International Association
for Cryptologic Research

Lattice-based zero-knowledge proofs are now efficient enough for practical use, but in all known constructions a single prover holds the entire witness and is therefore a single point of failure. Thresholdizing them is understood only for three-round $\Sigma$-protocols, which certify shortness only $\textit{approximately}$. The $\textit{exact}$ statements needed by applications such as anonymous credentials require more rounds and rely on rejection sampling, and neither property survives thresholdization.

We construct the first lattice-based threshold zero-knowledge proof systems for exact relations. The witness is Shamir-shared among $\mathtt{n}$ parties, any $\mathtt{t}$ of them can jointly produce a proof, and the proof has the same form as a single-prover proof, only a factor $\sqrt{\mathtt{t}}$ larger, with verification unchanged. We thresholdize the product proof of Attema, Lyubashevsky, and Seiler (CRYPTO 2020) and the exact proof of Esgin, Nguyen, and Seiler (ASIACRYPT 2020), making both rejection-free using Hint-MLWE and evaluating them over threshold homomorphic encryption. We define threshold commit-and-prove protocols with the corresponding zero-knowledge and simulation-extractability notions, and prove our constructions secure against passive adversaries that statically corrupt at most $\mathtt{t}-1$ parties.

Of independent interest, we show that the Fiat--Shamir transforms of both proof systems are simulation-extractable in the random oracle model, and that MLWE remains hard when secrets are drawn from the subring fixed by a ring automorphism.

Modern public-key cryptography is threatened by advances in quantum computing. As a result, there has been a shift towards cryptographic algorithms that can resist attacks by a quantum computer. However, these algorithms use significantly longer keys, and produce larger ciphertexts and digital signatures than their classical counterparts. These bigger sizes pose problems for devices that are bandwidth- and/or power-limited, and wish to establish a secure, quantum resistant communication channel with another device.

In order to reduce the overhead of using these algorithms in challenging environments while maintaining security posture, we present Compact Authenticated Key Exchange – Hiding Identities (CAKE-HI). To evaluate our protocol, we compare the key exchange handshake size and computational efficiency of mutual authenticated TLS and CAKE-HI. Measurements show that CAKE-HI significantly reduces the handshake size and the computational overhead of establishing a quantum-secure link.

In addition, we formalize and prove security properties about CAKE-HI in the symbolic and computational model using the protocol analysis frameworks Verifpal and CryptoVerif.

Private repositories remain readable to Git hosts despite transport and at-rest encryption. We present SafeHub, an end-to-end encrypted Git hosting system. It encrypts repository contents and semantic metadata - file names, commit messages, authors, branches, issues, pull requests, and refs - so the host sees only ciphertext, opaque identifiers, lengths, and order.

Each repository is a Messaging Layer Security (MLS) group, providing admin-mediated membership, post-compromise healing, and per-invite history windows. Ordinary Git behavior is preserved within each member's window: branches, merges, and blame still work. Forward-only members start from a join shallow snapshot rather than the full past.

Confidentiality alone is not enough: Git's hash-linked objects do not protect mutable refs. SafeHub records refs in an encrypted, device-signed, hash-chained manifest that detects rollback against a member's own anchor and host forks when members compare checkpoints; force-pushes require administrator co-signatures. We specify a single ideal functionality F_safehub for the system and prove that SafeHub universally composably realizes it against a malicious server and adaptive member corruptions, in a hybrid model over group key agreement and certification, assuming secure erasure in the quantum random oracle model.

Our NIST PQ Category-5 Rust prototype measures full-stack push, pull, fetch, clone, merge, rebase, and force-push on a client-server pair of AWS Graviton4 hosts, together with the epoch rotation and consolidation that Git has no counterpart for. Against Git on its lowest-overhead native transport, wall-clock push runs 1.45x plain Git at a 0.05 MB delta and 0.98x at a 5 MB one, its marginal cost 46.7 ms/MB against Git's 49.3. We compare SafeHub with five other systems - plain Git, git-crypt, git-remote-gcrypt, and a reimplementation of the closest peer - over a single transport, with clients and remotes on separate hosts. The comparison separates designs whose cost follows the edit from designs whose cost follows the whole file. For a fixed 1 KiB edit, with the edited file growing from 10 KiB to 8 MiB, SafeHub's cost per update remains constant at 6.7 kB, because it seals the packfile Git has already built, whereas the systems that encrypt each file individually grow with the file and reach 8.39 and 13.4 MB. On that shared transport SafeHub is the fastest of the six at push, pull, fetch, merge, rebase, and force-push, each constant in history depth, and its stored size matches plain Git to within 0.2%, whereas the per-file encryption used by the other systems costs 13 to 21 times as much. The cost that does not amortize is clone, which grows with sealed history: a host that cannot read a repository cannot repack it.

