Blind signatures are a central tool for privacy-preserving protocols. They allow users to obtain signatures from a signer without the signer seeing the signed message. For instance, it enables electronic cash: signatures correspond to coins which can be issued by the bank in a privacy-preserving manner via blind signing. To mitigate the risk of key compromise, threshold blind signatures allow the distribution of the signing key amongst N parties. While recent works have focused on improving the security of this primitive in the classical setting, no construction is known to date in the post-quantum setting. We present the first construction of a threshold blind signature secure in the post-quantum setting, based on lattices. We prove its security under an interactive variant of the SIS assumption introduced in [Agrawal et al., CCS’22]. Our construction has a reasonable overhead of a factor of roughly 1.4 X to 2.5 X in signature size over comparable non-threshold blind signatures over lattices under heuristic but natural assumptions.

The advent of quantum computing poses a fundamental threat to classical cryptographic assumptions. While algorithms such as RSA and Elliptic-Curve Cryptography are secure against classical adversaries, they would be efficiently broken by a sufficiently powerful quantum adversary. Yet, despite rapid industrial and academic progress, the timeline for achieving a Cryptographically Relevant Quantum Computer (CRQC) remains uncertain and opaque. In this work, we propose a mechanism to monitor quantum capabilities through economic incentives. We introduce QCAP, a trustless distributed protocol for deploying a quantum canary address alert. QCAP enables the creation of publicly auditable cryptographic challenges whose solutions would reveal the existence of quantum computers capable of breaking the Elliptic Curve Discrete Logarithm problem. The protocol is decentralized, secure, efficient, and verifiable, featuring adjustable difficulty and native Bitcoin compatibility. A proof-of-concept implementation demonstrates the feasibility of QCAP as a Bitcoin-based early-warning system for the emergence of quantum computational power.

This paper systematically analyzes the security of the two-branch Unified Feistel Lai Massey (UFLM) structure with independent random round functions under chosen plaintext and chosen ciphertext attacks, focusing on its indistinguishability from a random permutation. UFLM uses an invertible linear layer represented as a $2 \times 2$ block matrix $\varphi$ with blocks $A_{11}, A_{12}, A_{21}, A_{22}$. Previously, Dai et al. proved that when $A_{12}$ is invertible, $4$-round UFLM achieves CCA security and resists up to $\mathcal{O}(2^{n/2})$ queries, where the UFLM input is $2n$ bits. Our work imposes no restriction on $A_{12}$. We determine the minimal number of rounds for UFLM to achieve CPA and CCA security, fully determined by the parameters $T(A_{12}^{\top}, A_{11}^{\top})$ and $T(A_{12}, A_{22})$. For UFLM with enough rounds to be secure, the query bound is primarily determined by the rank of $A_{12}$. For all UFLM with too few rounds to be secure, we present successful distinguishing attacks that require at most four queries. Our results rigorously show, for the first time, that when $A_{12}$ has full rank, UFLM requires the fewest rounds to achieve CPA and CCA security and attains the highest query bound. Nevertheless, when $A_{12}$ is not full rank, CPA and CCA security can still be achieved by increasing the number of rounds unless $T(A_{12}^{\top}, A_{11}^{\top}) = \infty$ or $T(A_{12}, A_{22}) = \infty$. At last, for involutory $\varphi$, we find UFLM achieves CPA and CCA security if and only if $A_{12}$ has full rank.

The security of lattice-based cryptography relies critically on the concrete hardness of the approximate shortest vector problem (Approx-SVP). For cryptographic-sized instances, existing Approx-SVP rank reduction conditions may be overly aggressive, as they implicitly assume access to a large number of extremely short lattice vectors. In this work, we systematize and refine Approx-SVP rank reduction conditions from a feasibility perspective. We identify that, in the context of the dimension-for-free (D4f) technique, the existence of a single sufficiently short vector is the essential requirement, and we derive two refined and compact rank reduction conditions accordingly. The first condition is based on geometric properties of lattice sieving, while the second incorporates a basis-quality-dependent probabilistic bound. These results are validated through extensive experiments on high-dimensional lattices, where the compact condition outperforms prior methods by up to a factor of $60$ in dimensions $850$ and $925$. To reliably realize these conditions in high dimensions, we present APBKZ, an adaptive Pump-based lattice reduction strategy that dynamically selects the blocksize and D4f parameters according to the evolving Gram-Schmidt profile. We further introduce HeadAPBKZ, a head-focused execution mode that restricts reduction to a critical prefix once the rank reduction condition is satisfied. Combining these advances, we develop an improved concrete security estimation framework for the MSIS problem. Applied to Dilithium, our analysis indicates that, when compact rank reduction behavior is integrated with the D4f technique, the estimated concrete security of Dilithium is reduced by 3.65-6.09 bits relative to the conservative Core-SVP baseline, providing a more realistic concrete assessment. We also derive an analytic approximation whose closed-form estimates remain close to the numerical estimation, with discrepancies of only about 1.1 bits.

Reed–Solomon (RS) codes underpin a wide range of cryptographic protocols, from verifiable secret sharing (VSS) to blockchain data availability (DA). An RS code commitment enables a prover to distribute codeword fragments among many parties while allowing each recipient to verify that its fragment is consistent with a RS code. Existing constructions either rely on homomorphic polynomial commitments, which incur redundant commitments and expensive group operations, or use FRI-based interactive proofs, which achieve fast proving but suffer from prohibitively large communication. We present UltraProofs, a new RS code commitment framework that achieves linear-time proof generation while remaining compatible with any multilinear polynomial commitment. Our key technical contribution is an evaluation-consolidation protocol that reduces $n$ evaluation proofs at distinct RS points to a single randomized evaluation, eliminating redundant commitments and removing the need for homomorphic structure. We further design a tailored multilinear PCS, LightLigero, which achieves $O(\lambda \log n)$ proof size and maintains $O(n \log n)$ prover time. UltraProofs attains asymptotically optimal prover complexity with concrete speedups in practice: in VSS, it reduces prover time by $2.4\times$ and proof size by $4\times$ compared to HydraProofs (S&P'25); in DA, it cuts per-node communication by up to $2{\sim}5\times$ relative to FRIDA (Crypto'24) while retaining similar prover cost. By decoupling verifiable RS encoding from any specific PCS instantiation, UltraProofs provides a flexible, efficient, and modular foundation for large-scale verifiable storage and distributed cryptographic systems.

HiAE is a well-designed AEAD scheme using AES round functions, delivering outstanding performance on both ARM and x86 processors. Some existing AEAD schemes such as Rocca (ToSC 2021) have been shown to be vulnerable when attackers can repeatedly query the decryption oracle with forged ciphertexts and random tags until a valid tag is accepted. Motivated by this, we use algebraic techniques to analyze the security of HiAE under the same setting. Firstly, we employ the meet-in-the-middle technique and guess-and-determine technique to recover the state and derive a key-related equation resulting from two layers of AES round functions. Secondly, by adopting an algebraic approach to study the properties of the round function, we decompose the equation into byte-level equations for divide-and-conquer. Finally, we utilize the guess-and-determine technique to recover the key. Collectively, these techniques enable us to present the full key-recovery attack on HiAE. Our attack achieves a data complexity of $2^{130}$ and a time complexity of approximately $2^{209}$, leveraging both encryption and decryption oracles with a success probability of 1. We emphasize that our attack considers a stronger scenario than HiAE's original security model, and thus does not invalidate its original security claims.

Threshold signatures distribute trust across multiple parties, eliminating single points of failure and reducing insider and key-exfiltration risks—properties that are increasingly important for high-assurance deployments and recently emphasized by NIST’s Multi-Party Threshold Cryptography (MPTC) initiative. We present a practical t-out-of-n threshold variant and emulation of MAYO, a post-quantum signature candidate to NIST’s call for additional signatures. Our proposal builds upon the threshold MAYO design of Celi, Escudero and Niot (PQCrypto2025), which we significantly refine to achieve practical performance. To this end, we introduce two algorithmic modifications to MAYO tailored for the distributed setting: (1) Explicit-Salt MAYO, which allows for pre-determined salts to enable a single-round online phase; and (2) Depth-Reduced MAYO, which restructures the signing algorithm to minimize the depth of secret-dependent operations. We then propose a unified protocol framework that integrate these techniques, plus other MPC specific optimizations, with the goal of minimizing online latency. Finally, we provide a concrete instantiation and local emulation in the dishonest majority setting, secure against active adversaries. Our emulation shows that threshold signing is practical at typical threshold sizes and amenable to deployment. By releasing an open-source implementation and reporting end-to-end performance, this work offers a concrete reference for the thresholdization of post-quantum signatures. Clearly the aforementioned framework is not limited to MAYO, and can be applied to the UOV family of signatures more generally.

Private BitTorrent trackers enforce upload-to-download ratios to prevent free-riding, but suffer from three critical weaknesses: reputation cannot move between trackers, centralized servers create single points of failure, and upload statistics are self-reported and unverifiable. When a tracker shuts down, users lose their contribution history and cannot prove their standing to new communities. We address these problems by storing reputation in smart contracts and replacing self-reports with cryptographic attestations. Peers sign receipts for received pieces; the tracker aggregates them via BLS signatures and updates reputation. If a tracker is unavailable, peers fall back to an authenticated distributed hash table (DHT): stored reputation acts as a public key infrastructure (PKI), preserving access control without the tracker. Reputation is portable across tracker failures through single-hop migration in factory-deployed contracts. We also address the privacy implications of publishing public keys and reputations tied to private trackers on a public ledger: we propose ephemeral session keys to prevent linking peer identities, zero-knowledge membership proofs for anonymous DHT participation, and confidential reputation using homomorphic commitments. We formalize the security requirements, prove four security properties under standard cryptographic assumptions, and evaluate a prototype. Measurements show that transfer receipts add less than 5\% end-to-end overhead with typical piece sizes. To minimize signing overhead, we adopt a hybrid signature scheme: ECDSA signs individual piece receipts at transfer time for low per-operation latency, while BLS serves as the overarching scheme, enabling compact aggregation of many receipts into a single proof at report time. This design reduces client-side signing cost by an order of magnitude compared to using BLS throughout.

The expected emergence of cryptographically relevant quantum computers (CRQCs) will represent a singular discontinuity in the history of digital security, with wide ranging impacts. This whitepaper seeks to elucidate specific implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and potential mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem over the secp256k1 curve, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either $\leq 1200$ logical qubits and $\leq 90$ million Toffoli gates or $\leq 1450$ logical qubits and $\leq 70$ million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with $10^{-3}$ physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between "fast-clock" (such as superconducting and photonic) and "slow-clock" (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable "on-spend" attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling mechanism, as well as the enduring concern of "abandoned" assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of "digital salvage" to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the migration to PQC without delay.

Atomic swaps allow two parties to exchange coins across blockchains without trust. Most existing solutions support a 1-to-1 transaction; however, the value ratio of two cryptocurrencies is usually not 1-to-1. In addition, these solutions often rely on blockchains with explicit support structures for atomic swaps, typically hashed timelocks (HTLCs) or smart-contract scripting. Thyagarajan et al. (SP'22) provide a solution for n-to-m swaps utilizing adaptor signatures instead, which offer better privacy for the participants. Significantly, all these approaches need timed transactions or a similar substitute on both sides, but not every blockchain supports timed transactions. Hoenisch et al. (ESORICS'22) demonstrate a concrete swap procedure between Bitcoin and Monero, where only one side needs timed transactions. We build upon both of these ideas to provide a generic solution for any blockchain, where only one side needs timed transactions. We introduce a generic adaptor-signature protocol for n-to-m swaps. In doing so, we minimize assumptions compared to current solutions. Both sides lock their coins in shared (two-party signature) addresses, where they can only access the coins together. To prevent deadlocks, both parties are able to refund their coins from these addresses with pre-signed transactions. Our solution works with all relevant blockchains because it needs only standard signatures and a joint public key. Further, only one side needs timed transactions, and if each party acts in its best interest, there are two possible outcomes: If progress stalls, the side with timelocks refunds after a certain time, and the other side refunds immediately. Otherwise, one party redeems the other party's coins with pre-signed transactions, and the other party completes the swap after a timeout to prevent race conditions. We prove security in the universal composability framework and show privacy preservation via unlinkability and fungibility.

