homomorphic operations. Since modern, well-studied HE schemes are not algebraic, an important prerequisite for practical DEPIR is to find an efficient algebraic HE scheme. In this work, we study the properties of algebraic HE and try to make progress in solving this problem. We first prove a lower bound of 2^Ω(2^d) for the ciphertext ring size of post-quantum algebraic HE schemes (in terms of the depth d of the evaluated circuit), which demonstrates a gap between optimal algebraic HE and the existing schemes, which have a ciphertext ring size of 2^O(2^(2d)). As we are unable to bridge this gap directly, we instead slightly relax the notion of being algebraic. This allows us to construct a practically more efficient relaxed-algebraic HE scheme, which indeed leads to a more efficient instantiation and implementation of DEPIR. We experimentally demonstrate run-time improvements of more than 4x for benchmarked parameters and reduce memory queries by 23x for larger parameters compared to prior work. Notably, our relaxed-algebraic HE scheme relies on a new variant of the Ring Learning with Errors (RLWE) problem that we call {0, 1}-CRT RLWE. We give a formal security reduction from standard RLWE, and estimate its concrete security. Both the {0, 1}-CRT RLWE problem and the techniques used for the reduction may be of independent interest.

We show a black box barrier against constructing public key quantum money from obfuscation for evasive functions. As current post-quantum obfuscators based on standard assumptions are all evasive, this shows a fundamental barrier to achieving public key quantum money from standard tools. Our impossibility applies to black box schemes where (1) obfuscation queries made by the mint are classical, and (2) the verifier only makes (possibly quantum) evaluation queries, but no obfuscation queries. This class seems to capture any natural method of using obfuscation to build quantum money.

We study recent algebraic attacks (Briaud-Øygarden EC’23) on the Regular Syndrome Decoding (RSD) problem and the assumptions underlying the correctness of the attack’s complexity estimates. By relating these assumptions to interesting algebraic-combinatorial problems, we prove that they do not hold in full generality. However, we show that they are (asymptotically) true for most parameter sets, supporting the soundness of algebraic attacks on RSD. Further, we prove—without any heuristics or assumptions—that RSD can be broken in polynomial time whenever the number of error blocks times the square of the size of error blocks is larger than 2 times the square of the dimension of the code. Additionally, we use our methodology to attack a variant of the Learning With Errors problem where each error term lies in a fixed set of constant size. We prove that this problem can be broken in polynomial time, given a sufficient number of samples. This result improves on the seminal work by Arora and Ge (ICALP’11), as the attack’s time complexity is independent of the LWE modulus.

We use pairings over elliptic curves to give a collusion-resistant traitor tracing scheme where the sizes of public keys, secret keys, and ciphertexts are independent of the number of users. Prior constructions from pairings had size N^{1/3}. An additional consequence of our techniques is general result showing that attribute-based encryption for circuits generically implies optimal traitor tracing.

We study single-server private information retrieval (PIR) where a client wishes to privately retrieve the $x$-th entry from a database held by a server without revealing the index $x$. In our work, we focus on PIR with client pre-processing where the client may compute hints during an offline phase. The hints are then leveraged during queries to obtain sub-linear online time. We present {\em Plinko} that is the first single-server PIR with client pre-processing that obtains optimal trade-offs between client storage and total (client and server) query time for all parameters. Our scheme uses $t = \tilde{O}(n/r)$ query time for any client storage size $r$. This matches known lower bounds of $r \cdot t = \Omega(n)$ up to logarithmic factors for all parameterizations whereas prior works could only match the lower bound when $r = \tilde{O}(\sqrt{n})$. Moreover, Plinko is also the first {\em updateable} PIR scheme where an entry can be updated in worst-case $\tilde{O}(1)$ time. As our main technical tool, we define the notion of an {\em invertible pseudorandom function} ({\em iPRF}) that generalizes standard PRFs to be equipped with an efficient inversion algorithm. We present a construction of an iPRF from one-way functions where forward evaluation runs in $\tilde{O}(1)$ time and inversion runs in time linear in the inverse set (output) size. Furthermore, our iPRF construction is the first that remains efficient and secure for arbitrary domain and range sizes (including small domains and ranges). In the context of single-server PIR, we show that iPRFs may be used to construct the first hint set representation where finding a hint containing an entry $x$ may be done in $\tilde{O}(1)$ time.