Ghoshal, Ishai, Jain, and Sun recently introduced a novel quasipolynomial-time distinguisher for GRS subcodes (including Goppa codes), leaving key recovery as an open problem. This note presents an approach for turning the distinguisher into a full key-recovery attack. The overall complexity is dominated by a few executions of the distinguisher, and the approach is experimentally validated on Goppa codes over $\mathbb{F}_4$. We conjecture that this recovery route applies to binary Goppa codes as well.

In the context of PKE schemes, Gagliardoni et al. proposed at PQCrypto 2021 a qIND-qCPA security notion (a superposition-based analogue of the classical IND-CPA security notion), by using the theory of so-called type-2 unitary operators. On one hand, this notion is very natural, closely mirrors the classical intuition, and can be handled without relying on complex techniques such as Zhandry’s compressed oracles. On the other hand, it is restricted to a certain class of PKE schemes (so-called isometric). Moreover, it is not immediately clear how to extend the definition to chosen-ciphertext attack (CCA) scenarios, mainly due to the possibility of decryption failures – something that is entailed by most quantum-resistant PKE schemes.

In this work, we use the theory of type-2 operators to extend superposition-based security notions to any PKE schemes, in the CPA and CCA setting, without Zhandry’s compressed oracle technique. We start first by showing that a trivial extension of Gagliardoni et al.’s techniques to the general case is not possible, even for the CCA1 case, by identifying barriers preventing the realization of a ‘natural’ type-2 decryption operator. Then we define a subclass of PKE schemes (which we call ‘strongly decryptable’ ), for which it is easy to circumvent the aforementioned barriers and to define superposition-based CCA1 and CCA2 notions.

Further, we introduce a novel transformation (that we call ‘purification’) which applies to any PKE scheme, producing a ‘quasi-PKE’ scheme, for which it is possible to define properties that mimic the security notions defined for strongly decryptable schemes; we can thus ‘unload’ the security definitions for an arbitrary PKE scheme on its purification. Finally, we show implications and separations between our security notions, as well as constructions.

Practical implementations of synchronous MPC protocols typically require each party to advance to the next round as soon as they have received all expected messages. This deviates from the theoretical synchronous round-based model, where instead each party advances in the next round after a timeout. To capture this gap between theory and practice, Asharov, Chandramouli, Cohen and Ishai in Eurocrypt 2025 proposed a new model where the adversary is super-rushing. In this, the adversary can see future messages of some honest parties before delivering current-round messages to slower ones. In this work, we study super-rushing security in both the computational and statistical settings, and design round-preserving compilers that transform standard synchronous MPC protocols into ones secure against super-rushing adversaries. Ours is the first work to investigate the security of computational MPC protocols against a super-rushing adversary.

RIPEMD-160 is an ISO/IEC hash function standard based on the Merkle-Damgård structure with a double-branch compression function. There have been many attempts at modular differential attacks on reduced RIPEMD-160, with the best previous result being a 40-step practical collision attack achieved in 2023. That attack constructs a simple local collision in round 2 of the left branch to minimize uncontrolled conditions. To achieve this, differences must be introduced into many message words, which constrains the maximum number of steps that can be attacked. To overcome this limitation and target more steps, we propose a new differential characteristic structure that abandons the sparse local collision in round 2 and instead uses a single continuous differential characteristic spanning rounds 1 to 2 for each branch. This structure allows us to inject a difference into only one message word. Using an automatic search tool based on the high-performance parallel SAT-solver PRS, we identify suitable differential characteristics by imposing more control over conditions, differences, and the probability of proper propagation. Based on the differential characteristics, we identify three colliding message pairs for 42-step RIPEMD-160 with theoretical time complexity of approximately $2^{47.4}$, thereby improving the best practical collision attack by 2 steps on this hash function.

