International Association
for Cryptologic Research

Computing cube roots in quadratic extensions of finite fields is a subroutine that arises in elliptic-curve point decompression, hash-to-curve and isogeny-based protocols. We present a new algorithm that, for $p \equiv 1 \pmod{3}$ –which holds in all settings where $\mathbb{F}_{p^2}$ cube roots arise in practice– reduces the $\mathbb{F}_{p^2}$ cube root to operations entirely in the base field $\mathbb{F}_p$ via the algebraic torus $\mathbb{T}_2(\mathbb{F}_p)$ and Lucas sequences. We prove correctness in all residuosity cases and implement the algorithm using the $\texttt{gnark-crypto}$ open-source library. Benchmarks on six primes spanning pairing-based and isogeny-based cryptography show $1.6$–$2.3\times$ speed-ups over direct (addition chain) exponentiations in $\mathbb{F}_{p^2}$. We also extend the approach to $p \equiv 2 \pmod{3}$ and, more generally, to any odd $n$-th roots in quadratic towers $\mathbb{F}_{p^{2^k}}$ with $\gcd(n, p+1) = 1$.

Succinct arguments based on interactive oracle proofs (IOPs) have achieved remarkable efficiency improvements and are now widely adopted in applications. State-of-the-art IOPs involve protocols for testing proximity to constrained interleaved linear codes, and enjoy essentially optimal parameters. However, recent IOP constructions provide no privacy guarantees, which remain a must for many applications.

We present an IOP of proximity for testing constrained interleaved linear codes that achieves (honest-verifier) zero-knowledge, while incurring a negligible overhead compared to the (non-zero-knowledge) state of the art. In line with recent constructions, our construction satisfies round-by-round knowledge soundness with a straightline extractor and negligible error.

We propose a definition of (honest-verifier) zero-knowledge for interactive oracle reductions (IORs) that we prove is compatible with composition, and then obtain our result by constructing and modularly composing several lightweight zero-knowledge IORs. Our key technical contributions are a zero-knowledge sumcheck IOR and a zero-knowledge code-switching IOR that fit the strict efficiency requirements of our setting; these contributions and other technical complications entailed overcoming several challenges with new notions and protocols. Finally, along the way, we highlight the efficiency benefits of high-distance codes obtained from dispersers, which may be of independent interest.

We study the problem of minimizing round complexity in the context of succinct classical argument systems for quantum computation. All prior works either require at least 8 rounds of interaction between the quantum prover and classical verifier, or rely on the idealized quantum random oracle model (QROM). We design: 1. A 4-round public-coin (except for the first message) argument system for batchQMA lan- guages. Our results come in two flavors: (a) Under the post-quantum hardness of functional encryption and learning with errors (LWE), we achieve optimal communication complexity (i.e., all message sizes are independent of batch size). (b) Under the post-quantum hardness of LWE, we achieve optimal communication com- plexity except for the verifier’s first message. 2. A 6-round private-coin argument system for monotone policy batchQMA languages, under the post-quantum hardness of LWE. The communication complexity is independent of the batch size as well as the monotone circuit size. One of our main technical contributions is a new approach to prove soundness without rewind- ing cheating provers. We bring the notion of straight-line partial extractability to argument systems for quantum computation. All previous works crucially relied on rewinding cheating provers, thus needed “state-preserving” succinct arguments of knowledge (AoKs) for NP to prove soundness.

Anonymous Credentials (or ACs) enable users to prove claims with strong privacy guarantees, protecting credential holders from being tracked by issuers and verifiers. However, these privacy guarantees imply that a credential holder cannot be held accountable for misuse (e.g., selling credential checks online for proving ??? > 18). The lack of accountability may raise questions about the adoption of ACs into national iden- tity systems (e.g., European EUDI or Swiss e-ID), which might lead to the issuing authorities resorting to credential systems with weaker privacy guarantees (e.g., batch issuance of one-show credentials). This shows that the lack of account- ability can adversely impact the levels of privacy enjoyed by users. Hence, in this paper, we discuss transferability attacks on ACs and introduce a framework for providing accountability in AC systems. In addition to issuers, holders and verifiers, it assumes the existence of: (i) a law enforcement body (the police) and a judicial body (the judge) that work together to find information on credential misuse and; (ii) one or more digital privacy advocates, called the NGO(s), that ensure the system is not used for tracking people. We introduce the cryptographic forensic trail (CFT), which is attached to each credential show. The CFT can be used for obtaining more information about an individual if and only if the police have probable cause and can convince the judge to issue a corresponding search warrant. Then, the police, the judge, and the NGO(s) run a multiparty protocol for decrypting relevant trails only. The protocol mimics checks and balances of a healthy democracy, in which neither law enforcement nor justice can track people as they will. Even if both branches colluded, the NGO(s) can detect the misuse and block further use. In addition to possible extensions, we discuss performance constraints on mobile phones and argue that practical feasi- bility of the CFT is within reach.