Conventional hash functions are often inefficient in zero-knowledge proof settings, leading to design of several ZK-friendly hash functions. On the other hand, lookup arguments have recently been incorporated into zero-knowledge protocols, allowing for more efficient handling of ``ZK-unfriendly'' operations, and hence ZK-friendly hash functions based on lookup tables. In this paper, we propose a new ZK-friendly hash function, dubbed Polocolo, that employs an S-box constructed using power residues. Our approach reduces the numbers of gates required for table lookups, in particular, when combined with Plonk, allowing one to use such nonlinear layers over multiple rounds. We also propose a new MDS matrix for the linear layer of Polocolo. In this way, Polocolo requires fewer Plonk gates compared to the state-of-the-art ZK-friendly hash functions. For example, when t = 8, Polocolo requires 21% less Plonk gates compared to Anemoi, which is currently the most efficient ZK-friendly hash function, where t denotes the size of the underlying permutation in blocks of F_p. For t = 3, Polocolo requires 24% less Plonk gates than Reinforced Concrete, which is one of the recent lookup-based ZK-friendly hash functions.

Noisy linear algebraic assumptions with respect to random matrices, in particular Learning with Errors ($\LWE$) and Alekhnovich Learning Parity with Noise (Alekhnovich $\LPN$), are among the most investigated assumptions that imply post-quantum public-key encryption (PKE). They enjoy elegant mathematical structure. Indeed, efforts to build post-quantum PKE and advanced primitives such as homomorphic encryption and indistinguishability obfuscation have increasingly focused their attention on these two assumptions and their variants. Unfortunately, this increasing reliance on these two assumptions for building post-quantum cryptography leaves us vulnerable to potential quantum (and classical) attacks on Alekhnovich $\LPN$ and $\LWE$. Quantum algorithms is a rapidly advancing area, and we must stay prepared for unexpected cryptanalytic breakthroughs. Just three decades ago, a short time frame in the development of our field, Shor's algorithm rendered most then-popular number theoretic and algebraic assumptions quantumly broken. Furthermore, within the last several years, we have witnessed major classical and quantum breaks on several assumptions previously introduced for post-quantum cryptography. Therefore, we ask the following question: \begin{center} \emph{In a world where both $\LWE$ and Alekhnovich $\LPN$ are broken, can there still exist noisy linear assumptions that remain plausibly quantum hard and imply PKE?} \end{center} To answer this question positively, we introduce two natural noisy-linear algebraic assumptions that are both with respect to random matrices, exactly like $\LWE$ and Alekhnovich $\LPN$, but with different error distributions. Our error distribution combines aspects of both small norm and sparse error distributions. We design a PKE from these assumptions and give evidence that these assumptions are likely to still be secure even in a world where both the $\LWE$ and Alekhnovich $\LPN$ assumptions are simultaneously broken. We also study basic properties of these assumptions, and show that in the parameter settings we employ to build PKE, neither of them are ``lattice'' assumptions in the sense that we don't see a way to attack them using a lattice closest vector problem solver, except via $\NP$-completeness reductions.