This note collects, in compressed form, some techniques for modular multiplication with word-size (“short-limb”), or at most a-handful-of-words sized moduli as they are used in implementations of lattice-based cryptography: Barrett reduction and multiplication (in signed and unsigned flavors, with exact error, range, and canonicality analyses), Montgomery reduction and multiplication (including the folded-constant form, the precise equivalence with Barrett multiplication, even moduli, the multi-limb case, and the k-reduction), Plantard multiplication (the original unsigned algorithm, the signed variant, and a variant taking signed inputs to the canonical unsigned representative in [0,q)), and modular multiplication via the explicit Chinese remainder theorem. These are compressed out of my lecture slides in the class Post-Quantum Cryptography at National Taiwan University 2020--2025 (EE 5176/921 U2540). All numerical examples, ranges, and windows stated here have been verified by exhaustive or randomized machine search; several constants and ranges correct typos and miscalculations that circulated after lectures.

Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing $\langle r, m \rangle$ (mod $2$) for a hidden string $m$ and a random challenge $r$, to one that is capable of extracting the entirety of $m$. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing $\langle r, m \rangle$ given uniformly random identical challenges $r$. This allows to upgrade any unclonable encryption scheme satisfying "search" security to one satisfying the gold standard of unclonable "indistinguishability". As a corollary, we show that the simplest candidate unclonable encryption scheme from BB84 states satisfies unclonable indistinguishability.

This result was discovered by GPT-5.6 Ultra after a few interactions. Our prompts included recent results on unclonable encryption by Ananth and Sahai, and Ragavan.

Towards bridging the gap between passively and actively secure multiparty computation (MPC), the use of sublinear distributed zero-knowledge (DZK) proofs gained popularity. Such proofs enable extending a passively secure protocol by adding a verification step whose communication is sublinear in the circuit size. For arbitrarily many parties and a dishonest majority, adding a trusted dealer enables efficient computation, as recently shown by Asterisk (IEEE S&P'24) without requiring DZK. This setting is also compatible with DZK, as shown by Boyle et al. (CRYPTO'21). Unfortunately, their approach is not tailored to computation over a ring $\mathbb{Z}_{2^k}$, often favored for concrete efficiency and practicality, resulting in high computational overhead. In the honest majority setting with few parties, Li et al. (CCS'24) optimized DZK to rings, achieving significant performance improvements.

In this work, we propose the first sublinear verification protocol that is both, designed for the $n$-party dishonest majority setting with a dealer, and tailored to computation over a ring $\mathbb{Z}_{2^k}$, combining and improving upon both approaches above. Previous approaches used $n$ DZK proofs to check correct behavior for each individual party. Instead, we show how to verify in a single, novel DZK proof that all parties together behave correctly. This decreases the communication complexity for verification from $\mathcal{O}(n \cdot \log m)$ to $\mathcal{O}(n + \log m)$ ring elements per party for $m$ multiplications. Hence, for the first time, active security using DZK scales well with the number of parties $n$. We provide the first public implementation for DZK with arbitrary $n$ and a dealer and show its practical efficiency. For $m=10^6$ multiplications across 30 layers, communication increases by only 0.7% over the passively secure base protocol with only moderate computation overhead. This becomes especially useful in a WAN setting, where we achieve active security at only 34% run time overhead over the passive variant. Compared to Asterisk (IEEE S&P'24), our protocol has 1.8x better communication and improves run time by 2.5x in WAN and 11.9x in LAN.

Non-local search-to-decision asks whether two noncommunicating parties, given the two shares of a bipartite encoding of a uniformly random string $x\in \mathbb{F}_2^n$, can both predict the same random parity $\langle r,x\rangle$ without there also being local measurements with which both parties recover $x$. We prove that if their optimal probability of both recovering $x$ by local measurements is $p$, then their probability of both answering a common parity challenge correctly is at most $\min\{1,\frac12+5p^{1/22}\}$. The result is motivated by applications to unclonable cryptography, including unclonable encryption and quantum copy-protection. The proof is information-theoretic and does not provide an efficient extractor. The proof and the exposition were developed with assistance from ChatGPT using GPT-5.6 Sol Pro and Codex in the Ultra reasoning mode.