Multivariate quadratic (MQ) signatures offer fast signing and verification with short signatures, but their practicality is often limited by large public keys. Recent schemes, such as MAYO, address this limitation by employing the "whipping" technique. This method utilizes emulsifier matrices—the core component underlying Beullens' MAYO scheme—to expand a mini-UOV map into a larger one while ensuring that signing reduces to solving a linear system that is full-rank with high probability. In this work, we focus on modifying these fundamental emulsifier matrices themselves to achieve better performance and smaller key sizes. First, we propose lifting the emulsifier matrices to an extension field while maintaining the base UOV map over the ground field. By leveraging the whipping technique to keep the variable-to-equation ratio close to one, this structural modification effectively avoids known lifted system attacks. Second, we enhance rectangular emulsifier matrices—originally introduced in prior work—with a structured block design that accelerates signing and verification while preserving the necessary full-rank behavior. This approach allows the underlying UOV instance to utilize fewer equations, yielding significantly smaller public keys and potentially faster operations. By combining both techniques, we design a new variant MAYO$^−_L$ and provide a detailed security analysis against known forgery and key-recovery attacks, and propose parameter sets that improve public key and signature sizes at comparable security levels. Finally, we discuss the applicability of our lifting improvement to SNOVA, demonstrating that this enhancement can be integrated into other UOV-based schemes employing the whipping technique.

Several modern applications, such as Signal or WireGuard, use efficient Noise-like implicit authentication key exchanges that require only a small number of exponentiations and two interactions. These protocols have been proven to be secure under the 'strong Diffie–Hellman' (SDH) assumption in the random oracle model (ROM). At ESORICS 2021, Ramacher, Slamanig and Weninger presented an extension to the implicit authenticated key exchange security model, which enables strong privacy properties to be captured in addition to key-secrecy, including man-in-the-middle privacy (ensuring privacy even if a session is interrupted) and forward privacy. They also proposed a protocol to instantiate their model. In this paper, we present an efficient Noise-like protocol that achieve privacy in this model. Our protocol is as efficient as Noise-like protocols that do not guarantee privacy in terms of exponentiations. Moreover, our protocol requires three interactions, which is optimal for this privacy model. It is also more efficient than the ESORICS 2021 protocol in terms of both exponentiations and interactions. Finally, we propose another round-optimal protocol, slightly less efficient in terms of exponentiations, but secure under the CDH assumption in the ROM.

Searchable encryption enables efficient querying over outsourced data while limiting server-side leakage. Existing methods for associative aggregation queries on multidimensional array data suffer from significant limitations: * Use range structures that precompute ranges yielding either: ** Storage size proportional to the total domain size (Demertzis et al., TODS 2018/Falzon et al., PVLDB2022). ** Or linear-time search in the worst case (Chang et al., IEEE TKDE 2021). * Bucket-based methods (Espiritu, Markatou, Tamassia, PoPETS 2022) are only practical when the largest bucket is small. Fully homomorphic encryption (FHE) approaches (Kushnir, Moskowich, Shaul, PoPETS 2024) remain computationally impractical. Due to strong attacks on range schemes with access pattern leakage (Falzon et al., CCS 2020), we consider the task of oblivious search. We propose oblivious segment trees, which offer efficient storage and search. Our approach achieves polylogarithmic query complexity. Storage depends on the number of distinct values per dimension, not on the domain size. Under typical data distributions, segment trees are provably shorter than standard alternatives. We evaluate performance on datasets with 1–3 dimensions and up to $5$ million entries. Across multidimensional datasets, our method reduces the number of stored items by $10$ to $10^{10}$ compared to prior non-FHE approaches. On a 32-thread machine, server-side query processing remains under $1.2$ seconds.

Non-malleable codes allow a sender to transmit a message to a receiver, while providing a ``best-possible'' integrity guarantee to ensure that no attacker---who cannot already decode the message---can meaningfully tamper the message in transit. If tampered, the received message should either be invalid or unrelated to the original message. Non-malleable time-lock puzzles (TLPs) are a special case of non-malleable codes for bounded polynomial-depth tampering with very efficient encoding. In this work, we give generic techniques for constructing non-malleable codes and non-malleable TLPs with improved rate, which captures the ratio of a message's length to its encoding length. A key contribution of our work is identifying a security notion for non-malleability, which we term ``CCA-hiding'', sufficient for our compilers. CCA-hiding is a relaxation of CCA-security for encryption or commitments to the fine-grained setting of codes, and requires that the encoded message remains hidden, even given a decoding oracle for any other codeword. Intriguingly, CCA-hiding does not imply non-malleability in the fine-grained setting, as is the case for encryption and commitments. Using our new techniques, we give the following constructions: -- Rate-1 CCA-hiding TLPs in the plain model. -- Rate-1 non-malleable codes for bounded polynomial-depth tampering in the auxiliary-input random oracle model (AI-ROM). -- Rate-(1/2) non-malleable TLPs in the AI-ROM.

Threshold Schnorr signatures enable $t$-out-of-$n$ parties to collaboratively produce signatures that are indistinguishable from standard Schnorr signatures, ensuring compatibility with existing verification systems. While static-secure constructions are well understood and achieve optimal round complexity, obtaining full adaptive security - withstanding up to $t-1$ dynamic corruptions under standard assumptions has proven elusive: Recent impossibility results (CRYPTO’25) either rule out known proof techniques for widely deployed schemes or require speculative assumptions and idealized models, while positive examples achieving full adaptivity from falsifiable assumptions incur higher round complexity (EUROCRYPT’25, CRYPTO’25). We overcome these barriers with the first round-optimal threshold Schnorr signature scheme that, under a slightly relaxed security model, achieves full adaptive security from DDH in the random oracle model. Our model is relaxed in the sense that the adversary may adaptively corrupt parties at any time, but each signer must refresh part of their public key after a fixed number of signing queries. These updates are executed via lightweight, succinct, stateless tokens, preserving the aggregated signature format. Our construction is enabled by a new proof technique, equivocal deterministic nonce derivation, which may be of independent interest.

Designing dynamic searchable symmetric encryption (DSSE) supporting conjunctive keyword queries over encrypted document collections is an important research area. Unfortunately, state-of-the-art conjunctive DSSE schemes such as ODXT (Patranabis et al., NDSS '21), and SDSSE-CQ and its variants (Zuo et al., PoPETS '25) either fail to achieve the desired levels of security (in particular, forward and/or backward privacy), or incur prohibitively large communication requirements and client-side computational overheads, which is undesirable for practical applications. In addition, all known conjunctive DSSE schemes that are both forward and backward private are quantum-broken due to their inherent reliance on discrete log-hard, prime-order cyclic groups. In this paper, we address the open question of designing practically efficient, low-leakage, forward and backward private conjunctive DSSE with small communication requirements and small client-side overheads. Towards this goal, we introduce the first systematic and rigorously formal notions of backward privacy for conjunctive queries that naturally extend the corresponding notions of backward privacy for single-keyword DSSE. Next, as our main contribution, we propose a new framework for conjunctive DSSE called fp-GA-ODXT that improves upon both ODXT and SDSSE-CQ-variants by achieving full-fledged forward privacy and strong backward privacy guarantees, while incurring small client-side computation and low communication overheads. We then demonstrate two instantiations of our fp-GA-ODXT framework: 1) A concretely efficient, classically secure instance based on discrete log-hard groups and an RSA-based trapdoor permutation, which we implement and benchmark. Our experiments demonstrate that we achieve smaller communication overheads and client-side computation for both updates and conjunctive searches as compared to both ODXT and SDSSE-CQ-variants. These come at the cost of a mild increase in server computation (which we view as an acceptable tradeoff in practice). 2) A post-quantum instantiation based on lattices and isogenies of supersingular elliptic curves, thus solving the longstanding open question of designing asymptotically efficient, forward and backward private conjunctive DSSE schemes with post-quantum security.

AI agents and custodial services are increasingly being entrusted as intermediaries to conduct transactions on behalf of institutions. The stakes are high: The digital asset market is projected to exceed \$16 trillion by 2030, where exchanges often involve proprietary, time-sensitive goods. Although industry efforts like Google’s Agent-to-Payments (AP2) protocol standardize how agents authorize payments, they leave open the core challenge of fair exchange: ensuring that a buyer obtains the asset if and only if the seller is compensated without exposing sensitive information. We introduce proxy adaptor signatures (PAS), a new cryptographic primitive that enables fair exchange through delegation without sacrificing atomicity or privacy. A stateless buyer issues a single request and does not need to manage long-term cryptographic secrets while proxies complete the exchange with a seller. The seller is guaranteed payment if the buyer can later reconstruct the purchased witness; meanwhile, the proxies remain oblivious to the witness throughout the protocol. We formalize PAS under a threshold model that tolerates the collusion of up to $t-1$ proxies. We also present an efficient construction from standard primitives that is compatible with Bitcoin, Cardano, and Ethereum. Finally, we evaluate a Rust implementation that supports up to 30 proxies. Our prototype is concretely efficient: buyer and seller computations take place in microseconds, proxy operations in milliseconds, and on-chain costs are equivalent to those of a standard transaction without fair exchange.

FHEW/TFHE bootstrapping suffers from a structural rigidity: the accumulator's ring dimension $N$ is limited by the input ciphertext modulus $q$ (typically $q \le 2N$), and thus the message space $t$. This coupling forces $N$ to grow with $t$, leading to inflated parameters and thereby high computational costs. In this work, we overcome this limitation by replacing the ring structure with a free $\mathcal{R}_N$-module $\bigoplus_{i=0}^{\tau-1}\mathcal{R}_N \cdot X^i$. This generalization decouples $N$ from $q$ through a flexible parameter $\tau$. We prove that computation in this extended algebra efficiently reduces to base-ring operations, enabling a new bootstrapping algorithm with improvements in both performance and precision. Theoretically, our approach reduces the asymptotic complexity of standard FHEW/TFHE bootstrapping from quadratic $\tilde{O}(t^2)$ to quasi-linear $\tilde{O}(t)$ in the message space $t$. Compared with prior Extended Bootstrapping methods over discrete cyclotomic ring [PKC'23, TCC'25, Asiacrypt'25], our framework constitutes an algebraic generalization that enables more flexible parameter selection. Experimental results demonstrate that our method achieves speedups of 1.40$\times$--2.77$\times$ over the state-of-the-art sorted extended bootstrapping [Asiacrypt'25].

This paper presents an optimized implementation of the Hamming Quasi-Cyclic (HQC) key encapsulation mechanism, leveraging the additive fast Fourier transform (FFT) for polynomial multiplication. A primary challenge in applying FFT-based multiplication to HQC is that the polynomial degrees slightly exceed powers of two, making standard FFT approaches inefficient. To address this, we propose a new method combining the Frobenius additive FFT (FAFFT) with the Chinese Remainder Theorem (CRT) to efficiently multiply polynomials of these specific degrees. Such a combination is made possible by our new interpretation of FAFFT's Encode step as ring isomorphisms, from which we derive an exact formula for the modulus of any FAFFT-based polynomial multiplier. In addition to the multiplication algorithm, we replace the Berlekamp-Massey decoder with an Extended Euclidean Algorithm (EEA) based method. The regular data flow of EEA facilitates the use of our highly optimized GF(256) SIMD arithmetic, leading to a faster execution speed. Benchmarks demonstrate that our FFT-based approach significantly outperforms traditional Toom-Karatsuba methods, even at lower degrees, on the Arm Cortex-M4 platform. Our integrated optimizations result in a 19.5% and 20.4% speedups for the encapsulation and the decapsulation processes compared to the current state-of-the-art HQC-1 implementation.

A proof of knowledge certifies that the prover “knows” a secret. This property is established by the existence of an extractor that, given access to the prover, can extract the secret. Unfortunately, this does not imply that a single entity has access to the secret in the clear, as it may be secret-shared among several parties and the proof computed using multiparty computation (MPC), or the secret may be embedded in a trusted execution environment (TEE) that only allows limited access to it. Often, the ability to encumber a secret in this way breaks the security of a system; vote selling in e-voting schemes is one example. To address this, two recent papers introduced the notions of “Proofs of Complete Knowledge” (PoCK) [Kelkar et al., CCS’24] and “Individual Cryptography” [Dziembowski et al., CRYPTO’23]. While the goals and constructions in those works differ, both rely on the same key idea to prevent encumbrance. To compute a proof, the prover must evaluate a hash function on a huge number of inputs. One then assumes that only a fraction of those can be encumbered, while for the rest the prover must know the inputs in the clear, and these clear inputs are sufficient to extract the secret. Computing a huge number of hashes is a challenge even for an honest prover (who has the secret in the clear), so those works suggest using outdated Bitcoin mining hardware to make the scheme practical. By forcing the prover to evaluate the hashes in a sequential manner, we could get meaningful security against encumbrance with far fewer hashes, especially against MPC, where round complexity is a major bottleneck. As a concrete instantiation of this idea, we define and construct Sequential Proofs of Complete Knowledge (SPoCK). Our construction uses the PoCK of Kelkar et al. (which are based on Fischlin’s straight-line extractable proofs of knowledge). The computation of this PoCK is then embedded into the computation of the Proof of Sequential Work from [Cohen&Pietrzak, EUROCRYPT’18]. SPoCK thus have the potential to enable complete-knowledge or individual-cryptography primitives where honest parties can use standard hardware. We also propose a variant of this scheme that requires a large amount of memory throughout the evaluation, providing better security also against TEEs.