Although privately programmable pseudorandom functions (PPPRFs) are known to have numerous applications, so far, the only known constructions rely on Learning with Error (LWE) or indistinguishability obfuscation. We show how to construct a relaxed PPPRF with only one-way functions (OWF). The resulting PPPRF satisfies 1/poly security and works for polynomially sized input domains. Using the resulting PPPRF, we can get new results for preprocessing Private Information Retrieval (PIR) that improve the state of the art. Specifically, we show that relying only on OWF, we can get a 2-server preprocessing PIR with polylogarithmic bandwidth while consuming $\widetilde{O}_\lambda(N^{\frac12 + \eps})$ client space and $N^{1+\eps}$ server space for an arbitrarily small constant $\eps \in (0, 1)$. In the 1-server setting, we get a preprocessing PIR from OWF that achieves polylogarithmic {\it online} bandwidth and $\widetilde{O}_\lambda(N^{\frac12 + \eps})$ {\it offline} bandwidth, while preserving the same client and server space as before. Our result, in combination with the lower bound of Ishai, Shi, and Wichs (CRYPTO'24), establishes a tight understanding of the bandwidth and client space tradeoff for 1-server preprocessing PIR from Minicrypt assumptions. Interestingly, we are also the first to show non-trivial ways to combine client-side and server-side preprocessing to get improved results for PIR.

In this work, we consider the problem of secure key leasing, also known as revocable cryptography (Agarwal et. al. Eurocrypt' 23, Ananth et. al. TCC' 23), as a strengthened security notion of its predecessor put forward in Ananth et. al. Eurocrypt' 21. This problem aims to leverage unclonable nature of quantum information to allow a lessor to lease a quantum key with reusability for evaluating a classical functionality. Later, the lessor can request the lessee to provably delete the key and then the lessee will be completely deprived of the capability to evaluate the function. In this work, we construct a secure key leasing scheme to lease a decryption key of a (classical) public-key, homomorphic encryption scheme from standard lattice assumptions. Our encryption scheme is exactly identical to the (primal) version of Gentry-Sahai-Waters homomorphic encryption scheme with a carefully chosen public key matrix. We achieve strong form of security where: * The entire protocol (including key generation and verification of deletion) uses merely classical communication between a classical lessor (client) and a quantum lessee (server). * Assuming standard assumptions, our security definition ensures that every computationally bounded quantum adversary could only simultaneously provide a valid classical deletion certificate and yet distinguish ciphertexts with at most negligible probability. Our security relies on the hardness of learning with errors assumption. Our scheme is the first scheme to be based on a standard assumption and satisfying the two properties mentioned above. The main technical novelty in our work is the design of an FHE scheme that enables us to apply elegant analyses done in the context of classically verifiable proofs of quantumness from LWE (Brakerski et. al.(FOCS'18, JACM'21) and its parallel amplified version in Radian et. al.(AFT'21)) to the setting of secure leasing. This connection leads to a modular construction and arguably simpler proofs than previously known. An important technical component we prove along the way is an amplified quantum search-to-decision reduction: we design an extractor that uses a quantum distinguisher (who has an internal quantum state) for decisional LWE, to extract secrets with success probability amplified to almost one. This technique might be of independent interest.

A central direction of research in secure multiparty computation with dishonest majority has been to achieve three main goals: 1. reduce the total number of rounds of communication (to four, which is optimal); 2. use only polynomial-time hardness assumptions, and 3. rely solely on cryptographic assumptions in a black-box manner. This is especially challenging when we do not allow a trusted setup assumption of any kind. While protocols achieving two out of three goals in this setting have been designed in recent literature, achieving all three simultaneously remained an elusive open question. Specifically, it was answered positively only for a restricted class of functionalities. In this paper, we completely resolve this long-standing open question. Specifically, we present a protocol for all polynomial-time computable functions that does not require any trusted setup assumptions and achieves all three of the above goals simultaneously.

