International Association
for Cryptologic Research

Multi-Scalar Multiplication is a critical operation in most pairing-based zero knowledge proofs. In a lot of studies, memory limitations have often been reported to be the primary bottleneck preventing the calculation of larger MSMs. In this paper, we are particularly interested in the acceleration of this operation on devices with limited memory. Pippenger’s algorithm (also known as bucket method) is the most efficient and, consequently, the most widely used method to calculate Multi-Scalar Multiplications. We propose an optimization of Pippenger’s algorithm which is at least as efficient as the original, and significantly more effective when operating under limited memory. The main idea is to use an adapted number of buckets depending on the available memory instead of $2^w −1$. We conducted tests on the curve BLS12-381 with Multi-Scalar Multiplications ranging from $2^8$ to $2^{14}$ points. The results obtained demonstrate that we have a very significant gain (up to $40\%$) for very limited memories. This gain gradually decreases as more memory becomes available, until we achieve performance comparable to Pippenger’s once memory is no longer limited. For example, in a Multi-Scalar Multiplication with $2^{13}$ points, we observe a gain of $40\%$ with only $1$ KB of memory, $20\%$ with $15$ KB, $15\%$ with $35$ KB, and so on, down to $1.5\%$ once memory is no longer a constraint.

Ensuring the integrity and traceability of data transformations in distributed systems presents significant challenges, particularly in environments where data privacy and decentralization are paramount. This paper introduces a novel secure lineage verification system based on Directed Acyclic Graphs (DAGs) and homomorphic hash functions, VERDICT. Our approach represents data artifacts and their transformations as two interconnected DAGs: a Data DAG tracking data dependencies and an Event DAG capturing causality between transformation events. We propose a level-based DAG compression technique that decomposes these graphs based on distance from genesis nodes, enabling efficient verification through skip DAG structures. The system incorporates bucket indexing and Merkle tree verification to provide cryptographic guarantees of data and event existence. We present formal algorithms for DAG construction, level-based hashing, skip DAG traversal, and verification processes. Security analysis demonstrates the system’s resistance to tampering and modification attacks while maintaining privacy. Replay attacks are prevented through an application-layer challenge-response mechanism. Our approach has significant applications in federated learning environments and decentralized architectures, where it can serve as a notary component for tracing events without compromising data confidentiality. Theoretical analysis shows that our method achieves verification in ?(log?) time in the number of DAG levels, independent of the number of nodes per level, making it suitable for large-scale distributed systems.

Hybrid Homomorphic Encryption (HHE) is emerging as a practical alternative to fully homomorphic encryption by offloading computational overhead to the cloud. Despite the growing number of HHE schemes and implementations, no unified evaluation methodology currently exists. In this work, we present a comprehensive and reproducible benchmarking framework covering both standard and HE-friendly HHE schemes. We analyze and evaluate 19 open-source HHE frameworks, comprising 218 distinct ciphers' benchmarks, across diverse HE libraries and programming languages. To ensure fair comparison, we interpret the main results under an HHE-128 security target, separating standardized or author-claimed 128-bit settings from below-target measurements. Our contributions include a unified repository, a language-agnostic benchmarking tool, and detailed metrics on runtime and memory usage. The results offer actionable insights into the security-aware performance trade-offs of each design and lay the groundwork for standardizing future HHE evaluations.

Post-quantum signatures built from Fiat--Shamir transforms of zero-knowledge identification protocols---including LESS, CROSS, and MEDS---use GGM-tree seed compression to shrink signatures, revealing only the seeds of public rounds while hiding the challenge-dependent ones. This mechanism introduces a fault-attack surface: faulting the seed-publication can expose hidden seeds alongside their zero-knowledge responses, enabling recovery of secret information. We introduce the Generic ZK Seed Tree (GZKST), a unified abstraction of GGM-tree generation, challenge partitioning, and seed publication across these schemes, and formalize its correctness and seed-hiding invariants. We show that prior attacks on LESS-v1 and LESS-v2 violate the same invariant despite targeting different implementation layers and tree constructions, derive generic key-recovery algorithms from this view, and bound the number of effective faulted signatures needed for full recovery---only a few successful queries suffice for every MEDS parameter set. We further demonstrate the attacks in practice through clock-glitch fault injection against the MEDS reference implementation on an ARM Cortex-M4 (ChipWhisperer-Lite), identifying multiple exploitable surfaces in tree traversal and path construction that enable complete tree disclosure, partial subtree recovery, or leakage of hidden leaves.