Determining whether an arbitrary access structure can be realized by an ideal linear secret sharing scheme is an important research topic. we use linear codes as the main tool to construct matrices $H$ and $G$ over a finite field $\mathbb{F}_q$ for a given access structure $\Gamma_{\min}$, and show that a necessary and sufficient condition for the existence of an ideal linear secret sharing scheme realizing $\Gamma_{\min}$ is that the equation $GH^{\mathsf{T}}=0$ has a solution. If this equation has a solution, then $H$ serves as the parity-check matrix of a linear code that realizes $\Gamma_{\min}$, and $G$ is the corresponding generator matrix. Furthermore, we prove that the result is equivalent to the following statement: there exists an ideal linear code for realizing the $\Gamma_{\min}$ if and only if it is the port of a matroid that is representable over $\mathbb{F}_q$.

The recent digital signature scheme proposed by Grigoriev, Monico, and Shpilrain (GMS26) attempts to leverage the NP-hardness of tropical matrix factorization as its security foundation. We present a systematic cryptanalysis revealing multiple structural vulnerabilities. First, we demonstrate an existential forgery attack in the chosen-hash model requiring only polynomial-time operations. Second, we establish that the scheme is fundamentally malleable, allowing an adversary to generate arbitrarily many distinct valid signatures for any observed message—thereby breaking strong unforgeability. Third, we show that collecting a polynomial number of honest signatures enables partial key recovery through probabilistic leakage of private key entries. Finally, we present an SMT-based key recovery attack that, given only two valid signatures, recovers the full private key in seconds for the recommended parameters. Our attacks do not rely on solving the claimed NP-hard problem but exploit algebraic properties of the signing equations. Combined, they demonstrate that the scheme fails to achieve the standard security notions of existential unforgeability, strong unforgeability, and key confidentiality.

Quadratic Boolean functions (that is, Boolean functions of algebraic degree at most 2), bent Boolean functions (i.e. maximally nonlinear Boolean functions in even numbers of variables) and, as we prove in this paper, partially-bent Boolean functions (i.e. affine extensions of bent functions to linear super-spaces), share a strong property: all their restrictions to affine hyperplanes are plateaued (i.e. have a Walsh transform valued in a set of the form $\{0,\pm \lambda\}$, where $\lambda$ is a positive integer called the amplitude). In this paper we determine for any $n$ and $k

Deep learning's hunger for high-quality data has catalyzed a burgeoning economy of decentralized data marketplaces. However, a fundamental trust deficit stifles this ecosystem: buyers fear data poisoning, while sellers fear data leakage. Although the Shapley value offers a rigorous economic framework for fair compensation, its calculation traditionally requires a Trusted Third Party (TTP) to access raw data, creating a single point of failure for privacy. Verifying data valuation without compromising confidentiality remains an open challenge.

In this paper, we present ZK-DV, the first Zero-Knowledge Proof (ZKP) system designed for verifiable, privacy-preserving data valuation. ZK-DV enables a seller to prove that a claimed valuation score (based on Gradient Shapley) is mathematically consistent with the underlying private data and the buyer's model, without revealing either. Our key technical insight is the architectural coupling of model training and valuation: we construct a specialized arithmetic circuit that combines the valuation logic into the backpropagation, extracting marginal utility scores from intermediate gradients. This design, implemented via the GKR protocol with a hybrid commitment strategy, amortizes the heavy cryptographic overhead through batched processing. Extensive experiments on the MNIST dataset demonstrate that ZK-DV is practical: by optimizing batch sizes, we achieve a $2.7\times$ speedup in proof generation, while maintaining a quantization fidelity of $\rho=1.0$ and a low verification cost ($< 0.2$s). ZK-DV thus bridges the gap between cryptographic integrity and economic fairness, paving the way for trustless data exchange

This paper introduces the structured generic-group model, an extension of Shoup’s generic-group model (from Eurocrypt 1997) to capture algorithms that take advantage of some non-generic structure of the group. We show that any discrete-log algorithm in a group of prime order $q$ that exploits the structure of at most a $\delta$ fraction of group elements, in a way that we precisely define, must run in time $\Omega(\min(\sqrt{q},1/\delta))$. As an application, we prove a tight subexponential-time lower bound against discrete-log algorithms that exploit the multiplicative structure of smooth integers, but that are otherwise generic. This lower bound applies to a broad class of index-calculus algorithms. We prove similar lower bounds against algorithms that exploit the structure of small integers, smooth polynomials, and elliptic-curve points.