Redeemable real-world asset tokens can trade onchain faster than their backing assets can be sold or settled. An immediate-exit facility cannot treat reported net asset value (NAV) as fully liquid. Within our scope, the mechanisms we compare do not jointly provide permissionless access, order-splitting resistance, and favorable small exits.

In this paper, we propose a Proprietary Request for Quote (Prop RFQ), an onchain facility that prices exits against available reserves and mitigates, but does not eliminate, split-order incentives. Its quote combines NAV, an order-size curve, a funded-liquidity wall, decaying sell pressure, and a cadence response to repeated sells. The design seeks to keep isolated small exits useful while limiting reserve depletion and gains from splitting a concentrated exit. We evaluate the implemented Solana pricing path with fixed workloads and ablations, then sweep 15,120 parameter configurations. At the reference parameters, cadence reduces aggregate split advantage by 9.67% against matched pressure-only pricing, improves 34 of 40 split workloads, and raises worst-case reserve remaining from 10.49% to 17.66%. No simple policy or Prop RFQ ablation in our comparison dominates the reference configuration on common metrics. After correcting epoch rollover, implementation quotes match the explicitly rolled model at every tested recovery point. However, low-value sells enable cheap cadence griefing.

In 1978, Yao studied the subset product problem and proved its NP-completeness. Later, Galbraith, Zobernig, and Li considered a prime-based modular variant and studied its average-case hardness. More recently, Li introduced the general problem of unknown-coefficient multivariate exponential system solving and studied its hardness systematically in an abstract setting. Li's framework implies a noisy modular variant of subset product as a special case. In this paper, we study this noisy subset product problem in a concrete setting, prove equivalence relations among several related variants, and use these results to construct a post-quantum non-alternating key exchange scheme, with a natural one-sided interpretation as a key encapsulation mechanism. Unlike other noise-based schemes, such as lattice-based schemes, our construction does not rely on an additional reconciliation plaintext. Instead, the receiver is able to recover the sender's ephemeral secret key itself. Moreover, we reduce indistinguishability security directly to the search version of the noisy subset product problem, without relying on a separate decisional assumption.

Modern vehicles have evolved into highly interconnected Software-Defined Cyber-Physical Systems (CPS), integrating embedded electronics, wireless communications, artificial intelligence, and Advanced Driver Assistance Systems (ADAS). While these technological advances have significantly improved vehicle safety, efficiency, and driving automation, they have also introduced a rapidly expanding cyber-physical attack surface. Consequently, automotive cybersecurity has become an active research area encompassing attacks on physical vehicle components, access and authentication mechanisms, electronic and software systems, and autonomous driving technologies. Although numerous studies and surveys have investigated these security threats, the existing literature remains fragmented, often focusing on specific vehicle subsystems or individual technologies. This paper presents a comprehensive survey of attacks and defense mechanisms targeting modern vehicles through a unified and orthogonal taxonomy that classifies the literature into four research directions: attacks on vehicle body and physical systems, vehicle access and engine start systems, electronic and software systems, and ADAS and autonomous driving systems. For each direction, the associated security issues, representative attacks, and existing countermeasures are systematically reviewed and analyzed. Furthermore, the survey identifies current research trends, highlights existing research gaps, and discusses future challenges toward the development of comprehensive and resilient automotive security solutions.

Copy-protection is one of the main applications of quantum information in cryptography. In copy-protection, we encode a functionality in a reusable quantum state so that it cannot be split into two states (called freeloader adversaries) that remain simultaneously useful. Despite a long line of research, previous works have only been able to show security with respect to independently sampled challenges in the plain-model. However, arguably a more natural security notion considers the two freeloader adversaries receiving the same challenge. This so-called identical-challenge security notion is also connected to other fundamental quantum cryptographic primitives such as unclonable bits (i.e. unclonable encryption) and copy-protection of point functions.