In this paper, we prove the post-quantum security of the Tweakable Key-Alternating Feistel cipher (TKAF) with a public random function in the Q1 model, under the assumption that the adversary is given quantum access to the internal primitive. Specifically, our target is the TKAF studied in the classical setting by Yan et al. (ACNS 2020), where the tweak is injected into the round-key XOR via a hash function of $\epsilon$-AXU family. Our proof draws on the post-quantum security proof for the (non-tweakable) key-alternating Feistel ciphers by Basak et al. (ASIACRYPT 2025), and adapts it to the tweakable setting and further to the multi-key setting, where an adversary can access multiple classical oracles. As a result, we prove that the 3-round TKAF is post-quantum TPRP-secure and the 4-round TKAF is post-quantum STPRP-secure. Specifically, under the assumption that the adversary is given classical access to $\ell$ independently specified oracles, at least $\mathrm{\Omega} (2^{n/3}/\ell^{2/3})$ classical and quantum queries or $\mathrm{\Omega}(\epsilon^{-1/2})$ classical queries are required to break the post-quantum TPRP security of the 3-round TKAF and to break the post-quantum STPRP security of the 4-round TKAF.

We prove a folklore characterization of the BN pairing subgroup as the kernel of a relative trace map on the $n$-torsion points.

Approval phishing is a form of Web3 phishing that exploits token approval mechanisms to trick users into granting attackers spending authority over their tokens. As attackers increasingly hijack legitimate websites, URL-based detection alone becomes insufficient, leaving crypto wallets as the last line of defense. Based on the characteristics of approval mechanisms, we propose four wallet-based interventions for mitigating approval phishing: Spending Cap Suggestion, Active Spender Warning, Passive Spender Warning, and Delayed Confirmation. We evaluate the interventions through a between-subjects experiment (n = 364) and semi-structured interviews (n = 23). Compared with the control group, the Spending Cap Suggestion condition significantly increases the likelihood that users set spending caps. The Active Spender Warning, Passive Spender Warning, and Delayed Confirmation conditions all increase cancellation rates of phishing tasks, although the increases are statistically significant only for Active Spender Warning and Delayed Confirmation conditions. The effectiveness of the interventions varies across users, as users may struggle to interpret suspicious cues and focus on transaction outcomes while overlooking approval details. Our findings highlight the need to strengthen defenses against such attacks by increasing users' awareness of post-approval consequences and supporting approval-parameter verification at the moment of authorization.

Nation State Agencies go to great lengths to obtain signal intelligence, including backdooring cryptographic standards and equipment. Although the existence of these backdoor efforts is common knowledge, only few of known backdoored systems have been publicly analysed.

In this paper we present the first detailed $\textit{forensic cryptanalysis}$ of the backdoored UA-8295 message terminal and we try to answer questions how the UA-8295's backdoor was designed and for which attack. Towards a better understanding of real-world backdoor design, we posit a $\textit{Backdoor Conjecture}$ that provides handles to reason about the design of backdoors and the attacks they are designed for.

Audio recordings are often used as evidence, but modern forgery tools make their origin harder to verify. Existing authentication methods require releasing the original signed recording, which exposes sensitive source content as well as provenance information. Redacting the audio avoids that disclosure, but doing so also invalidates the original signature. Revealing the edit operations to prove edit compliance can also disclose the redacted content. This creates a conflict for existing approaches: authenticating a released audio file requires disclosing the original audio, edit operations, or identity of the recording device, but preserving privacy requires keeping all three hidden.