The CKKS fully homomorphic encryption scheme enables efficient homomorphic operations in terms of throughput, but its bootstrapping algorithm incurs a significant latency. In this work, we introduce SHIP, a novel bootstrapping algorithm for CKKS ciphertexts. SHIP enjoys a very shallow homomorphic multiplicative depth compared to state-of-the-art CKKS bootstrapping algorithms. Bootstrapping depth directly impacts the required Ring-LWE modulus, and hence the Ring-LWE degree. The massive depth saving allows us to report the first bootstrapping of CKKS ciphertexts for full-dimensional cleartext vectors in ring degree N=2^{13}, without resorting to an expensive scheme switching to DM/CGGI. SHIP also enjoys great parallelizability, with minimal communication between threads. The combined ring size reduction and high parallelizability lead to very low latency. In ring degree N=2^{13}, our experimental implementation runs in 215ms on a 32-core CPU for real-valued cleartext vectors. This is 2.5x lower than the smallest latency we could observe with the HEaaN library (using 48 cores). For binary cleartext vectors, the latency is lowered to 174ms, which is 2.2x lower than Bae et al [Eurocrypt'24] (with 32 cores).

In this work, we study the singular locus of the varieties defined by the public keys of UOV and VOX, two multivariate signature schemes submitted to the additional NIST call for post-quantum signature schemes. We give a new attack for UOV^+ and VOX targeting singular points of the underlying UOV key. Our attack lowers the security of the schemes, both asymptotically and in number of gates, showing in particular that the parameter sets proposed for these schemes do not meet the NIST security requirements. More precisely, we show that the security of VOX/UOV^+ was overestimated by factors $2^{2}, 2^{18}, 2^{37}$ for security levels I, III, V respectively. As an essential element of the attack on VOX, we introduce a polynomial time algorithm performing a key recovery from one vector, with an implementation requiring only $15$ seconds at security level V.

Cryptographic proof systems have a plethora of applications: from building other cryptographic tools (e.g., malicious security for MPC protocols) to concrete settings such as private transactions or rollups. In several settings it is important for proof systems to be non-malleable: an adversary should not to be able to modify a proof they have observed into another for a statement for which they do not know the witness. Proof systems that have been deployed in practice should arguably satisfy this notion: it is crucial in settings such as transaction systems and in order to securely compose proofs with other cryptographic protocols. As a consequence, results on non-malleability should keep up with designs of proofs being deployed. Recently, Arun et al. proposed Jolt (Eurocrypt 2024), the first efficient proof system whose architecture is based on the lookup singularity approach (Barry Whitehat, 2022). This approach consists of representing a general computation as a series of table lookups. The final result is a SNARK for a Virtual Machine execution (or SNARK VM). Both SNARK VMs and lookup-singularity SNARKs are architectures with enormous potential and will probably be adopted more and more in the next years (and they already are). As of today, however, there is no literature regarding the non-malleability of SNARK VMs. The goal of this work is to fill this gap by providing both concrete non-malleability results and a set of technical tools for a more general study of SNARK VMs security (as well as “modular” SNARKs in general). As a concrete result, we study the non-malleability of (an idealized version of) Jolt and its fundamental building block, the lookup argument Lasso. While connecting our new result on the non-malleability of Lasso to that of Jolt, we develop a set of tools that enable the composition of non-malleable SNARKs. We find this toolbox valuable in its own right.

We introduce an efficient SNARK for towers of binary fields. Adapting Brakedown (CRYPTO '23), we construct a multilinear polynomial commitment scheme suitable for polynomials over tiny fields, including that with just two elements. Our commitment scheme, unlike those of previous works, treats small-field polynomials with no embedding overhead. We further introduce binary-field adaptations of HyperPlonk (EUROCRYPT '23)'s product and permutation checks and of Lasso (EUROCRYPT '24)'s lookup. Our binary PLONKish variant captures standard hash functions—like Keccak-256 and Grøstl—extremely efficiently. With recourse to thorough performance benchmarks, we argue that our scheme can efficiently generate precisely those Keccak-256-proofs which critically underlie modern efforts to scale Ethereum.