A verifiable delay function (VDF), introduced by Boneh et al. [CRYPTO’18], on input $(x,T)$ produces an output $(y,\pi)$ where computing $y$ requires $T$ inherently sequential steps, and $\pi$ is a proof certifying correctness. VDFs have found numerous applications, and many of these rely on the assumption that honest parties can evaluate the VDF nearly as fast as adversaries. To support this assumption, significant effort has been invested in developing dedicated VDF hardware (ASICs). However, such devices are expensive and produced in limited quantities, leaving only a small number of parties with access to fast VDF evaluation. A natural workaround is to offer “VDFs as a service,” where a server equipped with specialized hardware evaluates instances on behalf of clients. This approach, however, is unsuitable when the VDF input must remain private. In this work, we introduce and construct blind VDFs, enabling secure VDF outsourcing without revealing the input. Inspired by blind signatures, our protocol allows a client to transform an input $x$ into a blinded instance $\alpha$, which is evaluated by the server. The server returns a result $\beta$, from this and its local state, the client can unblind to recover the correct output $(y,\pi)$, while the server learns nothing about $x$. We realize this notion by constructing a blinded version of Pietrzak’s VDF [ITCS’19]. In the original scheme, computing $y$ requires $T$ sequential steps, while generating the proof $\pi$ can be done in $O(T/S)$ parallel time using $O(S)$ space (e.g., $O(\sqrt{T})$ time and space). In our blind variant, the server performs the $T$ sequential steps and sends $O(S)$ data to the client, who completes the unblinding in $O(T/S)$ time. By allowing slightly more interaction, we obtain a protocol where the client’s work is small, while the server performs essentially the same computation as in the unblinded VDF.

In this work, we propose the first code-based $\mathsf{uPKE}$ from the hamming quasi-cyclic public key encryption scheme $(\mathsf{hqcPKE})$ of Gaborit et al. by integrating an efficient key-update mechanism utilizing a carefully designed deterministic sampling algorithm. Our sampling algorithm exploits a structured permutation set preserving Hamming weight and satisfying specific algebraic properties that is of independent interest. More positively, our protocol allows unbounded key updates free from the cumulative error issues inheriant to lattice based designs and supports asynchronous key updates, authorizing senders to update the public key independently. We formally establish the security of the proposed construction against indistinguishability under chosen-randomness and chosen-plaintext attack $(\mathsf{IND}\text{-}\mathsf{CR}\text{-}\mathsf{CPA})$ in standard model considering decisional quasi-cyclic syndrome decoding with parity $(\mathsf{DQCSDP})$ assumption. We emphasize that in comparison with existing post-quantum secure asynchronous schemes supporting unbounded updates, our construction achieves in the standard model instead of random oracle model significantly improved storage and communication efficiency, particularly in terms of public key size, ciphertext size and update ciphertext size. From a computational perspective, our design enables a more efficient public key update procedure and exhibits comparable performance for key generation, encryption, decryption and secret key update.

Functional encryption generates sophisticated keys for users so that they can learn specific functions of the encrypted message. We provide a generic construction of chosen ciphertext attacks (CCA) secure public-key functional encryption (PKFE) for all polynomial-size circuits. Our PKFE produces succinct ciphertexts that are independent of the size and depth of the circuit class under consideration. We accomplish our goal in two steps. First, we define a new cryptographic tool called constrained witness pseudorandom function (CWPRF) which is motivated by combining WPRF of Zhandry (TCC 2016) and constrained PRF of Boneh and Waters (ASIACRYPT 2013). More specifically, CWPRF computes pseudorandom values associated with NP statements and generates constrained keys for boolean functions. We can recompute the pseudorandom value corresponding to a particular statement either using a public evaluation key with a valid witness for the statement or applying a constrained key for a function that satisfies the statement. We construct CWPRF by coupling indistinguishability obfuscation (iO) and CPRF supporting all polynomial-size functions. In the second and main technical step, we show a generic construction of a CCA secure PKFE for all circuits utilizing our CWPRF. It has been observed that obtaining PKFE supporting all circuits is already a complex task and iO-based constructions of PKFEs are only proven to be chosen plaintext attacks (CPA) secure. On the other hand, existing CCA secure functional encryption schemes are designed for specific functions such as equality testing, membership testing, linear function etc. We emphasize that our construction presents the first CCA secure PKFE for all circuits along with succinct ciphertexts.

We present CLAASP-MP, a monomial prediction (MP) tool based on the three-subset division property without unknown subset (3SDP-woU), integrated into CLAASP, a library for automated analysis of symmetric key cryptographic primitives. The propagation rules of 3SDP-woU are encoded as a Mixed Integer Linear Programming (MILP) model generated directly from the CLAASP component graph, covering the main building blocks used in modern symmetric designs, including S-boxes, linear layers, Boolean word operations, modular addition and multiplication, and linear and nonlinear feedback shift register updates. Using this model for selected output bits, CLAASP-MP computes algebraic normal form (ANF) (for a small number of rounds), derives superpolies for a chosen cube, and computes a tight upper bound on the algebraic degree with respect to plaintext, key, or IV variables. A monomial is absent if its ANF coefficient is zero, if it does not appear in the superpoly, or if the algebraic degree is too small for it to occur; in all such cases, the output is balanced and yields an integral distinguisher. We evaluate \name{} on block ciphers, permutations, and stream ciphers implemented in \claasp{}. We introduce an exact bit-level MILP modeling technique for modular multiplication and apply it to provide the first independent algebraic analysis of the MSX block cipher, identifying integral properties that persist up to 7 rounds for MSX-128. Furthermore, we reproduce known distinguishers and identify new cubes for several block ciphers and extend the best-known integral distinguishers of ChaCha and Salsa permutations from 6 and 5 rounds, respectively, to 6.75 rounds. We also discovered new integral distinguishers for Bivium using several 36-dimensional cubes and extended the exact computation of the algebraic degree of Trivium to later initialization clocks while reproducing many published superpolies. These results show that CLAASP-MP provides a unified and practical MILP-based framework for monomial prediction and algebraic analysis across a wide range of symmetric primitives.

In this paper, we propose an enhanced variant of the F4 algorithm specifically designed for efficiently solving multivariate quadratic (MQ) problems, which are central to many post-quantum cryptographic schemes. Our approach overcomes a major inefficiency of conventional F4 by integrating a Hilbert-driven strategy that determines the optimal number of S-polynomials to generate at each degree, thereby reducing unnecessary zero reductions. We further introduce refined pair selection techniques that prioritize candidates yielding S-polynomials with smaller leading terms, which in turn minimizes the dimensions of intermediate matrices used during reduction. Experimental results show that our implementation outperforms state-of-the-art systems such as M4GB and Magma's F4 in both single-core and multi-core environments. Notably, our method sets new records in the Fukuoka MQ Challenge for Type VI problems over F(31) with m = 21,22,23,24 demonstrating the robustness and practical impact of our approach in solving highly challenging MQ instances. According to the computational complexity estimation formula], the problem with m = 24 is approximately 47,627 times harder than the previous record case with m = 20.

Lattice-based cryptography, as an active branch of post-quantum cryptography (PQC), has drawn great attention from side-channel analysis researchers in recent years. Despite the various side-channel targets examined in previous studies, detail on revealing the secret-dependent information efficiently is less studied. In this paper, we propose adaptive EM side-channel attacks with carefully constructed ciphertexts on Kyber, which is a finalist of NIST PQC standardization project. We demonstrate that specially chosen ciphertexts allow an adversary to modulate the leakage of a target device and enable full key extraction with a small number of traces through simple power analysis. Compared to prior research, our techniques require fewer traces and avoid building complex templates. We practically evaluate our methods using both a reference implementation and the ARM-specific implementation in pqm4 library. For the reference implementation, we target the leakage of the output of the inverse NTT computation and recover the full key with only four traces. For the pqm4 implementation, we develop a message-recovery attack that leads to extraction of the full secret key with between eight and 960 traces, depending on the compiler optimization level. We discuss the relevance of our findings to other lattice-based schemes and explore potential countermeasures.

Distributed Key Generation (DKG) is a vital security foundation for decentralized technologies like blockchain and threshold signatures. However, existing asynchronous DKG (ADKG) protocols face bottlenecks in rigid configuration, limited throughput, and poor scalability, failing to meet the dynamic security management demands of large-scale services.In this paper, we propose an efficient suite of ADKG protocols that support flexible threshold configurations. First, we design a Flexible-Threshold Asynchronous Complete Secret Sharing (FT-ACSS) protocol using bivariate polynomials and zero-knowledge proofs. In an $n \ge 3f+1$ network, FT-ACSS enables dealers to freely configure the threshold $t \in [f, n-f)$, surpassing the limitations of traditional fixed $f$ or $2f$ thresholds. Furthermore, FT-ACSS implements a batch processing mechanism to share up to $t$ secrets simultaneously with $O(\lambda n^2)$ communication cost. We additionally extend the Schnorr protocol into $m$-Schnorr to support multi-secret commitments, significantly reducing amortized resource overhead.Combined with RBC and ABA, these components form a complete FT-ADKG protocol. Theoretical and experimental evaluations demonstrate that our scheme offers superior flexibility and efficiency compared to state-of-the-art protocols, providing a practical security management solution for large-scale asynchronous distributed systems.

We investigate the security of AES-128/192/256 when implemented as ReLU-based neural networks via the natural sum-of-corners construction. Although these implementations are bit-exact on Boolean inputs, they extend AES into a continuous piecewise-linear function over $\mathbb{R}^{128}$. We show that under real-valued oracle access, such neural realizations admit deterministic linear-time master-key recovery. The attack exploits a geometric property of the natural XOR (AddRoundKey) layer: for corner parameter c < 1, ReLU activations partition the input space into key-dependent linear regions. Using symmetric perturbations, exactly one key hypothesis preserves linear-region membership, enabling bitwise recovery through simple output-equality tests. We formalize this phenomenon via a local separability lemma and obtain attack complexity O(128R) neural queries for R rounds. Experiments over 1,000 independent random keys for AES-128, AES-192, and AES-256 achieve 100% recovery success. The vulnerability is independent of key size and round count; it stems solely from exposing a key-dependent XOR layer inside a continuous neural architecture. Our results reveal a fundamental gap between Boolean security and geometric security in neural implementations of cryptographic primitives.

The security of multivariate public-key cryptography, a major approach to post-quantum cryptography, is based on the computational hardness of solving systems of multivariate quadratic equations over finite fields (the MQ problem). The MQ problem consists of solving a system of quadratic equations over a finite field of size $q$, with $n$ variables and $m$ polynomials. The existence probability of solutions to the MQ problem plays a central role in analyzing the security of multivariate cryptography. However, explicit bounds for fixed parameters $(q,n,m)$ have not been sufficiently studied. In this work, we evaluate the existence probability for randomly generated MQ systems with fixed parameters by analyzing the coefficient space arising from the MQ system. Using the inclusion--exclusion principle, we obtain a lower bound (approximately $0.625$) and an upper bound (approximately $0.667$) on the existence probability, focusing on the case $m=n$. We also derive upper and lower bounds on the probability that the number of solutions is exactly one in the case $m=n$. Finally, we analyze the existence probability of solutions to the MQ problem in the case $m \neq n$.

Block ciphers are versatile cryptographic ingredients that are used in a wide range of applications ranging from secure Internet communications to disk encryption. While post-quantum security of public-key cryptography has received significant attention, the case of symmetric-key cryptography (and block ciphers in particular) remains a largely unexplored topic. In this work, we set the foundations for a theory of post-quantum security for block ciphers and associated constructions. Leveraging our new techniques, we provide the first post-quantum security proofs for the key-length extension scheme FX, the tweakable block ciphers LRW and XEX, and most block cipher encryption and authentication modes. Our techniques can be used for security proofs in both the plain model and the quantum ideal cipher model. Our work takes significant initial steps in establishing a rigorous understanding of the post-quantum security of practical symmetric-key cryptography.

We study efficient non-arithmetic operations in (G)BFV with arbitrary plaintext modulus. We design scheme conversions between (G)BFV and Discrete CKKS, allowing (G)BFV ciphertexts to use radix-based integer computation in the Discrete CKKS setting. This gives asymptotically faster logical operations: for plaintext modulus $p$, homomorphic comparison runs in $O(\log p \log\log p)$ for BFV and $O(\log\log p)$ for GBFV.