In this work, we propose $\textit{Privacy-Preserving Audio Authentication Systems}$ (PPAAS). PPAAS uses a single relation that binds source provenance and edit correctness to the same hidden witness. This witness includes both the attested source recording and device attestation, so the verifier can be convinced that the released audio came from an authorized device and was obtained through allowed edits, without learning the source recording, the edit operations, or which enrolled device produced it. We formalize this notion and provide two constructions adapted to different editing scenarios. The first is a $\textit{segmentation-based}$ construction that requires zero-knowledge proofs only for actively edited segments and is therefore well-suited to sparse edits. The second is an $\textit{iteration-based}$ construction that uses Incrementally Verifiable Computation (IVC) with zero-knowledge compression to fold repeated checks into a single proof, which is efficient for dense edits. Our evaluations show the practicality of both constructions: the segmentation-based approach minimizes cost for sparse edits, whereas the iteration-based approach becomes preferable as edit density increases.

Secure Multi-Party Computation (MPC) is a cryptographic primitive that enables multiple parties to jointly compute a function over their inputs without revealing the inputs. An MPC protocol is required to provide security against adversarial behavior, typically considered in two classic models: the \textit{semi-honest} model, where adversaries follow the protocol but attempt to learn additional information from the transcript, and the \textit{malicious} model, where adversaries may arbitrarily deviate from the protocol. Protocols secure against semi-honest adversaries are often more efficient, but in many real-world applications the stronger guarantee of malicious security is required.

In this work, we propose an efficient MPC protocol secure against static malicious adversaries controlling at most $t

Given a fixed security order, the randomness and latency of masked hardware present a trade-off. This trade-off has not been structurally examined well enough to enable an efficient search for a user-optimal (randomness/latency efficient) masked design. Gadget-based masking has simplified masking using masked functions called \textit{gadgets} corresponding to simpler (unmasked) functions as building blocks for larger masked designs. These gadgets, in turn, have masking-order dependent latency-randomness costs, lending a structure to the randomness and latency of gadget-based masked hardware. This structure enables automated Design-Space Exploration (DSE) of gadget-based masked hardware that takes in a user's constraints on randomness (or latency) to arrive at the latency (randomness)- optimal assignment of gadgets with less area and vice versa.

This article introduces a software-level DSE approach the basis of which are the two DSE algorithms - Minimize Latency under Randomness Constraints (MLRC) and Minimize Randomness under Latency Constraints (MRLC) which are duals of each other. While prior work solves the problem of optimizing masked hardware by formulating a global SAT optimization, our results show that gadget-based masked hardware using Probe-Isolating Non-Interference (PINI) gadgets embody a structured trade-off lending efficient heuristic-based solutions instead of relying on heavy global optimizations. This gives our tool comparable to superior area results in under a millisecond - a speedup of several orders of magnitude - to the SOTA.

SQIsign is the leading isogeny-based post-quantum digital signature scheme under consideration in NIST's standardization process. All published security results, including the first complete proof (CRYPTO 2025), establish only existential unforgeability under chosen-message attack (EUF-CMA). It is known informally that SQIsign does not achieve strong unforgeability (SUF-CMA) due to the non-uniqueness of its two-dimensional isogeny representation.

We make three contributions. First, we identify a concrete malleability vector in the SQIsign v2.0 specification: the basis change matrix $M_{\mathrm{chl}}$ in the signature can be negated modulo $2^N$ to produce a distinct valid signature for the same public key and message. This is the direct structural analog of ECDSA's $(r,s)$ versus $(r,n-s)$ malleability. We provide a proof-of-concept against the C reference implementation at all three NIST security levels.

Second, we propose a minimal fix: canonical matrix encoding, where the signer normalizes $M_{\mathrm{chl}}$ and the verifier rejects non-canonical forms. We prove that after canonicalization, the response encoding is injective (each mathematical response isogeny maps to exactly one byte string), using the structure of reducible gluings of abelian varieties.

Third, we prove that the modified scheme achieves SUF-CMA in the quantum random oracle model: the sigma protocol's honest-verifier zero-knowledge and special soundness together with computationally unique responses (established by our encoding injectivity result) imply SUF-CMA. This is the first SUF-CMA result for any SQIsign variant.