An Oblivious Pseudo-Random Function (OPRF) is a two-party protocol for jointly evaluating a Pseudo-Random Function (PRF), where a user has an input x and a server has an input k. At the end of the protocol, the user learns the evaluation of the PRF using key k at the value x, while the server learns nothing about the user's input or output. OPRFs are a prime tool for building secure authentication and key exchange from passwords, private set intersection, private information retrieval, and many other privacy-preserving systems. While classical OPRFs run as fast as a TLS Handshake, current *quantum-safe* OPRF candidates are still practically inefficient. In this paper, we propose a framework for constructing OPRFs from post-quantum multi-party computation. The framework captures a family of so-called "2Hash PRFs", which sandwich a function evaluation in between two hashes. The core of our framework is a compiler that yields an OPRF from a secure evaluation of any function that is key-collision resistant and one-more unpredictable. We instantiate this compiler by providing such functions built from Legendre symbols, and from AES encryption. We then give a case-tailored protocol for securely evaluating our Legendre-based function, built from oblivious transfer (OT) and zero-knowledge proofs (ZKP). Instantiated with lattice-based OT and ZKPs, we obtain a quantum-safe OPRF that completes in 0.57 seconds, with less than 1MB of communication.

The (parallel) classical black pebbling game is a helpful abstraction which allows us to analyze the resources (time, space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$ on a (parallel) computer. In particular, the parallel black pebbling game has been used as a tool to quantify the (in)security of Data-Independent Memory-Hard Functions (iMHFs). However, the classical black pebbling game is not suitable to analyze the cost of quantum preimage attack. Thus, Blocki, Holman, and Lee (TCC 2022) introduced the parallel reversible pebbling game as a tool to analyze resource requirements for a quantum computer. While there is an extensive line of work analyzing pebbling complexity in the (parallel) black pebbling game, comparatively little is known about the parallel reversible pebbling game. Our first result is a lower bound of $\Omega\left(N^{1+\sqrt{\frac{ 2-o(1)}{\log N}}}\right)$ on the reversible cumulative pebbling cost for a line graph on $N$ nodes. This yields a separation between classical and reversible pebbling costs demonstrating that the reversibility constraint can increase cumulative pebbling costs (and space-time costs) by a multiplicative factor of $N^{(\sqrt 2 + o(1))/\sqrt{\log N}}$ --- the classical pebbling cost (space-time or cumulative) for a line graph is just $\mathcal{O}(N)$. On the positive side, we prove that \emph{any} classical parallel pebbling can be transformed into a reversible pebbling strategy whilst increasing space-time (resp. cumulative memory) costs by a multiplicative factor of at most $\mathcal{O}\left(N^{\sqrt{\frac{8}{\log N}}}\right)$ (resp. $\mathcal{O}\left(N^{\mathcal{O}(1)/\sqrt[4]{\log N}}\right)$). We also analyze the impact of the reversibility constraint on the cumulative pebbling cost of depth-robust and depth-reducible DAGs exploiting reversibility to improve constant factors in a prior lower bound of Alwen, Blocki, and Pietrzak (Eurocrypt 2017). For depth-reducible DAGs we show that the state-of-the-art recursive pebbling techniques of Alwen, Blocki, and Pietrzak (Eurocrypt 2017) can be converted into a recursive reversible pebbling attack without any asymptotic increases in pebbling costs. Finally, we extend a result of Blocki, Lee, and Zhou (ITCS 2020) to show that it is Unique Games-hard to approximate the reversible cumulative pebbling cost of a DAG $G$ to within any constant factor.

We present a new distinguisher for alternant and Goppa codes, whose complexity is subexponential in the error-correcting capability, hence better than that of generic decoding algorithms. Moreover it does not suffer from the strong regime limitations of the previous distinguishers or structure recovery algorithms: in particular, it applies to the codes used in the Classic McEliece candidate for postquantum cryptography standardization. The invariants that allow us to distinguish are graded Betti numbers of the homogeneous coordinate ring of a shortening of the dual code. Since its introduction in 1978, this is the first time an analysis of the McEliece cryptosystem breaks the exponential barrier.