Current industry-standard block cipher modes of operation, such as CBC and GCM, are fundamentally limited by the birthday bound $O(2^{n/2})$, a constraint that has evolved from a theoretical concern into a practical security bottleneck in contemporary high-throughput, high-data-volume environments. To address this, the cryptographic community and NIST are prioritizing Beyond Birthday Bound (BBB) security to extend the operational security margin toward the full block size $O(2^n)$. Achieving BBB security requires a departure from traditional constructions, primarily utilizing three methodologies: XOR of Permutations (XORP), Tweakable Block Ciphers (TBCs), and Fresh Rekeying. While none of these innovative BBB modes have been formally standardized, NIST has initiated the Accordion Mode project, defining a new primitive class: the Tweakable Variable-Input-Length Strong Pseudorandom Permutation (VIL-SPRP). This primitive treats the entire message as a single, indivisible block and expects the submission of BBB-secure variants. To contribute to this standardization effort, we propose a simple BBB-secure variant of the HCTR2 algorithm. We first explain the core BBB methodologies, then discuss the operational mechanism of HCTR2, and finally present our proposed BBB-secure construction.

In this paper, we prove the security of symmetric-key constructions in an adversary model called the Q1MK model, which combines the Q1 model, where the adversary makes classical online queries and quantum offline queries, and the multi-key (multi-user) setting. Specifically, under this model, we prove the security of two symmetric-key constructions: the tweakable Even-Mansour cipher (TEM) and the FX construction (FX), as starting points for understanding the post-quantum security of symmetric-key constructions in this adversary model. Our security proofs are based on the hybrid argument technique introduced by Alagic et al. at EUROCRYPT 2022. First, we prove that in order to break TEM in the Q1MK model, $\Omega(2^{\kappa/3})$ classical and quantum queries are needed, regardless of the number of target $\kappa$-bit keys. Then, before turning to the Q1MK security analysis of FX, we revisit the security proof of FX in the standard Q1 model proposed in version 20230317:200508 of ePrint 2022/1097 and tighten it. By the modified proof, we show that in order to break FX with $(\kappa + n)$-bit secret key in the Q1 model, $\Omega(2^{(\kappa+n)/3})$ classical and quantum queries are needed. We then apply this analysis to the Q1MK setting, and we show that in order to break FX in the Q1MK model, $\Omega(2^{(\kappa + n - u)/3})$ classical and quantum queries are needed, when $2^u$ ($\le 2^{\kappa}$) independent keys are in use.

In this work, we consider dishonest majority MPC protocols with $(1-\epsilon)n$ corrupted parties for some constant $\epsilon\in (0,1/2)$. In this setting, there exist MPC protocols with unanimous abort that achieve constant communication in both online and offline phases via a packed secret sharing scheme. Departing from their approaches, we revisit the ``committee-based'' approach to design an efficient MPC protocol with constant online and offline communication complexity. To balance the communication load of each party, our protocol adopts multiple committees, each of constant size. The computation of circuit $C$ is then divided into layers, each assigned to one committee. To securely transmit messages between committees, we introduce the handoff gates, incurring only a slight communication overhead. Furthermore, we leverage circuit-dependent preprocessing and incremental checking to improve the online efficiency. Compared to other MPC protocols in the same corruption setting, our protocol achieves the smallest concrete total communication complexity. Building upon our multi-committee unanimous-abort protocol, we upgrade it to identifiable abort by adapting a technique from (Rivinius, EUROCRYPT 2025). To integrate this technique into our setting, we adjust the verification timing and introduce a king party to reduce the communication complexity of openings. This yields the first identifiable-abort MPC protocol with constant communication complexity in the sub-optimal dishonest majority setting.

Hierarchical deterministic (HD) wallets, standardized as BIP32, allow users to manage a tree of cryptographic key pairs from a single master seed. A defining feature is non-hardened derivation: child public keys can be derived from a parent public key alone, enabling watch-only wallets where a server generates fresh receiving addresses while the signing key remains offline. Existing constructions rely on the algebraic structure of elliptic curve public keys, and recovering this functionality in the post-quantum setting is an open problem. We present two post-quantum HD wallet constructions. The first uses ML-DSA and supports hardened (private-key-dependent) derivation with proofs of unlinkability and unforgeability. The second, our primary contribution, uses Raccoon-G, a variant of the Raccoon signature scheme with Gaussian-distributed secrets. We modify Raccoon-G to publish full, unrounded public keys, preserving linearity. Since the sum of Gaussians is again Gaussian with predictable wider variance, derived keys remain statistically close to freshly generated ones, enabling non-hardened public key derivation. We prove unlinkability and unforgeability under standard lattice assumptions, and introduce a method for generating rerandomizable Raccoon-G key pairs from fixed randomness with provable existential unforgeability. Both constructions are implemented in Rust. To our knowledge, this is the first post-quantum HD wallet con- struction that recovers BIP32’s full public key derivation functionality with provable security under standard assumptions.