We show that the certificateless signature scheme [IEEE ITJ, 26852-26865, 2024] is insecure against public key replacement attack. An adversary can forge signatures for any message by replacing the signer's public key. We find the two components $\delta_A$ and $T_A$ of signature $\sigma_A=(m_A, ID_A, \delta_A, T_A)$ are not tightly bound to the target message $m_A$ and the singer's identity $ID_A$. The inherent flaw results in that the adversary can find an efficient signing algorithm functionally equivalent to the valid signing algorithm. The findings could be helpful for researchers unfamiliar with the designing techniques for certificateless signatures.

The main contribution of this paper is to introduce Subspace Differential Uniformity (SDU) for S-boxes and block ciphers. The SDU is essentially a measure of how well any function spreads input differences clustered in affine subspaces away from affine clusters in output differences. We provide some lower bounds for the SDU and describe an efficient algorithm for computing the SDU. Moreover, we provide results for some popular classes of S-boxes up to $n=8$.

Secure computation allows multiple parties to jointly evaluate a function without leaking their individual inputs. An intrinsic issue with these techniques is that they do not offer any protection against parties which may contribute bad quality or even maliciously crafted data. We introduce TRIP, a protocol which protects against malicious manipulations of the input in secure computation of linear regression tasks. Linear regression is the cornerstone in many machine learning tasks, and hence creating secure protocols for this task is a crucial step towards secure machine learning. Our protocol utilizes a novel combination of techniques from secure computation, robust statistics, and differential privacy. On synthetic data, TRIP recovers the planted ground truth; on real-world datasets, its model remains close to the clean OLS baseline under up to 40\% target corruption. In terms of efficiency, our protocol runs up to $250\times$ faster than an MPC-only baseline for $10^6$ samples. Even in the smallest parameter setting, TRIP is $10\times$ faster than our baseline.

Euclidean lattices are an interesting object of study in many regards and can have a rich structure arising from various constructions, e.g., from number field extensions. A particularly interesting class is the one of well-rounded lattices, as they relate to the well-known densest sphere packing problem in geometry, theta function minimization, and the famous Minkowski and Woods conjectures. In addition to being an important mathematical object in their own right, lattices also play a central role in many applications. This paper offers a survey of structured lattices and discusses their recent applications in lattice-based cryptography and secure wireless communications. Our goal is to spark the interest of mathematicians and adjacent communities in these fascinating topics in the intersection of lattices, number theory, cryptography, and wireless communications.

Threshold signatures allow a quorum of parties to jointly produce a signature while preventing any smaller subset from doing so. Following NIST's post-quantum standardization, designing threshold schemes compatible with the newly selected primitives is a pressing task. In particular, no prior threshold signature scheme produces signatures verifiable under the unmodified FALCON verification algorithm - the NIST-selected post-quantum scheme with the smallest signatures and keys.

In this work, we present the first such threshold FALCON signing protocol, establishing its feasibility. Our technical contributions are threefold. First, we adapt the MPC-based discrete Gaussian sampling protocol of Wei et al. [CCS:WYFCW23] to support private centers and standard deviations, as required by FALCON's signing process. Second, we carry out a Rényi divergence analysis of the Klein sampler under fixed-point arithmetic, showing that $73$ bits of precision suffice to achieve the same security as the FALCON specification. Third, we design an efficient MPC protocol for the Klein sampler that exploits the fixed trapdoor basis to construct a pseudorandom correlation generator for authenticated VOLE using only two-party DPFs, reducing per-signature communication significantly over standard authenticated triple generation. We implement and benchmark our protocol in two settings: $N$-party signing with all-but-one corruption, and 3-party signing with honest majority, demonstrating that threshold FALCON signing is feasible for applications where compatibility with the FALCON standard is required.