To counteract side-channel attacks, a masking scheme splits each intermediate variable into $n$ shares and transforms each elementary operation (e.g., field addition and multiplication) to the masked correspondence called gadget, such that intrinsic noise in the leakages renders secret recovery infeasible in practice. A simple and efficient security notion is the probing model ensuring that any $n-1$ shares are independently distributed from the secret input. One requirement of the probing model is that the noise in the leakages should increase with the number of shares, largely restricting the side-channel security in the low-noise scenario. Another security notion for masking, called the random probing model, allows each variable to leak with a probability $p$. While this model reflects the physical reality of side channels much better, it brings significant overhead. At Crypto 2018, Ananth et al. proposed a modular approach that can provide random probing security for any security level by expanding small base gadgets with $n$ share recursively, such that the tolerable leakage probability $p$ decreases with $n$ while the security increases exponentially with the recursion depth of expansion. Then, Bela{\"{i}}d et al. provided a formal security definition called Random Probing Expandability~(RPE) and an explicit framework using the modular approach to construct masking schemes at Crypto 2020. In this paper, we investigate how to tighten the RPE definition via allowing the dependent failure probabilities of multiple inputs, which results in a new definition called related RPE. It can be directly used for the expansion of multiplication gates and reduce the complexity of the base multiplication gadget from $\mathcal{O}(n^2\log n)$ proposed at Asiacrypt 2021 to $\mathcal{O}(n^2)$ and maintain the same security level. Furthermore, we describe a method to expand any gates (rather than only multiplication) with the related RPE gadgets. Besides, we denote another new RPE definition called Multiple inputs RPE used for the expansion of multiple-input gates composed with any gates. Utilizing these methods, we reduce the complexity of the 3-share circuit compiler to $\mathcal{O}(|C|\cdot\kappa^{3.2})$, where $|C|$ is the size of the unprotected circuit and the protection failure probability of the global circuit is $2^{-\kappa}$. In comparison, the complexity of the state-of-the-art work, proposed at Eurocrypt 2021, is $\mathcal{O}(|C|\cdot\kappa^{3.9})$ for the same value of $n$. Additionally, we provide the construction of a 5-share circuit compiler with a complexity $\mathcal{O}(|C|\cdot\kappa^{2.8})$.

The public comments received for the review process for NIST (SP) 800-38A pointed out two important issues that most companies face: (1) the limited security that AES can provide due to its 128-bit block size and (2) the problem of nonce-misuse in practice. In this paper, we provide an alternative solution to these problems by introducing two optimally secure deterministic authenticated encryption (DAE) schemes, denoted as DENC1 and DENC2 respectively. We show that our proposed constructions improve the state-of-the-art in terms of security and efficiency. Specifically, DENC1 achieves a robust security level of $O(r^2\sigma^2\ell/2^{2n})$, while DENC2 attains a near-optimal security level of $O(r\sigma/2^{n})$, where $\sigma$ is the total number of blocks, $\ell$ is maximum number of blocks in each query, and $r$ is a user-defined parameter closely related to the rate of the construction. Our research centers on the development of two IV-based encryption schemes, referred to as IV1 and IV2, which respectively offer security levels of $O(r^2\sigma^2\ell/2^{2n})$ and $O(r\sigma/2^{n})$. Notably, both of our DAE proposals are nearly rate 1/2 constructions. In terms of efficiency, our proposals compare favorably with state-of-the-art AE modes on contemporary microprocessors.