In this work, first we make progress on the definitional foundations of these primitives, and then prove security in the plain model for our new stronger definitions, in particular also resolving the question of copy-protection with identical challenges and copy-protection of point functions. In more detail, we obtain the following results.

-- Copy-protecting decryption keys (Single-decryptor encryption).} We define a new natural security notion for single-decryptor encryption (SDE) called {correlated challenge security}, and show that implies all previous security definitions for SDE, including identical-challenge security. Then, we prove that, assuming indistinguishability obfuscation (iO) and one-way functions, the SDE construction of Kitagawa and Yamakawa (TCC'25) satisfies correlated challenge security. We also provide an almost complete characterization of the relationship among previous SDE security notions.

--Copy-Protecting General Functionalities with Correlated Challenges. We define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits, plus auxiliary information before and after splitting. Security requires only conditionally uniform bits and $\lambda^c$ average conditional min-entropy in each point separately, for any constant $c>0$; thus, in particular the challenge points may be identical. Assuming polynomially secure post-quantum iO and quantum-hard LWE, we construct correlated UPO for arbitrary polynomial-size keyed circuits with input length at least $\lambda^c$, answering the open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and Çakan-Goyal (EUROCRYPT'26).

--Applications Our results yield the first plain-model copy protection for point functions, $k$-point functions, and compute-and-compare programs under natural security definitions, and identical-challenge copy protection for general puncturable functionalities.

The technical core of our results is a new decisional monogamy theorem for coset states, which both simplifies the proofs and generalizes the results of existing copy-protection constructions, which may be of independent interest.

Rijndael-256 (R256), the 256-bit block variant of the Rijndael family, is practically relevant in ongoing NIST draft discussions on wider-block standardization and in several NIST post-quantum signature candidates. Relative to AES, R256 combines a wider $4\times8$ state with non-standard ShiftRows offsets $(0,1,3,4)$, invalidating key assumptions behind many AES-oriented optimizations. We study how these mismatches manifest on three targets and develop three corresponding adaptation strategies: wider classical bitslicing on Cortex-M4, Reuse with Reshuffling on AArch64, and Amortize the Mismatch on CUDA. This yields a bitsliced Cortex-M4 implementation with secret-independent control flow and memory access patterns (4,962 cycles/block), an AArch64 pre-shuffle design that reuses the AESE instruction with AddRoundKey folded in (up to 6,520 MB/s), and a CUDA shared-memory T-table implementation reaching 81.16 GiB/s; we report throughput on AArch64 and CUDA because per-block cycle measurement is not directly available on those platforms. Replacing the R256 cryptographic core in four NIST PQC reference codebases on Apple M2, with minimal integration changes where needed, yields signing speedups of $1.18\times$--$114.3\times$ and verification speedups up to $155.6\times$, with the end-to-end gain governed by each scheme's R256 fraction.

We show that the CRT-FHE scheme of Pradhan et al. is insecure for laws within its assumed error distribution range. The secret key follows from the public key by a single ring inversion whenever the public multiplier is a unit. The plaintext is recovered from any ciphertext under such a law without the secret key, for every multiplier, giving chosen-plaintext advantage $1/2$. We further show that the transformation from ordinary Ring-LWE to CRT-RLWE does not preserve the error distribution, so it does not establish that CRT-RLWE is at least as hard as Ring-LWE.

One mechanism underlies both. The Chinese remainder theorem (CRT) function is reduced modulo $p_1p_2$ while its output is used modulo a coprime modulus $q$, so under every zero-preserving section an error in $p_2\mathcal{R}$ encodes to zero. The law $p_2B_1$ is so confined, meets the stated conditions, and decrypts correctly. Confinement is not a weakness of scale: scaling any baseline law by $p_2$ leaves its ordinary Ring-LWE problem exactly equivalent, while the reduced encoder destroys every error it produces. The reduction discrepancy is a multiple of $p_1p_2$ and not of $q$, so the small-error premise of the proof cannot remove it, and at the reported parameters a single error coefficient refutes the identity while satisfying that premise. The centered binomial $B_2$ separates the coefficient laws at total variation distance $3/8$, and at the reported dimension that distance between the induced polynomial laws is exponentially close to one.