Let $E$ be an elliptic curve over a perfect field $K$. A function $f\in K(E)$ is a compression of degree 2 on $E$ if $f(-P) = f(P)$ for all $P\in E$, and the field extension $K(f)\subset K(E)$ is of degree 2. For a finite subgroup $G\subset E$ over $K$ a function $w\in K(E)$ we will call a $G$-compression if $w(\pm P +G) = w(P)$ for all $P\in E$, and the field extension $K(w)\subset K(E)$ is of degree $2|G|$. We will show that $w\in K(E)$ is a $G$-compression if and only if $w = f\circ \Phi$ for a separable isogeny $\Phi:E\to E'$ over $K$ with $\ker \Phi=G$, an elliptic curve $E'/K$, and a compression $f\in K(E')$ of degree 2 on $E'$. This allows to obtain a doubling, a differential addition, and a method for point recovery for $G$-compressions using known properties of compressions of degree 2. For $G$-compressions $w$ studied in the literature on an extended Jacobi quartic, a twisted Edwards curve, a twisted Jacobi intersection, and a twisted Hessian curve (for the first and third model additional conditions on coefficients are assumed) we will give the decomposition $w = f\circ \Phi$ as above, and the function induced by the dual isogeny $\widehat{\Phi}$ and compressions of degree 2, which can be used for point recovery. For the first three models this isogeny $\Phi$ is to a Montgomery curve over $K$, and has the first coordinate $x(\Phi)=1/w$. We also give isomorphisms from some models of elliptic curves to a Montgomery curve.

HAWK is a signature scheme based on the module lattice isomorphism problem, and the only lattice-based candidate in the third round of NIST's call for additional post-quantum signatures. Its specification claims that HAWK achieves the BUFF (Beyond UnForgeability Features) security properties "as is", without applying the generic BUFF transform, citing the analysis of Aulbach, Düzlü, Meyer, Struck, and Weishäupl (PQCrypto'24).

We refute this claim for HAWK exactly as specified. Several of the BUFF games let the adversary register a public key of its own choosing, yet the HAWK reference verifier performs almost no validity check on a key beyond decoding it. We exhibit degenerate "weak" public keys under which the all-zero signature verifies for all random-oracle challenges except the negligible symmetry-breaking corner case, and use them to break the three BUFF properties whose games let the adversary supply both the verification key and the signature: message-bound signatures, malicious strong universal exclusive ownership, and weak non-resignability.

We trace these breaks to gaps in the BUFF proofs for HAWK of Aulbach et al.: one missing case analysis, and three steps that silently assume properties of the adversarially chosen keys as if they come from honest key generation. Honest key generation already enforces bounds that would reject our weak-key family on the attacks we exhibit. We prove that enforcing this norm floor at verification yields message-bound security for constant keys, but we make no claim that it fully restores BUFF security.

In this paper, we study garbled circuits in the random oracle model against a computationally unbounded adversary with $T$ queries to a (programmable) random oracle. From Yao's garbled circuits (SFCS 1986) to Three-Halves (CRYPTO 2021), the garbled circuit size has been reduced from $8|C|(\log T+\kappa)$ bits to $1.5|C|(\log T+\kappa)$ bits for achieving a statistical error of $2^{-\kappa}$, where $|C|$ is the circuit size and $\kappa$ is the statistical security parameter. However, no known result achieves $o(|C|\kappa)$ bits of garbled circuit size by now, and it is widely believed that a garbled circuit must have $\Omega(|C|\kappa)$ bits in the random oracle model. In this work, we present the first garbling scheme that achieves $o(|C|\kappa)$ bits of garbled circuit size in the random oracle model. In particular, for a circuit $C$ of size $|C|$ and depth $D$, the achieved garbled circuit size is $O(|C|\log T+D\kappa^2\log T)$ bits. This breaks the long-standing $\Omega(|C|\kappa)$ barrier on the garbled circuit size.

We extend our garbling scheme to a maliciously secure two-party computation protocol with communication of $O(|C|\log T+D(\log T+\kappa)^2\log T+{\sf poly}(\kappa,\log T))$ bits against any $T$-query adversary assuming parallel oblivious transfers and a (programmable) random oracle. The protocol only requires 1 OT round and 3 one-way communication rounds. If only requiring one of the two parties to have output, a similar communication complexity can be achieved for constructing a non-interactive secure computation (NISC) protocol, which only relies on the preprocessing of bit-OT correlations and a random oracle. Compared to a concurrent work on NISC by Ishai et al. (EUROCRYPT 2026) in the same setting, we achieve a better amortized communication cost per gate at the cost of an additional term related to the circuit depth. The NISC protocol with a similar communication cost can also be constructed from a (slightly stronger version of) semi-malicious 2-round OT protocol.