The rapid adoption of Transformer-based AI has been driven by accessible models such as ChatGPT, which provide API-based services for developers and businesses. However, as these online inference services increasingly handle sensitive inputs, privacy concerns have emerged as a significant challenge. To address this, secure inference frameworks have been proposed, but their high computational and communication overhead often limit practical deployment. In plaintext settings, token drop is an effective technique for reducing inference cost; however, our analysis reveals that directly applying such methods to ciphertext scenarios is suboptimal due to distinct cost distributions in secure computation. We propose SecDTD, a dynamic token drop scheme tailored for secure Transformer inference. SecDTD advances token drop by shifting the dropping to earlier inference stages, effectively reducing the cost of key components such as Softmax. To support this, we introduce two core techniques. Max-Centric Normalization (MCN): A novel, Softmax-independent scoring method that enables early token drop with minimal overhead and improved normalization, supporting more aggressive dropping without accuracy loss. OMSel: A faster, oblivious median selection protocol that securely identifies the median of importance scores to support token drop. Compared to existing sorting-based methods, OMSel achieves a 16.9 times speedup while maintaining security, obliviousness and randomness. We evaluate SecDTD through 48 experiments across eight GLUE datasets under various network settings using the BOLT and BumbleBee frameworks. SecDTD achieves 4.47 times end-to-end inference acceleration without degradation in accuracy.

Privacy-preserving deep learning addresses privacy concerns in Machine Learning as a Service (MLaaS) using Homomorphic Encryption (HE) for linear computations. Nevertheless, the high computational cost remains a challenge. While prior work has attempted to improve the efficiency, most are built upon models originally designed for plaintext inference. These models are inherently limited by architectural inefficiencies when adapted to HE settings. We argue that substantial efficiency improvements can be achieved by designing networks specifically tailored to the unique computational characteristics of HE, rather than retrofitting existing plaintext models. Our design comprises two main components: the building block and the overall architecture. The first, StriaBlock, targets the most expensive HE operation—Rotation. It integrates ExRot-Free Convolution and a novel Cross Kernel, completely eliminating the need for external Rotation and requiring only 19% of the internal Rotation operations compared to plaintext models. The second component, the architectural principle, includes the Focused Constraint Principle, which limits cost-sensitive factors while preserving flexibility in others, and the Channel Packing-Aware Scaling Principle, which dynamically adapts bottleneck ratios based on ciphertext channel capacity that varies with network depth. These strategies efficiently control the local and overall HE cost, enabling a balanced architecture for HE settings. The resulting network, StriaNet, is comprehensively evaluated. While prior works primarily focus on small-scale datasets such as CIFAR-10, we conduct an extensive evaluation of StriaNet across datasets of varying scales, including large-scale (ImageNet), medium-scale (Tiny ImageNet), and small-scale (CIFAR-10) benchmarks. At comparable accuracy levels, StriaNet achieves speedups of 9.78 times, 6.01 times, and 9.24 times on ImageNet, Tiny ImageNet, and CIFAR-10, respectively.

We propose the first collaborative SNARK based on error-correcting codes that is scalable, i.e., the proof computation overhead is distributed among the $N$ provers. As a starting point, we introduce the notion of $(t,l)$-zero-knowledge collaborative codes that ensure that, when collaboratively computing a codeword over a distributed message, no coalition of up to $t$ corrupted parties learns any additional information about the message, even having queried up to $l$ codeword positions. We show that tensor codes consisting of the composition of two Reed-Solomon codes satisfy our definition, while also being foldable. We then propose a collaborative interactive oracle proof of proximity (coIOPP) for testing codeword closeness in our code, show how it can be made a zero-knowledge IOPP using randomness logarithmic in the size of the message (as opposed to linear with prior approaches), and we use it to construct a coIOPP for multi-linear polynomial evaluation. To compile our coIOPPs into non-interactive arguments, we prove that a natural extension of the compiler of Ben-Sasson-Chiesa-Spooner~(TCC 2016) in the collaborative setting preserves round-by-round (knowledge) soundness against quantum adversaries, which may be of independent interest for future work in collaborative SNARKs. Finally, we use an optimized collaborative version of the Spartan PIOP to build the first transparent and post-quantum secure scalable collaborative SNARK. Our experimental evaluation demonstrates that our scheme consistently outperforms the best existing (non-post-quantum secure) scalable collaborative SNARKs, both in end-to-end prover time and in total communication among provers, for all tested configurations.

In the area of white-box cryptography implementations, many existing protections are susceptible to attacks derived from physical cryptanalysis, which can be applied with minimal human effort and no prior design knowledge. The absence of a clear and comprehensive security model hinders the development of effective countermeasures against these attacks. We introduce the Haystack ciphers, a formal model for the security of white-box countermeasures against such attacks. In this model, the countermeasures are represented simply as symmetric-key encryption schemes. We show that their chosen-plaintext (IND-CPA) security is closely related to the resistance of the countermeasures against computational trace-based attacks. Similarly, their chosen-ciphertext (IND-CCA) security is closely associated with the resistance against fault injection attacks in the white-box model. Secure Haystack ciphers constitute the next formal milestone for advancing white-box designs and countermeasures, the minimal requirement that is not currently clearly achieved but is plausibly feasible with available tools. We review the white-box literature with respect to our model and bridge the gap between white-box and fault attacks, which are very powerful but were only partially considered in the white-box literature so far. We study known fault protections from the physical cryptography literature and present new fault attacks in the white-box setting, which raises the need and shapes the requirements for future secure countermeasures against fault attacks.

Discrete Gaussian sampling (DGS) is a fundamental method for generating random noise in various post-quantum cryptographic key generation and signature schemes. However, DGS has been shown to be highly susceptible to side-channel analysis, and several countermeasures have been developed. Masking, a robust countermeasure, is widely employed to secure these schemes against side-channel attacks. Due to the non-linear arithmetic operations involved, DGS has traditionally been considered unsuitable for efficient masked implementations. In this work, we propose $\textsf{MAGNET}$: an efficient masking design for the novel discrete Gaussian sampler based on Boolean circuits introduced by Wei et al. at ACM CCS 2023. With $\textsf{MAGNET}$, we demonstrate that DGS can be implemented in a masking-friendly manner. Previous masked DGS approaches in the literature have relied on computation-intensive floating point operations or table-lookup-based techniques using Cumulative Distribution Tables (CDT). In contrast, we show that DGS can be efficiently masked for moderate orders without relying on heavy computation or precomputed large lookup tables. In addition to delivering good performance at a small standard deviation $\sigma$, the efficiency of $\textsf{MAGNET}$ becomes increasingly significant in large $\sigma$ settings. $\textsf{MAGNET}$ achieves up to $17\times$ speed-up at $\sigma = 256$, and $56\times$ speed-up at $\sigma = 1024$ over the CDT-based sampler of Gérard and Rossi (2019). We provide an arbitrary-order C implementation and a first-order ARM Cortex-M4 implementation of $\textsf{MAGNET}$. We validate the practical security of the first-order implementation through Test Vector Leakage Assessment (TVLA) and systematic hardening of gadgets that exhibit side-channel leakage.

In this paper, we propose a new widely applicable technique for constructing low-depth S-box circuits, which we call SLICE (Segmented Low‑depth Iterative Circuit Exploration). SLICE reduces circuit depth by partitioning circuits into subcircuits and applying bit-level optimizations. To mitigate the optimization cost of subcircuits with large bit-widths or high AND depth, SLICE temporarily reduces their bit-width during the search, making low-depth circuit construction feasible for various S-box sizes. Furthermore, we refine the eBPD algorithm with the aim of minimizing XOR gate count in terms of area, and apply it to the constructed circuits to achieve an additional reduction. Our proposed method is simple yet powerful, especially in practical applications. This work focuses on three practically deployed cases, namely the AES, Ascon S-box circuits and Dillon’s 6-bit APN S-box used in FIDES, and additionally considers the cube $x^3$ S-box. For the AES S-box, we present 14-, 13- and 12-depth circuits, whereas the previous lowest depth was 14. Notably, the 12-depth design sets a new overall depth record for AES S-box circuits, while the 13-depth design records the most hardware-efficient circuit in terms of the area$\times$delay metric (ADP). For the Ascon S-box, we present the first 4-depth circuit. For Dillon's S-box and the cube $x^3$ S-box, we also derive new low-depth circuits that improve upon the best previously known depths. All of our proposed S-box circuits achieve better ADPs than previous designs. We believe that SLICE will be useful for evaluating both existing and novel S-box designs.

Secure multi-party computation (MPC) enables mutually distrustful parties to jointly evaluate a function on their private inputs. Classic MPC protocols, however, assume a static set of participants in which every party must remain online throughout the entire computation. Recent advances have introduced MPC models with dynamic participation, such as Fluid MPC, in which computation steps are delegated to a sequence of committees that change across epochs. This approach improves robustness, enabling parties to go offline once their roles are complete. Yet, this flexibility comes at a cost: the most efficient dynamic-participation MPC protocols still incur communication overheads exceeding traditional MPC by more than an order of magnitude. In this work, we formalize the communication complexity of $(d,n)$-threshold secret-sharing-based Fluid MPC. We prove a tight trade-off between communication cost and the adversary's corruption threshold, showing that linear communication complexity $O(n)$ is impossible when the corruption threshold $t$ exceeds a proportion of $d$. Matching this bound, we construct a protocol with a communication cost of $9.3n$ elements per multiplication gate against a semi-honest adversary and $37.3n$ elements against a malicious adversary. A C++ implementation confirms that our approach brings the cost of fluidity within practical limits.

TFHE is one of the most promising scheme in the literature for an adoption of Fully Homomorphic Encryption (FHE) in practice. The core reason of its good performances is the powerful Programmable Bootstrapping (PBS) operation, that enables to homomorphically evaluate a Look-Up Table (LUT) on a ciphertext while simultaneously reducing its noise. However, the computational cost of running a PBS degrades severely when the size of the plaintext space increases, making it intractable for precision larger than 8 bits. So, evaluating a LUT larger than 2^8 is not considered possible with the "vanilla'' TFHE scheme. In this paper, we propose a technique to accelerate LUT evaluation at high precision, that significantly enhances the state of the art. Our method beats the original PBS for spaces larger than 6 bits, and is competitive with the WoP-PBS (the reference of the state of art) while being conceptually simpler. Moreover, our method relies on the standard PBS of TFHE, and therefore does not require the design of new advanced homomorphic operators, which facilitates its integration into larger homomorphic compilation systems.

In a (non-interactive) multi-signature scheme, parties independently generate keys and produce signatures on a common message, which can be aggregated into a single signature verifiable with respect to the set of public keys. Existing multi-signature constructions, however, suffer from at least one of two limitations: either (1) aggregate signatures cannot be further aggregated, or (2) verification requires auxiliary information beyond the set of public keys, such as the aggregation topology. We argue that these limitations significantly restrict the applicability of multi-signatures in large-scale distributed systems, such as proof-of-stake blockchains. To address this gap, we initiate the formal study of hint-free multi-signatures, which support multi-hop aggregation while allowing verification using only the set of public keys. To the best of our knowledge, the only previously known (folklore) construction that is fully hint-free relies on recursive SNARKs, which introduces unclear heuristics for security (e.g., proving statements about random oracle relations) or inherently limits the depth of the aggregation topology. We show that hint-free multi-signatures can be realized without proof recursion, in the standard model. At a high level, we show how to publicly normalize BLS multi-signatures so that verification depends only on the set of public keys rather than a multi-set. While our scheme is not practical (it uses indistinguishability obfuscation), it establishes the feasibility of the primitive provides a foundation for future work on practical constructions.

The adoption of Distributed Ledger Technology (DLT) for critical financial infrastructures like Central Bank Digital Currencies (CBDCs) is hindered by a significant performance gap. Permissioned blockchains such as Hyperledger Fabric, which are conceptually suitable and have become popular platform used in many production deployments today, are nevertheless limited by architectural bottlenecks. Their monolithic peer design and consensus mechanisms prevent them from achieving the required scale for such demanding applications. This paper presents Fabric-X, a fundamental re-architecture of Hyperledger Fabric that addresses these challenges end-to-end. We have open-sourced Fabric-X as part of the Linux Foundation Decentralized Trust at \url{github.com/hyperledger/fabric-x}. We decompose the monolithic peer into independently scalable microservices for endorsement, validation, and committing. To maximize parallelism, we introduce a transaction dependency graph that enables the safe, concurrent validation of transactions across multiple blocks. Complementing the peer redesign, we introduce Arma, a novel sharded Byzantine Fault Tolerant (BFT) ordering service that dramatically increases throughput by ordering compact transaction digests rather than full transaction payloads. We implemented and benchmarked this framework with a UTXO-based CBDC application. Our evaluation demonstrates a peak throughput exceeding 100,000 transactions per second (TPS)—a multiple-orders-of-magnitude improvement over the standard implementation. This work proves that permissioned DLTs can be engineered for national-scale payment systems, providing a resilient and highly performant foundation for practical CBDC deployments and the integration of advanced, computationally intensive features.