Secure Messaging apps have seen growing adoption, and are used by billions of people daily. However, due to imminent threat of a "Harvest Now, Decrypt Later" attack, secure messaging providers must react know in order to make their protocols hybrid-secure: at least as secure as before, but now also post-quantum (PQ) secure. Since many of these apps are internally based on the famous Signal's Double-Ratchet (DR) protocol, making Signal hybrid-secure is of great importance. In fact, Signal and Apple already put in production various Signal-based variants with certain levels of hybrid security: PQXDH (only on the initial handshake), and PQ3 (on the entire protocol), by adding a PQ-ratchet to the DR protocol. Unfortunately, due to the large communication overheads of the Kyber scheme used by PQ3, real-world PQ3 performs this PQ-ratchet approximately every 50 messages. As we observe, the effectiveness of this amortization, while reasonable in the best-case communication scenario, quickly deteriorates in other still realistic scenarios; causing many consecutive (rather than $1$ in $50$) re-transmissions of the same Kyber public keys and ciphertexts (of combined size 2272 bytes!). In this work we design a new Signal-based, hybrid-secure secure messaging protocol, which significantly reduces the communication complexity of PQ3. We call our protocol "the Triple Ratchet" (TR) protocol. First, TR uses erasure codes to make the communication inside the PQ-ratchet provably balanced. This results in much better worst-case communication guarantees of TR, as compared to PQ3. Second, we design a novel "variant" of Kyber, called Katana, with significantly smaller combined length of ciphertext and public key (which is the relevant efficiency measure for "PQ-secure ratchets"). For 192 bits of security, Katana improves this key efficiency measure by over 37%: from 2272 to 1416 bytes. In doing so, we identify a critical security flaw in prior suggestions to optimize communication complexity of lattice-based PQ-ratchets, and fix this flaw with a novel proof relying on the recently introduced hint-MLWE assumption. During the development of this work we have been in discussion with the Signal team, and they are actively evaluating bringing a variant of it into production in a future iteration of the Signal protocol.

In this paper, we introduce \textsf{DeuringVUF}, a new Verifiable Unpredictable Function (VUF) protocol based on isogenies between supersingular curves. The most interesting application of this VUF is \textsf{DeuringVRF} a post-quantum Verifiable Random Function (VRF). The main advantage of this new scheme is its compactness, with combined public key and proof size of roughly 400 bytes, which is orders of magnitude smaller than other generic purpose post-quantum VRF constructions. We also show that this scheme is practical by providing a first non-optimized C implementation that runs in roughly 20ms for verification and 350ms for evaluation. The function at the heart of our construction is the one that computes the codomain of an isogeny of big prime degree from its kernel. The evaluation can be performed efficiently with the knowledge of the endomorphism ring using a new ideal-to-isogeny algorithm introduced recently by Basso, Dartois, De Feo, Leroux, Maino, Pope, Robert and Wesolowski that uses computation of dimension $2$ isogenies between elliptic products to compute effectively the translation through the Deuring correspondence of any ideal. On the other hand, without the knowledge of the endomorphism ring, this computation appears to be hard. The security of our \textsf{DeuringVUF} holds under a new assumption call the one-more isogeny problem (OMIP). Another application of \textsf{DeuringVUF} is the first hash-and-sign signature based on isogenies. While we don't expect the signature in itself to outperform the recent variants of SQIsign, it remains very competitive in both compactness and efficiency while providing a new framework to build isogeny-based signature that could lead to new interesting applications.

We introduce WHIR, a new IOP of proximity that offers small query complexity and exceptionally fast verification time. The WHIR verifier typically runs in a few hundred microseconds, whereas other verifiers in the literature require several milliseconds (if not much more). This significantly improves the state of the art in verifier time for hash-based SNARGs (and beyond). Crucially, WHIR is an IOP of proximity for constrained Reed–Solomon codes, which can express a rich class of queries to multilinear polynomials and to univariate polynomials. In particular, WHIR serves as a direct replacement for protocols like FRI, STIR, BaseFold, and others. Leveraging the rich queries supported by WHIR and a new compiler for multilinear polynomial IOPs, we obtain a highly efficient SNARG for generalized R1CS. As a comparison point, our techniques also yield state-of-the-art constructions of hash-based (non-interactive) polynomial commitment schemes for both univariate and multivariate polynomials (since sumcheck queries naturally express polynomial evaluations). For example, if we use WHIR to construct a polynomial commitment scheme for degree 2^22, with 100 bits of security, then the time to commit and open is 1.2 seconds, the total communication has size 63 KiB, and the verification time is 360 microseconds.