With the growing deployment of secure multi-party computation (MPC) in data-intensive applications, the offline generation and distribution of authenticated multiplication triples has become a key scalability bottleneck. Existing software-only preprocessing protocols, such as MASCOT and LowGear, typically incur substantial interaction and computation costs when the number of participants or the triple demand is large. This paper proposes a trusted execution environment (TEE) server–assisted aggregated offline deployment scheme that moves expensive interactive preprocessing into a remotely attested enclave and distributes participant-specific authenticated triple shares over authenticated-encrypted channels. Conceptually, the enclave serves as a TEE-backed pseudorandom correlation generator (PCG) that outputs authenticated correlated randomness for MPC with one-way delivery. We design an end-to-end workflow covering remote attestation, per-participant session establishment, and encrypted distribution. The proposed protocol applies to both semi-honest and malicious adversaries; we provide a security analysis against malicious adversaries with abort. Experimental results show clear efficiency improvements over MP-SPDZ implementations of MASCOT and LowGear. Specifically, the proposed scheme achieves a generation rate three times that of MASCOT, while exhibiting linear scalability up to 100k participants. Furthermore, by employing a streaming processing strategy, it efficiently supports the generation of up to 10M triples with an amortized time significantly lower than that of purely software-based protocols, enabling practical and highly scalable preprocessing for large-scale heterogeneous MPC deployments.

Public-key encryption (PKE) is a fundamental primitive in modern cryptography, and many PKE schemes have been standardized and widely deployed. To reason about security in complex and highly compositional environments, Zhandry and Zhang (CRYPTO 2020) initiated the study of indifferentiability for public-key cryptosystems. However, their construction for PKE departs substantially from the design paradigms used in practice, and to date no practical public-key encryption schemes are known to achieve indifferentiability.

In this work, we further investigate indifferentiability for public-key encryption, asking whether it can be achieved for practical, standardized schemes. We provide evidence that the answer is yes: slightly augmented standardized group-based encryption schemes can indeed achieve provable indifferentiability. Our contributions are threefold:

-- Identifying a barrier in the existing ideal PKE model: We revisit the ideal PKE definition of Zhandry and Zhang and identify an artificial requirement---namely, pseudorandom public keys and ciphertexts---that constitutes an inherent barrier to achieving indifferentiability from groups.

-- Redefining the idealized model for PKE: We propose a revised ideal PKE model that removes this pseudorandomness requirement, thereby opening the possibility of achieving indifferentiable public-key encryption from practical group-based schemes. --Making standardized PKE indifferentiable: We consider two public-key encryption schemes standardized in ISO/IEC 18033-2---Elliptic Curve Integrated Encryption Scheme (ECIES) and Public-Key Secure Encryption (PSEC)---and show that, under slight augmentation, both are indifferentiable from our revised ideal PKE.

In conclusion, our work advances the development of indifferentiable yet practical public-key encryption schemes, enabling future research and protocol design to build on standard PKE schemes while enjoying strong composability guarantees.

Ring signatures provide signer anonymity for ad hoc sets of public keys. Generic Abe-Ohkubo-Suzuki (AOS) transforms are well understood for plain Fiat--Shamir and hash-and-sign signatures, but not for their rejection-sampling variants: Fiat--Shamir with aborts (FSwA) and hash-and-sign with retry (HSwR). We formalize AOS ring transforms for FSwA and HSwR and analyze their security in the quantum random-oracle model. For unforgeability, we reduce security under adaptive ring-signing queries to security without signing queries using essentially the same assumptions as in security proofs for the corresponding ordinary signatures; handling adaptive corruption additionally requires the simulation property to remain valid after key exposure. Strong unforgeability additionally requires response uniqueness and special soundness for FSwA, or second-preimage resistance and non-invertibility for HSwR. The residual no-signing-query requirement admits generic reductions, but with loss exponential in the number of honest keys. Finally, an ML-DSA case study shows that augmented public keys achieve the required key-exposure simulation while identifying its limitations; we also identify conditions for candidate HSwR instantiations.