Memory-hard functions (MHFs) are a useful cryptographic primitive which can be used to design egalitarian proof of work puzzles and to protect low entropy secrets like passwords against brute-force attackers. Intuitively, a memory-hard function is a function whose evaluation costs are dominated by memory costs even if the attacker uses specialized hardware (FPGAs/ASICs), and several cost metrics have been proposed to quantify this intuition. For example, space-time cost looks at the product of running time and the maximum space usage over the entire execution of an algorithm. Alwen and Serbinenko (STOC 2015) observed that the space-time cost of evaluating a function multiple times may not scale linearly in the number of instances being evaluated and introduced the stricter requirement that a memory-hard function has high cumulative memory complexity (CMC) to ensure that an attacker's amortized space-time costs remain large even if the attacker evaluates the function on multiple different inputs in parallel. Alwen et al. (EUROCRYPT 2018) observed that the notion of CMC still gives the attacker undesirable flexibility in selecting space-time tradeoffs e.g., while the MHF Scrypt has maximal CMC $\Omega(N^2)$, an attacker could evaluate the function with constant $O(1)$ memory in time $O(N^2)$. Alwen et al. introduced an even stricter notion of Sustained Space complexity and designed an MHF which has $s=\Omega(N/\log N)$ sustained complexity $t=\Omega(N)$ i.e., any algorithm evaluating the function in the parallel random oracle model must have at least $t=\Omega(N)$ steps where the memory usage is at least $\Omega(N/\log N)$. In this work, we use dynamic pebbling games and dynamic graphs to explore tradeoffs between sustained space complexity and cumulative memory complexity for data-dependent memory-hard functions. We design our own dynamic graph (dMHF) with the property that {\em any} dynamic pebbling strategy either (1) has $\Omega(N)$ rounds with $\Omega(N)$ space, or (2) has CMC $\Omega(N^{3-\epsilon})$ --- substantially larger than $N^2$. We also present a dynamic version of DRSample (Alwen et al. 2017) for which {\em any} dynamic pebbling strategy either (1) has $\Omega(N)$ rounds with $\Omega(N/\log N)$ space, or (2) has CMC $\Omega(N^3/\log N)$.

Folding schemes enable incremental proving by compressing many relation instances into a small accumulator. Recent lattice-based constructions such as LatticeFold+ [CRYPTO '25] achieve post-quantum security, but prover performance is still dominated by expensive $\ell_\infty$ range checks used to control witness growth during folding and extraction. We present a final $\ell_2$-norm-check design that combines random-projection constraints (in the spirit of Rok and Roll [ASIACRYPT '25]) with an exact shortening step (in the spirit of SALSAA [ePrint 2025/2124]) to recover the original witness $\ell_2$-norm bound at extraction time. Integrated into the LatticeFold+ composition, this gives iterative folding with controlled norm growth, preserved binding and knowledge-soundness goals, and substantially lower prover cost on the dominant norm-check path, while maintaining a similar proof size and verification cost. Our approach is modular and can be applied to other lattice-based folding schemes, providing a practical path for efficient post-quantum folding constructions.

In a proof of space, a prover performs a complex computation with a large output. A verifier periodically checks that the prover still holds the output. The security goal for a proof of space construction is to ensure that a prover who erases even a portion of the output has to redo a large portion of the complex computation in order to satisfy the verifier. In existing constructions of proofs of space, the computation that a cheating prover is forced to redo is a small fraction (vanishing or small constant) of the original complex computation. The only exception is a construction of Pietrzak (ITCS 2019) that requires extremely depth-robust graphs, which result in impractically high complexity of the initialization process. We present the first proof of space of reasonable complexity that ensures that the prover has to redo almost the entire computation (fraction arbitrarily close to 1) when trying to save even an arbitrarily small constant fraction of the space. Our construction is a generalization of an existing construction called SDR (Fisch, Eurocrypt 2019) deployed on the Filecoin blockchain. Our improvements, while general, also demonstrate that the already deployed construction has considerably better security than previously shown. Technically, our construction can be viewed as amplifying predecessor-robust graphs. These are directed acyclic graphs in which every subgraph of sufficient relative size $\pi$ contains a large single-sink connected component of relative size $\alpha_\pi$. We take a predecessor-robust graph with constant parameters $(\pi, \alpha_\pi)$, and build a bigger predecessor-robust graph with a near-optimal set of parameters and additional guarantees on sink placement, while increasing the degree only by a small additive constant.

Side-channel analysis is a powerful technique to extract secret data from cryptographic devices. However, this task heavily relies on experts and specialized tools, particularly in the case of simple power analysis (SPA). Meanwhile, large language models (LLMs) have demonstrated remarkable capabilities in assisting users with complex tasks, yet their potential for fully automated SPA remains unexplored. In this paper, we propose a novel prompt framework specifically designed for SPA tasks, enabling non-experts to perform end-to-end automated analysis by providing traces and prompts to an LLM in a single interaction. Our framework consists of six components: role, reinforce, input, task description, chain-of-thought, and expert strategies, with three expert strategies instantiated for SPA. To validate the framework's effectiveness and generalizability, we establish a dataset comprising seven sets of real power traces from various implementations of public-key cryptosystems, including RSA, ECC, and Kyber, as well as eighteen sets of simulated power traces that illustrate typical SPA leakage patterns. We compare against a representative unsupervised horizontal clustering attack, which achieves only 52.04% accuracy. In contrast, our framework enables GPT-4o and DeepSeek-V3.1 to achieve overall average accuracies of 98.02% and 97.83%, respectively. Furthermore, our framework reduces the analysis time by over 93.09% compared to manual analysis at comparable accuracy, enabling non-experts to complete SPA tasks in minutes rather than hours. Notably, this work represents the first successful application of LLMs to achieve fully automated SPA.

We present an active attack against the PEARL-SCALLOP group action. Modelling Alice as an oracle that outputs the action by a secret ideal class on suitably chosen oriented elliptic curves, we show how to recover the secret using a handful of oracle calls (four for the parameter set targeting a security level equivalent to CSIDH-1024), by reducing to the computation of moderately-sized group action discrete logarithms. The key ingredient to the attack is to employ curves with non-primitive orientations inherent to the PEARL-SCALLOP construction. We provide methods for public-key validation — that is, for deciding whether a given orientation is primitive — and discuss their practicality.

Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require \emph{quantum} proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from \emph{plain} trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a \emph{round-efficient} classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a \emph{generalized communication compression compiler}, which, assuming collapsing hash functions, transforms any $T$-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.

To more accurately capture real-world network and adversarial behaviors, recent research has explored Byzantine Agreement (BA) under various mixed-fault models. The breakthroughs by Loss et al. (TCC'23, TCC'24) have established the feasibility of optimally resilient BA in some of these models. Specifically, their protocols tolerate up to $t$ byzantine parties, $r$ receive faulty parties, and $s$ send faulty parties in a network of $n > 2t + r + s$ parties. Initially, Loss et al. (TCC'23) considers a model in which a party may be either receive faulty or send faulty but not at the same time (called the non-overlapping setting). The extended model in Loss et al. (TCC'24) further accommodates the \textit{overlapping setting}, where a party can simultaneously exhibit both receive faulty and send faulty behaviors. However, despite this flexibility, both protocols incur a prohibitively high communication cost of $O(n^5)$ bits, leaving open the fundamental question of whether the optimal $O(n^2)$-bit complexity achieved by many classical BA protocols is attainable in the optimally resilient mixed-fault model (with overlapping faults or not). In this work, we answer these open questions affirmatively. We present a mixed-fault BA protocol that achieves the optimal expected $O(n^2\lambda)$ communication complexity while maintaining expected $O(1)$ round complexity and optimal (rushing and strongly adaptive) resilience. Our protocol supports the strongest overlapping setting, while matching the best-known complexity of classical BA protocols. To achieve this, we develop a series of novel techniques, carefully designed to ensure efficient and secure agreement even under the mixed-fault model. Beyond binary BA, we extend our protocol to a multi-valued BA setting, achieving an expected $O(\tfrac{n^2}{t}L + n^2\lambda^2)$ communication complexity and an $O(1)$ expected round complexity, where $t$ is the number of byzantine faults and $L$ is the bit-length of the input values. In particular, for $t = O(n)$, the communication reduces to $O(nL + n^2\lambda^2)$. Notably, our protocols operate under the same setup and cryptographic assumptions as those in Loss et al.

Folding is a powerful technique for constructing efficient succinct proof systems, especially for computations that are expressed in a streaming fashion. In this work, we present Cyclo, a new lattice-based folding protocol that improves upon LatticeFold+ [Boneh and Chen '25] in multiple dimensions and which incorporates, among others, the pay-per-bit techniques from Neo when folding constraints expressed over a field $\mathbb{F}_q$ [Nguyen and Setty '25]. Cyclo proposes a new framework for building lattice-based folding schemes that eliminates the need for norm checks \emph{on the accumulator} by adopting an amortized norm-refreshing design, ensuring that the witness norm grows additively per round within a (generously) bounded number of folds. This design simplifies the protocol and reduces prover overhead. In particular, Cyclo only performs range checks on the input \emph{non-accumulated} witness, and when applied to fold constraints over $\mathbb{F}_q$, it does not decompose any witnesses into low-norm chunks within the folding protocol itself. Cyclo, supporting a complete family of cyclotomic rings, combines two simple building blocks: an extension commitment that reduces the norm of the witness by decomposing it and recommitting, and an $\ell_\infty$ range test via a sum-check protocol. We demonstrate, by proving communication and runtime estimates, that the construction results in an efficient and proof-size-friendly folding scheme. We also establish an algebraic connection between $\mathcal{R}_q$ and $\mathbb{F}_q$ using the polynomial evaluation map, enabling efficient reduction from R1CS/CCS over $\mathbb{F}_q$ to a linear relation over $\mathcal{R}_q$, providing a new and simpler formulation of the techniques in [Nguyen and Setty '25]. In practical settings, Cyclo achieves succinct proof sizes on the order of $30$ KB, improving by an order of magnitude over LatticeFold+. Our efficiency benchmarks indicate that our protocol also outperforms LatticeFold+ in practice.

Modern SNARK constructions, almost ubiquitously, rely on a polynomial commitment scheme (PCS) --- a method by which a prover can commit to a large polynomial $P$ and later provide evaluation proofs of the form "P(x)=y" to the verifier. In the context of zkVMs (i.e., proof-systems for general-purpose RAM computations), the common design is to represent the computation trace as a sequence of tables, one per CPU instruction, and commit to the these tables, or even their individual columns, as separate polynomials. Committing separately to these polynomials has a large overhead in verification costs, especially in hash-based systems. In this work we drastically reduce this cost via a new construction which we call the jagged PCS. This PCS enables the prover to commit to the entire computation trace as a single polynomial, but then allows for the verifier to emulate access to the individual table or column polynomials, so that the arithmetization can proceed in the usual manner. The jagged PCS may be thought of as a sparse PCS for a very particular form of sparsity - namely, a "jagged" matrix in which each column has a different height. Our construction of the jagged PCS is highly performant in practice. In contrast to existing sparse PCS constructions for general sparse polynomials, the jagged PCS does not require the prover to commit to any additional oracles and the prover cost is dominated by 5 finite field multiplications per element in the trace area. Furthermore, we implement the verifier as an arithmetic circuit that depends only on the total trace area - thereby significantly reducing the problem of "combinatorial explosion" often encountered in zkVM recursion.

In a paper presented at CRYPTO18, Reparaz et al. introduce a new model called the ``Tile-Probe-and-Fault-Model''. This model proposes to cover more realistic side-channel attacks by considering so-called ``combined'' attacks, in other words attacks using both side-channel leakage and fault injection. In addition, they introduce CAPA, a combined ``Countermeasure Against Physical Attacks'', which is inspired by an MPC protocol called SPDZ. In this paper, by attacking the original Beaver triples generation described in CAPA, we demonstrate that the CAPA countermeasure is not secure in its model, by breaking the countermeasures with a simple resolution of a linear system.