Functional commitments (FCs) enable a prover to commit to a message and later produce a succinct proof of its image under any given admissible function. Unlike succinct non-interactive arguments (SNARGs), secure FCs can be realised under falsifiable assumptions in the standard model, making them attractive alternatives when fully algebraic constructions are desired. All known algebraic constructions of FC are either lattice-based or pairing-based. While a lattice-based FC for circuits with almost optimal complexities has been recently achieved [Wee, CRYPTO'25], state-of-the-art pairing-based FCs for bounded-width $w$ [Balbás-Catalano-Fiore-Lai (BCFL), TCC'23] and bounded-size $s$ circuits [Wee-Wu, EUROCRYPT'24] require prohibitive public parameter sizes $O(\lambda w^5)$ and $O(\lambda s^5)$, respectively.

In this work, we present a new algebraic pairing-based FC which achieves $O(\lambda w^3)$ public parameter size for bounded-width $w$ and unbounded depth $d$ circuits. The construction preserves all nice properties of BCFL: $O(\lambda)$ commitment size, $O(\lambda d^2)$ proof size, additive homomorphism, efficient verification, and chainability. For bounded-size $s$ circuits, we alternatively obtain $O(\lambda s^3)$ public parameters with $O(\lambda d)$ proofs. At the core of our scheme lies a new chainable FC for quadratic functions with commitments computed with respect to a power basis, as well as techniques for switching between different commitment bases.

Network-agnostic MPC protocols tolerate simultaneously a higher number of corruptions $t_s < n/2$ when the network is synchronous, and a lower number $t_a < n/3$ when the network is asynchronous. As such, they provide strong resilience, irrespective of the type of underlying communication network.

We focus on improving the communication complexity of network-agnostic MPC with optimal resilience $2t_s + t_a < n$. In this regime, there are no polynomial-time information-theoretic solutions and current computational protocols (without fully-homomorphic encryption) communicate $O(n^2)$ elements per multiplication gate.

In this work, we significantly advance the landscape by introducing the first information-theoretic protocol with quadratic communication per multiplication gate and the first computational protocol with linear communication per multiplication gate based solely on signatures and symmetric-key encryption.

Secure multiparty computation (MPC) allows a set of parties to jointly compute a function while keeping their inputs private. Classical MPC protocols assume either a synchronous or an asynchronous network. Synchronous protocols tolerate more corrupted parties but rely on a timing bound, while asynchronous protocols make no timing assumptions but handle fewer corruptions.

The network-agnostic model aims to combine the advantages of both. It requires security without knowing in advance whether the network is synchronous or asynchronous, guaranteeing resilience against up to $t_s$ corruptions in the synchronous case and $t_a$ corruptions in the asynchronous case. The optimal corruption threshold for perfect security has been established as $n = 2\max(t_s, t_a) + \max(2t_a, t_s) + 1$, but prior work either falls short of this threshold or requires exponential local computation.

In this work, we present the first perfectly secure network-agnostic MPC protocol with polynomial communication and computation complexity under the optimal threshold. Our protocol achieves expected communication complexity $\mathcal{O}((|C|n + (D+C_I)n^2 + n^6)\log n)$ bits for a circuit of size $|C|$ over a finite field $\mathbb{F}$ of size $\mathcal{O}(n)$, depth $D$, and input size $C_I$.

Our main technical contribution is a compiler that generates Beaver triples in the network-agnostic setting using synchronous and asynchronous triple-generation protocols in a black-box way. Beyond the cost of the underlying protocols, it only requires $\mathcal{O}(n^2)$ instances of network-agnostic Byzantine agreement.

Private Set Union (PSU) enables two parties to compute the union of their private sets without revealing anything beyond the union itself. Existing PSU protocols remain much slower than private set intersection (PSI), often by a factor of around $30\times$.