Graph neural network parameters are valuable intellectual property, and high-fidelity extraction enables model stealing, evasion, and downstream abuse. Prior cryptanalytic extraction can recover exact parameters in hard-label settings, yet existing methods focus on feedforward models and do not extend to message-passing graph neural networks. The obstacles include coupled queried nodes, hidden aggregation operators, and sign and scale ambiguities created by message passing. To our knowledge, this is the first cryptanalytic extraction framework for message-passing ReLU graph neural networks in hard-label settings where the oracle returns only the predicted class. We locate dual-point constraints on class-pair decision boundaries and activation hyperplanes, then recover hidden signatures with SVD-based extraction under a fixed ordered two-node query interface. We use ON/OFF distance comparisons to resolve hidden signs, then prove that diagonal scale factors propagate through the recovered prefix and cancel at the output layer. This four-stage recovery chain avoids explicit scale fitting while using only hard-label local queries. On ogbn-arxiv targets with up to 10,660 parameters, the attack achieves 100% prediction fidelity on 8,171 evaluated nodes with 48.68M node queries.

Existing Capture-the-Flag (CTF) platforms trust a single organizer, offer limited auditability, and are vulnerable to infrastructure-level manipulation. We propose zk–MPSFV, a zk-SNARK-based, multi-phase sub-flag verification scheme that replaces centralized scoring with an on-chain, zero-knowledge, publicly verifiable scoreboard. Challenges are decomposed into sub-challenges arranged as a directed acyclic graph (DAG): a team unlocks the next step only after proving completion of all parent nodes. Sub-flags and decryption keys are jointly generated by n organizers and released via an off-chain (t, n) Shamir–BLS threshold signature produced through multi-party computation (MPC), preventing any single organizer from leaking oraltering keys. Teams submit zk-PLONK proofs that the contract verifies, timestamps, and records immutably. Under standard assumptions (collision-resistant hashing, SNARK soundness/zero-knowledge, IND-CCA2 ECIES, and at least t honest organizers), we prove that zk–MPSFV achieves the stated security goals, including DAG-gated progress, anti-replay, and threshold-robust organizer security, while out-of-band flag sharing remains out of scope. On a three-organizer testbed with 30 simulated teams, setup costs 0.45 ms per sub-flag, proof generation averages 5.34 s on an 8 core system, and on-chain verification costs ≈ 170k L2 gas on zkSync Era with a median fee of 1.33 × 10−6 ETH (about $0.0046 at $3,435 ETH). Stress replays sustain ≈ 7 proof transactions/s up to 5000 proofs; extrapolating to 50,000 proofs (1000 teams × 50 submissions) yields ≈ 0.0665 ETH (about $200–$228) and ≈ 2 hours of settlement time. Overall, zk–MPSFV is practical for small- to mid-scale, audit-ready progression CTFs.

Registration-Based Encryption (RBE) is a public-key encryption mechanism which allows a user to register their identity (e.g. email address) and self-generated public key with a key curator (e.g. an organisation). The key curator aggregates these keys into a compact digest. Using only this digest and the recipient’s identity, anyone can encrypt messages to any registered user. As the key curator is not entrusted with any secrets, RBE presents a solution to the key escrow problem, which impedes the adoption of Identity-Based Encryption. This makes RBE an attractive solution for secure communication with and among members of an organisation while preserving user privacy. Despite recent advances [Döttling-Kolonelos-Lai-Lin-Malavolta-Rahimi, EUROCRYPT’23; Fiore-Kolonelos-de-Perthuis, ASIACRYPT’23], practical constructions of RBE are still limited to a small number of registered users (e.g. 1024), lack post-quantum security, or have ciphertext sizes scaling in the order of GB. The predominant way towards constructing practical RBE is a generic transformation from Laconic Encryption (LE). In this work, we identify an efficiency bottleneck in this transformation and present a new primitive called Batched Laconic Encryption (BLE) which admits a more succinct transformation to RBE. Our resulting RBE scheme is the first post-quantum construction that simultaneously supports a large number of registered users and asymptotically outperforms all comparable RBE schemes. Concretely, for at most $2^{30}$ registered users at 128-bit security, our scheme achieves a ciphertext size of 7 MB, improving on previously reported results by three orders of magnitude. We confirm our results through an open-source prototype implementation demonstrating that all algorithms execute within a few milliseconds. The post-quantum security of our construction is based on the standard Learning with Errors assumption, and our analysis enables several tweaks to significantly reduce ciphertext sizes in practical deployments.

Differential-linear distinguishers have been introduced by Langford and Hellman in 1994. They consist in combining, first, a differential distinguisher and second, a linear distinguisher and then study the bias between plaintexts with a difference and linear approximations of the two ciphertexts to create a differential-linear distinguisher. The original method has been improved by Bar-On et al. in 2019 where the table called the DLCT (Differential Linear Connectivity Table) has been introduced and more recently, in 2024 by Hadipour et al. where, as for the case of boomerang distinguishers, several intermediate tables are used to tune the computation of the middle part of the distinguisher. From a distinguisher, it is thus natural to try to mount some dedicated attacks. This step has been done by Broll et al. in 2021 and in 2022 for the case of SERPENT. In this paper, we propose a tool that directly searches for the best differential-linear attacks automating the work of Broll et al. using the differential-linear distinguishers proposed by Hadipour et al. More precisely, both searches (distinguishers and attacks) are done in the same step to improve the overall complexity of the differential-linear attack. We apply this tool to the case of SERPENT and PRESENT. The attack against SERPENT reaches 12 rounds with a time complexity equal to $2^{220.9}$ for a data/memory complexity equal to $2^{125.01}$. The attack against PRESENT-80 (PRESENT-128 respectively) reaches 16 (18 respectively) rounds with a time complexity equal to $2^{73.88}$ ($2^{124}$ respectively) for a data/memory complexity equal to $2^{57.88}$ ($2^{63.25}$ respectively).

Careful management of shares stored in the architectural, general-purpose register file is an important aspect of software-based implementations of masking, because it can impact the associated side-channel leakage. The erasure of residual shares, i.e., shares whose useful lifetime has expired, is one component of such management: erasing them can, for example, prevent subsequent, unintended share recombination. To support effective share erasure, this work makes two contributions. First, we present an analysis of the underlying problem, systematising associated concepts and terminology, and offering a concrete, motivating example. Second, we present the design, implementation, and evaluation of two components which can support solutions of said problem. These are 1) a policy, namely an extended ABI which provides clear semantics regarding the responsibility of caller and/or callee functions to erase shares, and 2) a mechanism for realising said policy, namely an extended ISA (or ISE) which allows more efficient erasure of shares than via the ISA alone. Although generic in nature, we present both components using the RISC-V base ISA; an associated prototype ISE implementation uses Ibex as a base core. Our evaluation results confirm that combined use of the components can eliminate leakage related to residual shares both effectively and efficiently.

A structured vector range argument proves that a committed vector $\mathbf{v}$ lies in a well-structured range of the form $[0,2^d-1]$. This structure makes the protocol extremely efficient, although it cannot handle more sophisticated range assertions, such as those arising from non-membership attestations. To address this gap, we study a more general setting not captured by prior constructions. In this setting, for each $i$, the admissible integer set for $v_i$ is a union of $k$ intervals $\mathsf{R}_i \overset{\text{def}}{=} \bigcup_{j=0}^{k-1}\left[l_{i,j},r_{i,j}\right]$. In this work, we present novel techniques to prove that $\mathbf{v} \in \mathbb{Z}^n_p$ lies within $\mathsf{R}_0 \times \mathsf{R}_1 \times \cdots \times \mathsf{R}_{n-1}$. We first introduce $\mathsf{RangeLift}$, a generic compiler that lifts a structured vector range argument to support such unstructured range assertions. Then we present $\mathsf{Spectra}$, a realization of $\mathsf{RangeLift}$ over the $\mathsf{KZG}$-based vector commitment scheme. $\mathsf{Spectra}$ achieves succinct communication and verifier time; its prover complexity is $O(n\,\tfrac{\log N}{\log\log N}\cdot \log(n\tfrac{\log N}{\log\log N}))$, where $N$ upper bounds the maximum interval size across all $\mathsf{R}_i$. Notably, $\mathsf{Spectra}$ is interval-agnostic, meaning its prover complexity is independent of the number of intervals $k$; therefore, its prover cost matches the single-interval case even when each $\mathsf{R}_i$ is composed of hundreds of thousands of intervals. We also obtain two new structured vector range arguments and a batching-friendly variant of the $\mathsf{Cq}^{+}$ lookup argument (PKC'24), which are also of independent interest. Experiments show that $\mathsf{Spectra}$ outperforms well-known curve-based vector range arguments on standard metrics while supporting strictly more expressive range assertions.

As efficient proof systems mature rapidly, more practical use cases that require zero-knowledge (ZK) guarantees are arising. Adding ZK typically requires either composing the non-zk base system with an expensive zk one that proves correctness of the cryptographic hashes performed by the base verifier, or alternatively making tightly coupled modifications to every component of the base protocol. We introduce VEIL, a lightweight and non-intrusive compiler for hash-based multilinear proof systems. VEIL achieves ZK without these drawbacks. Our approach decouples the protocol's algebraic interactions from the cryptographic hashing and applies a ZK wrapper solely to the algebraic components. This results in a simple, plausibly post-quantum, protocol that achieves a minimal prover overhead of $(1+o(1))$, while maintaining the architectural integrity of the base proof system. Our proof-of-concept implementation demonstrates that, over a $31$-bit base prime field, for a trace of $2^{29}$ field elements, compared to the non-zk proof system, VEIL has a prover overhead of about $3\%$, verifier overhead of $22\%$ and proof-size overhead of $12\%$.

Secure lookup table (LUT) protocols allow retrieving values from a table at secret indices, and have become a promising approach for the secure evaluation of non-linear functions. Most existing LUT protocols target the two-party setting, where the best protocols achieve a communication cost of $O(N)$ for a table of size $N$. MAESTRO (Morita et al., USENIX Security 2025) represents the state-of-the-art LUT protocol for AES in the three-party honest-majority setting, with a communication cost of $O(N^{1/2})$; malicious security is achieved with distributed zero-knowledge proofs. However, it only supports single-input tables over characteristic-2 fields $\mathbb{F}_{2^k}$ and lacks support for multi-input tables over rings $\mathbb{Z}_{2^k}$, which are more widely used in modern computation. Moreover, the $O(N^{1/2})$ cost remains expensive for large-scale applications; their efficient distributed zero-knowledge proofs are specialized for AES and cannot be easily applied to $\mathbb{Z}_{2^k}$. In this work, we present MARLUT, a new generalized and optimized LUT construction supporting multi-input tables over both rings $\mathbb{Z}_{2^k}$ and fields $\mathbb{F}_{2^k}$ with malicious security. We achieve this by (1) extending the semi-honest LUT protocol from MAESTRO, utilizing high-dimensional tensors to reduce its communication cost to $O(N^{1/3})$, and (2) designing a new distributed zero-knowledge proof for inner-product relations over $\mathbb{Z}_{2^k}$. Our distributed zero-knowledge proof is more efficient than the state-of-the-art work (Li et al., CCS 2024) and may be of independent interest. Experiments show that on a table of size $2^{16}$, our semi-honest LUT protocol reduces the offline computational and communication cost by a factor of $5.95$ and $3.23$, respectively. Our distributed zero-knowledge proofs show up to $7.07\times$ and $4.97\times$ speedups over the state-of-the-art protocol on ring $\mathbb{Z}_{2^8}$ and $\mathbb{Z}_{2^{16}}$, respectively.

Recent advances in Vector Oblivious Linear Evaluation (VOLE) protocols have enabled constant-round, fast, and scalable (designated-verifier) zero-knowledge proofs, significantly reducing prover computational cost. Existing protocols, such as QuickSilver [CCS’21] and LPZKv2 [CCS’22], achieve efficiency with prover costs of 4 multiplications in the extension field per AND gate for Boolean circuits, with one multiplication requiring a O(κ log κ)-bit operation where κ = 128 is the security parameter and 3-4 field multiplications per multiplication gate for arithmetic circuits over a large field. We introduce JesseQ, a suite of two VOLE-based protocols: JQv1 and JQv2, which advance state of the art. JQv1 requires only 2 scalar multiplications in an extension field per AND gate for Boolean circuits, with one scalar needing a O(κ)- bit operation, and 2 field multiplications per multiplication gate for arithmetic circuits over a large field. In terms of communication costs, JQv1 needs just 1 field element per gate. JQv2 further reduces communication costs by half at the cost of doubling the prover’s computation. Experiments show that, compared to the current state of the art, both JQv1 and JQv2 achieve at least 3.9× improvement in the online phase for Boolean circuits. For large field circuits, JQv1 has a similar performance, while JQv2 offers a 1.3× improvement. Additionally, both JQv1 and JQv2 maintain the same communication cost as the current state of the art. Notably, on the cheapest AWS instances, JQv1 can prove 9.2 trillion AND gates (or 5.8 trillion multiplication gates over a 61-bit field) for just one US dollar. JesseQ excels in applications like inner products, matrix multiplication, and lattice problems, delivering 40%- 200% performance improvements compared to QuickSilver. Additionally, JesseQ integrates seamlessly with the sublinear Batchman framework [CCS’23], enabling further efficiency gains for batched disjunctive statements.

Proof-of-burn has been used as a mechanism to destroy cryptocurrency in a verifiable manner. Despite its well known use, the mechanism has not been previously formally studied as a primitive. In this paper, we put forth the first cryptographic definition of what a proof-of-burn protocol is. It consists of two functions: First, a function which generates a cryptocurrency address. When a user sends money to this address, the money is irrevocably destroyed. Second, a verification function which checks that an address is really unspendable. We propose the following properties for burn protocols. Unspendability, which mandates that an address which verifies correctly as a burn address cannot be used for spending; binding, which allows associating metadata with a particular burn; and uncensorability, which mandates that a burn address is indistinguishable from a regular cryptocurrency address. Our definition captures all previously known proof-of-burn protocols. Next, we design a novel construction for burning which is simple and flexible, making it compatible with all existing popular cryptocurrencies. We prove our scheme is secure in the Random Oracle model. We explore the application of destroying value in a legacy cryptocurrency to bootstrap a new one. The user burns coins in the source blockchain and subsequently creates a proof-of-burn, a short string proving that the burn took place, which she then submits to the destination blockchain to be rewarded with a corresponding amount. The user can use a standard wallet to conduct the burn without requiring specialized software, making our scheme user friendly. We propose burn verification mechanisms with different security guarantees, noting that the target blockchain miners do not necessarily need to monitor the source blockchain. Finally, we implement the verification of Bitcoin burns as an Ethereum smart contract and experimentally measure that the gas costs needed for verification are as low as standard Bitcoin transaction fees, illustrating that our scheme is practical.

Polynomial commitment schemes (PCSs) are a fundamental cryptographic primitive that allows a prover to reveal evaluations for a committed polynomial. Motivated by the inefficiency of proof generation for large-scale computations as well as the concerns regarding third-party reliance and quantum threats, a line of recent works has focused on distributing code-based PCS, where the proving workload is distributed among multiple sub-provers to accelerate proof generation, while preserving transparent setup and plausible quantum resilience. However, for $M$ sub-provers generating an evaluation proof for a polynomial of size $N$, existing solutions either require $O(N)$ total communication among sub-provers, or incur an $O(M)$ overhead in proof size. In this paper, we introduce $\mathsf{Veloz}$, a novel distribution framework for code-based multilinear PCS, which for the first time achieves communication cost sublinear in $N$, and eliminates the dependence of proof size on the number of sub-provers, without compromising proving speed or security. At its core is a customized proof aggregation method from interleaved code that efficiently combines sub-proofs via minimum communication. We further present two instantiations of $\mathsf{Veloz}$: one based on Reed-Solomon code, $\mathsf{Veloz}_{\text{RS}}$, achieves $O(\frac{N}{M}\log{\frac{N}{\log{N}}})$ proving time, $O(\lambda \cdot \frac{\log^{2}{N}}{\log\log{N}} + M\cdot\frac{N}{\log{N}})$ communication, and $O(\lambda \cdot \frac{\log^{2}{N}}{\log\log{N}})$ proof size; the other based on the fast linear code from Brakedown (Golovnev et al., CRYPTO 2023), $\mathsf{Veloz}_{\text{Lin}}$, features $O(\frac{N}{M})$ proving time, $O(\lambda \cdot K + M\cdot\frac{N}{K})$ communication, and $O(\lambda \cdot K)$ proof size for $K \in [\sqrt[3]{N}, \sqrt{N}]$, while enjoying field agnosticity. We also implement both schemes in Rust and conduct a comprehensive performance evaluation. The experimental results demonstrate their linear scalability with increasing $M$. More specifically, for $N = 2^{30}$ and $M = 8$, $\mathsf{Veloz}_{\text{RS}}$ takes 74.8s for proof generation, achieving a 5.18 $\times$ speedup compared to running a single prover, while $\mathsf{Veloz}_{\text{Lin}}$ generates a proof in 26.9s and achieves a 7.02 $\times$ speedup.

Designing cryptographic hash functions that simultaneously achieve high throughput and strong provable security remains a fundamental challenge in symmetric cryptography. Traditional constructions, such as the Merkle-Damg\aa rd (MD) and SPONGE paradigms, inherently suffer from structural limitations: they either expose internal chaining values to length-extension attacks or impose a rigid trade-off between security (capacity) and efficiency (rate), bounding their architectural potential. In this paper, we introduce the \textbf{Compress-then-Randomize} paradigm, a modular design principle that structurally decouples a hash function into two independent components with distinct security objectives: (1) a \emph{variable-input-length} (VIL) compression component optimized for high-speed message absorption, requiring only collision resistance and multiple-preimage resistance; and (2) a \emph{fixed-input-length} (FIL) finalization component utilizing independent random permutations to ensure indifferentiability from a random oracle. This separation enables the VIL component to maximize processing throughput (approaching the full primitive width) while the FIL component provides robust randomness extraction, effectively mitigating length-extension attacks and achieving tight security bounds. Leveraging this paradigm, we propose the \textbf{Rocket hash family}, comprising two instantiations: \emph{Rocket-JH} (based on the JH iteration structure with wide-pipe design) and \emph{Rocket-DoubleCBC} (utilizing dual parallel Cipher-Block-Chaining lanes). Both constructions employ pairwise distinct round permutations and achieve superior message processing rates compared to conventional SPONGE-based designs, with Rocket-2 delivering more than $2\times$ the throughput of SHA3-512 for large messages. For practical instantiation without requiring multiple independent cryptographic primitives, we present \textbf{CTR-Perm}, a novel domain-separation technique that derives $2^w$ effectively independent round functions from a single large permutation using a counter-based input diversification. While backward queries introduce a heuristic assumption regarding preimage multiplicity (bounded by a negligible failure probability $\leq 2^{-526}$ for counter size $w \geq 64$ and hash length 512 bits), we prove the construction remains sound for practical message lengths up to $2^{w-8}$ blocks. Finally, to formalize the security-efficiency trade-off, we propose \textbf{Hash Effectiveness} (H.E.), a scale-invariant heuristic metric defined as the product of normalized security level and normalized processing rate. We demonstrate that conventional Merkle-Damg\aa rd and SPONGE constructions exhibit H.E. values fundamentally bounded by $1/8$, whereas the Rocket constructions achieve H.E. values approaching $1/4$ (specifically, $0.227$ for Rocket-2 with Keccak-$p$[1600]), thereby establishing a new Pareto frontier in hash function design.

We present $\BAT$ -- an IND-CCA secure key encapsulation mechanism (KEM) that is based on NTRU but follows an encryption/decryption paradigm distinct from classical NTRU KEMs. It demonstrates a new approach of decrypting NTRU ciphertext since its introduction 25 years ago. Instead of introducing an artificial masking parameter $p$ to decrypt the ciphertext, we use 2 linear equations in 2 unknowns to recover the message and the error. The encryption process is therefore close to the GGH scheme. However, since the secret key is now a short basis (not a vector), we need to modify the decryption algorithm and we present a new NTRU decoder. Thanks to the improved decoder, our scheme works with a smaller modulus and yields shorter ciphertexts, smaller than RSA-4096 for 128-bit classical security with comparable public-key size and much faster than RSA or even ECC. Meanwhile, the encryption and decryption are still simple and fast in spite of the complicated key generation. Overall, our KEM has more compact parameters than all current lattice-based schemes and a practical efficiency. Moreover, due to the similar key pair structure, $\BAT$ can be of special interest in some applications using Falcon signature that is also the most compact signature in the round 3 of the NIST post-quantum cryptography standardization. However, different from Falcon, our KEM does not rely on floating-point arithmetic and can be fully implemented over the integers.

This paper presents a unified framework for generic attacks on Generalized Feistel Ciphers, with a primary focus on Type 1, Type 2, and unbalanced contracting (U-Type 1) Feistel constructions with non-invertible round functions. In recent work, authors reveal a class of vulnerabilities exploitable via key independent multidimensional linear trails for Feistel Ciphers, yielding efficient generic distinguishing and key-recovery attacks. We extend the extended work by formalizing the application of generic multidimensional linear cryptanalysis to Generalized Feistel Ciphers. In this way, we improve upon existing results by extending the maximum number of rounds for the generic distinguishing attack to $t^2 + 2t - 1$ for Type 1 and U-Type 1, and to $2t + 3$ for Type 2. Moreover, we have the maximum number of rounds for generic key recovery attacks on (U)-Type 1 as $t^2+3t-2$ and Type 2 as $4t$. To the best of our knowledge, these findings yield the best results for the maximum number of rounds in key recovery attacks on the corresponding GFC. We further demonstrate the branch-permutation-independence of these attacks, proving that changing internal permutations does not affect the attack applicability, complexities or the maximum number of rounds for generic attacks. The effectiveness of our attacks is validated through experiments on the first-round AES candidate CAST-256 and the MPC-friendly block cipher GMiMC. Both theoretical and experimental results confirm that our proposed branch-permutation-independent generic attacks enhance the maximum number of rounds for generic attacks for GFC and reduce complexity across various interesting cases.

We give a public key encryption scheme with plausible quasi-exponential security based on the conjectured intractability of two constraint satisfaction problems (CSPs), both of which are instantiated with a corruption rate of $1 - o(1)$. First, we conjecture the hardness of a new large alphabet random predicate CSP (LARP-CSP) defined over an arbitrary but strongly expanding factor graph, where the vast majority of predicate outputs are replaced with random outputs. Second, we conjecture the hardness of the standard $k$XOR problem defined over a random factor graph, again where the vast majority of parity computations are replaced with random bits. In support of our hardness conjecture for LARP-CSPs, we give a variety of lower bounds, ruling out many natural attacks including all known attacks that exploit non-random factor graphs. Our public key encryption scheme is the first to leverage high corruption CSPs while simultaneously achieving a plausible security level far above quasi-polynomial. At the heart of our work is a new method for planting cryptographic trapdoors based on the label extended factor graph for a CSP. Along the way to achieving our result, we give the first uniform construction of an error-correcting code that has an expanding, low density generator matrix while simultaneously allowing for efficient decoding from a $1 - o(1)$ fraction of corruptions.

The YOSO (You Only Speak Once) model, introduced by Gentry et al. (CRYPTO 2021), helps to achieve strong security guarantees in cryptographic protocols for distributed settings, like blockchains, with large number of parties. YOSO protocols typically employ smaller anonymous committees to execute individual rounds of the protocol instead of having all parties execute the entire protocol. After completing their tasks, parties encrypt protocol messages for the next anonymous committee and erase their internal state before publishing ciphertexts, thereby enhancing security in dynamically changing environments. In this work, we consider the problem of secure multi-party computation (MPC), a fundamental problem in cryptography and distributed computing. We assume honest majority among the committee members, and work in the online-offline, i.e., preprocessing, setting. In this context, we present the first YOSO MPC protocol where efficiency---measured as communication complexity---improves as the number of parties increases. Specifically, for $0<\epsilon<1/2$ and an adversary corrupting $t<n(\frac{1}{2}-\epsilon)$ out of $n$ parties, our MPC protocol exhibits enhanced scalability as $n$ increases, where the online phase communication becomes independent of $n$. Prior YOSO MPC protocols considered $t$ as large as $(n-1)/2$, but a significant hurdle persisted in obtaining YOSO MPC with communication that does not scale linearly with the number of committee members, a challenge that is exagerbated when the committee size was large per YOSO's requirements. We show that, by considering a small ``gap'' of $\epsilon>0$, the sizes of the committees are only marginally increased, while online communication is significantly reduced. Furthermore, we explicitly consider fail-stop adversaries, i.e., honest participants who may inadvertently fail due to reasons such as denial of service or software/hardware errors. In prior YOSO work, these adversaries were grouped with fully malicious parties. Adding explicit support for them allows us to achieve even better scalability.