In this work, we present the first PSU protocol based on Invertible Bloom Lookup Tables (IBLTs), introducing a fundamentally new framework that departs from traditional, inefficient approaches. Our protocol exploits structural invariants between each party’s IBLTs and their union to compute the union efficiently without explicitly constructing a combined IBLT. Central to our approach is the notion of union peelability, which allows union elements to be recovered directly from the original IBLTs. We securely implement this functionality using only Oblivious Transfer (OT) and Oblivious Pseudorandom Function (OPRF) for equality checks, ensuring no information beyond the union is leaked.

As a result, for set sizes ranging from $2^{14}$ to $2^{20}$, our protocol achieves a runtime of $0.08$ to $2.95$ seconds in the LAN setting, which is comparable to state-of-the-art PSI. We also show substantial speedups over prior PSU work—up to $10\times$ faster in LAN settings and consistently faster in WAN scenarios—while maintaining linear computation and communication complexity with small constants.

Liquid democracy is a transitive vote delegation process. Previously, the advantages of liquid democracy over direct voting have been studied in settings where there is a ground truth “good” voting outcome. In this work, we analyse liquid democracy in a realistic setting with two opposing factions without a ground truth and under uncertainty. Formally, we consider ? voters who want to decide on some binary issue by voting. Each voter has a preference in {0, 1} that represents the opinion of the voter on these issues. That is, a voter with preference 0 prefers to vote for option 0. We refer to voters with the same preference as being in the same faction. The goal is for voters in the same faction to cooperatively decide on vote delegation strategies that maximise their probability of winning the election. In this setting, we present a practical distributed algorithm under realistic assumptions to decide on an approximately vote delegation strategy that involves minimal interaction and communication, and under incomplete information about the opposing faction. We then provide a complete analytical characterisation of optimal vote delegation strategies under complete information about the opposing faction. Finally, we show that finding optimal delegation strategies in the general setting is PSPACE-complete.

We present WOTS-Tree, a stateful hash-based signature scheme for Bitcoin that combines WOTS+ one-time signatures with a binary Merkle tree, supporting up to $2^{21}$ independent signatures per address. The construction instantiates XMSS with parameters specifically optimized for Bitcoin's UTXO model, using a dual hash function design: SHA-256 truncated to 128 bits ($n=16$, $w=256$) for WOTS+ chain evaluations, and full 256-bit SHA-256 for Merkle tree compression. Deployed as dual leaves within BIP-341 Taproot (compatible with the proposed BIP-360 Pay-to-Merkle-Root), the default (hardened) mode provides: (i) a fast-path for single-use UTXOs at 353 bytes, and (ii) a fallback tree for Replace-By-Fee and address reuse at 675 bytes ($K=1{,}024$). For Lightning channels, $K=2^{21}$ yields 1,028-byte witnesses with a 19-second one-time setup. An opt-in compact mode using truncated 128-bit Merkle nodes reduces witnesses to 515--692 bytes at the cost of reduced Merkle binding security ($\approx 60$ bits). WOTS-Tree achieves strict L1 verification bounds of 4,601 hashes ($\approx 0.009$ ms on SHA-NI hardware). The default parameterization provides 115.8-bit classical and 57.9-bit quantum forgery resistance, with the Merkle binding at $\approx 124$ bits, exceeding the WOTS+ forgery bound in both classical and quantum settings. We provide a complete security reduction with concrete bounds, a dual hash instantiation analysis, and a reference implementation with comprehensive test coverage. Default-mode witnesses are $4$--$7\times$ smaller than hypertree variants while aligning naturally with Bitcoin's spend-once transaction model.

Threshold and multi-signature schemes enable a group of signers to jointly sign messages. In the pairing-free discrete-logarithm setting, there have been extensive research efforts on two-round threshold and multi-signature schemes. A prominent category is partially non-interactive schemes, where the first round is message-independent and can be preprocessed offline. However, there exist gaps in security properties between partially non-interactive schemes and fully online schemes. While there are fully online schemes that achieve rewinding-free or fully adaptive security based on standard assumptions, existing partially non-interactive schemes require the adversary to act algebraically or rely on non-standard assumptions for these properties.

We bridge this gap by proposing a family of new constructions of partially non-interactive threshold and multi-signature schemes. Central to our constructions is a technique that renders HBMS (Bellare and Dai, Asiacrypt 2021) and its variants partially non-interactive. Specifically, we present the following instances: - The first partially non-interactive two-round multi-signature scheme with a rewinding-free reduction under standard assumptions. This scheme provides a tighter security guarantee against non-algebraic adversaries than all prior partially non-interactive schemes. - The first partially non-interactive two-round threshold signature scheme achieving fully adaptive security against non-algebraic adversaries under standard assumptions.