Zero-knowledge proofs (ZKPs) allow a prover to convince a verifier of a statement's truth without revealing any other information. In recent years, ZKPs have matured into a practical technology underpinning major applications. However, implementing ZKP programs remains challenging, as they operate over arithmetic circuits that encode the logic of both the prover and the verifier. Therefore, developers must not only express the computations for generating proofs, but also explicitly specify the constraints for verification. As recent studies have shown, this decoupling may lead to critical ZKP-specific vulnerabilities. Unfortunately, existing tools for detecting them are limited, as they: (1) are tightly coupled to specific ZKP languages, (2) are confined to the constraint level, preventing reasoning about the underlying computations, (3) target only a narrow class of bugs, and (4) suffer from scalability bottlenecks due to reliance on SMT solvers. To address these limitations, we propose a language-agnostic formal model, called the Domain Consistency Model (DCM), which captures the relationship between computations and constraints. Using this model, we provide a taxonomy of vulnerabilities based on computation-constraint mismatches, including novel subclasses overlooked by existing models. Next, we implement an IR-based bug detection tool, called CCC-Check, which is based on abstract interpretation. Our evaluation shows that CCC-Check is, on average, two orders of magnitude faster than the SoTA verification tool CIVER, while achieving comparable precision. Finally, using the DCM, we examine six widely adopted ZKP projects and uncover 15 previously unknown vulnerabilities. We reported these bugs to the projects' maintainers, 13 of which have since been patched. Of these 15 vulnerabilities, 12 could not be captured by existing models.

Masking is an effective defense against side-channel attacks, yet it remains costly under hardware constraints. The Caliptra Root-of-Trust is a representative case, where its masked ML-DSA implementation incurs about 6× area overhead. We propose a novel first-order masking solution that optimizes Caliptra, achieving significant improvements in area–delay efficiency. Compared to Caliptra’s ML-DSA reduction, our design achieves a 12.1× speedup, reducing LUTs by 86.7% and FFs by 94.5%, while improving area–delay efficiency by 91×. TVLA, with over 1,000,000 traces, shows no first-order leakage, satisfies Caliptra’s security requirements, and significantly improves implementation efficiency.

In the noisy $k$-XOR problem, one is given $y \in \mathbb F_2^M$ and must distinguish between the case where $y$ is uniform and the case where $y = Ax + e$, where $A$ is the adjacency matrix of a $k$-left-regular bipartite graph with $N$ variables and $M$ constraints, $x \in \mathbb F_2^N$ is random, and $e$ is noise with rate $\eta$. Lower bounds in restricted computational models such as Sum-of-Squares and low-degree polynomials are closely tied to the expansion of the underlying constraint graph, leading to conjectures that expansion implies hardness. We show that such conjectures are false by constructing an explicit family of graphs with near-optimal expansion for which noisy $k$-XOR is solvable in polynomial time. Our construction combines two powerful directions of work in pseudorandomness and coding theory that have not been previously put together. Specifically, our graphs are based on the lossless expanders of Guruswami, Umans and Vadhan (JACM 2009). Our key insight is that by an appropriate interpretation of the vertices of their graphs, the noisy XOR problem turns into the problem of decoding Reed-Muller codes from random errors. Then we build on a powerful body of work from the 2010s correcting from large amounts of random errors. Putting these together yields our construction. Concretely, we obtain explicit families for which noisy $k$-XOR is solvable in polynomial time at constant noise rate $\eta = 1/3$, with graphs satisfying $M = 2^{O(\log^2 N)}$, $k = (\log N)^{O(1)}$, and $(N^{1-\alpha}, 1-o(1))$-expansion. Under standard conjectures on Reed--Muller codes over the binary erasure channel, this extends to families with $M = N^{O(1)}$, $k = (\log N)^{O(1)}$, $(N^{1-\alpha}, 1-o(1))$-expansion, and polynomial-time algorithms at noise rate $\eta = N^{-c}$.

Retrieval-augmented generation (RAG) systems critically depend on a vector-retrieval stage that selects relevant documents from a large embedding database. In a RAG-as-a-Service setting, however, clients have no visibility into the server's proprietary embeddings and index structures, and thus cannot distinguish faithful execution from arbitrary deviations. This motivates service consistency for retrieval: the returned results must be consistent with executing an agreed approximate nearest neighbor search (ANNS) algorithm on a fixed, committed database together with a fixed, committed ANNS index, while revealing nothing beyond the outputs themselves. We present the first polynomial interactive oracle proof (PIOP) tailored to the widely deployed HNSW ANNS algorithm. Building on this PIOP, we introduce zkRAG, a zero-knowledge, succinct, non-interactive argument for RAG retrieval that enables practical verification. Our design achieves asymptotically optimal online prover efficiency, with prover time linear in the HNSW search trace length, while keeping verification succinct. We introduce several new techniques that may be of independent interest, including a hybrid lookup argument, a highly efficient checker-based PIOP for checking priority-queue updates, and an efficient checker for membership selector vectors. For a benchmark with $10^6$ vectors of dimension $128$, single-thread zkRAG proves a typical HNSW query in $50$ seconds-over $1000\times$ faster than existing baselines--while keeping verification lightweight, demonstrating the feasibility of efficient zero-knowledge service-consistent RAG retrieval.

In this report, we describe how block circulant (BC) codes can serve as an alternative to one-dimensional (1D) and two-dimensional (2D) Reed–Solomon (RS) codes in the Ethereum PeerDAS protocol. We begin by reviewing the implementation of 1D RS codes in PeerDAS and then present efficient encoding and reconstruction algorithms for BC codes, developed within the same implementation framework as the respective 1D RS algorithms. The proposed encoding algorithm also permits a graceful integration of KZG commitment scheme. Finally, we evaluate and compare the performance of BC codes in terms of code rate, stopping rate, and the size of the local codes they contain, against both 1D and 2D RS codes.

The Messaging Layer Security protocol MLS is standardized in IETF's RFC 9420 and allows a group of parties to securely establish and evolve group keys even if the servers are malicious. The core design of MLS is based on the TreeKEM protocol, which was significantly modified and extended during the standard's development. Over the last years, several partial security analyses have appeared of incomplete drafts of the standard. One of the major additions to MLS RFC 9420 (the final version of the standard) are the external operations, i.e., external commits and proposals. These additional operations have not been considered in any previous security analysis, while they can have a significant impact on the standard's security. In this work, we prove the consistency, confidentiality and authentication of MLS in RFC 9420. To this end, we formalize $\mathsf{ETK}$: External-Operations TreeKEM, which models RFC 9420 and includes the external commits and proposals. We propose a corresponding ideal functionality $\mathcal{F}_{\mathrm{ECGKA}}$ and prove that $\mathsf{ETK}$ realizes it. Our work is the first cryptographic analysis that considers both the final changes to the standard, and the first approach overall to cover external proposals and external commits. Compared to previous works that considered MLS drafts, our $\mathsf{ETK}$ protocol is by far the closest to the final MLS RFC 9420 standard. Our analysis implies that the core of MLS in RFC 9420 is an $\mathsf{ETK}$ protocol that realizes $\mathcal{F}_{\mathrm{ECGKA}}$. Notably, we show that when external proposals and commits are allowed, MLS achieves a weaker form of security than was suggested by previous analyses, because the external operations can be exploited to violate Post-Compromise Security guarantees. We show that the security of the protocol can be further strengthened by leveraging the standard's optional PSK mechanism, allowing another form of healing, and give a corresponding construction $\mathsf{ETK}^{\mathrm{PSK}}$ and ideal functionality $\mathcal{F}_{\mathrm{ECGKA}^{\mathrm{PSK}}}$.

The Oracle Module Learning with Errors (Oracle MLWE) assumption, recently introduced by Liu et al. (Asiacrypt~2025), strengthens standard (Module) LWE by allowing masked linear leakages of the secret under an adversarially-chosen challenge matrix. This feature is used for the construction of new efficient primitives such as Oracle MLWE-based multi-message multi-recipient KEM/PKE (mmKEM/mmPKE) without requiring public-key well-formedness proofs. In this work, we present a practical cryptanalytic attack on Oracle MLWE, which we call a neighborhood search attack. Our attack exploits adversarially-chosen matrices (or maliciously generated public keys), together with the small ring dimension and small-norm secrets required for correctness, showing that rounding errors can be recovered via a bounded search, leading to recovery of the underlying MLWE secret. To demonstrate the effectiveness of our attack, we apply it against the Oracle MLWE-based mmKEM of Liu et al. (Asiacrypt~2025), proving that its recommended parameter sets do not achieve the claimed security level. We further implement the attack in SageMath and report concrete timings, showing that an adversary controlling a moderate number of recipients can recover other recipients' encapsulated keys within a few seconds on a standard PC under the proposed parameters, which were claimed to achieve a 128-bit security level.

Functional Encryption (FE) is a concept that generalizes public-key encryption, allowing a party that owns a private key to find a function of the plaintext (instead of the plaintext itself). Multi-Party Functional Encryption (MPFE) generalizes this concept and adapts it to multi-party settings, allowing for decentralization in both the ciphertexts—which might originate from multiple sources—and the keys—thereby eliminating the necessity of a central authority and avoiding the introduction of a single point of trust and failure. The current paper presents a substantial foundation of MPFE to the non-specialist reader. It provides definitions, classifications, and discusses properties of MPFE and its relation with other cryptographic concepts. The potential applicability of MPFE, which covers multiple domains and use cases, is discussed. The paper investigates the real-world adoption of MPFE, including its presence in technical specifications or its availability in open-source libraries. Finally, the current study discusses challenges and therefore opens up new research directions.

When using Transport Layer Security (TLS), web users can connect to a server and trust that they are sending and receiving data with the intended web server. This guarantee, however, is not transferable: there is no immediate way for a client to convince an external party that a transcript or message originated from a particular server. Beginning with the DECO protocol of Zhang et al., there has been a line of work on "TLS oracles"—cryptographic protocols that allow a client to commit to, prove provenance, and disclose arbitrary properties of TLS application data to a verifier party. TLS oracles only require the server to run standard TLS, making them compatible with existing real-world web servers. In this work we introduce Ticket to Hide, a new TLS oracle protocol for TLS 1.3. We operate in the multi-server setting, previously explored in the DiStefano protocol by Celi et al., in which the client additionally wishes to hide the identity of the server they are communicating with among a set of $N$ publicly known servers. We leverage new features of TLS 1.3 in surprising ways to yield performance and security benefits, resulting in a protocol that is both faster and more private than previous work. Additionally, we are the first TLS oracle protocol to be compatible with post-quantum secure TLS key agreement and certificates. Our implementation, which builds on top of the Garble-then-Prove framework of Xie et al., scales to $N=100$ servers in less than 3 seconds of end-to-end time in a WAN setting—only 3.5$\times$ the latency of a regular TLS 1.3 interaction.

The Permuted Kernel Problem (PKP), introduced by Shamir, is a computationally hard problem underlying recent post-quantum signature schemes such as PERK, SUSHSYFISH and PKP-DSS. Among these, PERK is a second-round candidate in NIST's Additional Digital Signature Schemes post-quantum standardization process, SUSHSYFISH appeared at EUROCRYPT~2020, and PKP-DSS was one of the finalists in the CACR competition. The best known attacks on PKP rely on combinatorial meet-in-the-middle techniques, notably the algorithms of Koussa, Macario-Rat, and Patarin (KMP) and Santini, Baldi, and Chiaraluce (SBC), whose complexities remain super-exponential, with memory requirements of the same order as their time complexities. In this work, we obtain improved cryptanalytic results for PKP that strictly outperform all previously known attacks. In particular, although no parameter sets of PERK~v2.2.0 fall below the NIST security levels, we provide the first evidence that secret vector recovery for all PERK~v2.2.0 parameter sets can be achieved with complexity below their estimated bit-security levels. We additionally obtain improved bit-complexity estimates for the SUSHSYFISH and PKP-DSS parameter sets. We further introduce a Schroeppel--Shamir style time–memory trade-off in the PKP setting. Although PKP does not admit square-root memory as in the classical subset-sum problem, our adaptation achieves substantial memory reductions while keeping the time complexity close to the best known attacks. Overall, our results provide improved cryptanalytic insight into PKP and refine the current understanding of the concrete security of PKP-based signature schemes.

One of the main candidates of post-quantum cryptography is lattice-based cryptography. Its cryptographic security against quantum attackers is based on the worst-case hardness of lattice problems like the shortest vector problem (SVP), which asks to find the shortest non-zero vector in an integer lattice. Asymptotic quantum speedups for solving SVP are known and rely on Grover's search. However, to assess the security of lattice-based cryptography against these Grover-like quantum speedups, it is necessary to carry out a precise resource estimation beyond asymptotic scalings. In this work, we perform a careful analysis on the resources required to implement several sieving algorithms aided by Grover's search for dimensions of cryptographic interests. For such, we take into account fixed-point quantum arithmetic operations, non-asymptotic Grover's search, the cost of using quantum random access memory (QRAM), different physical architectures, and quantum error correction. We find that even under very optimistic assumptions like circuit-level noise of $10^{-5}$, code cycles of 100 ns, reaction time of 1 $\mu$s, and using state-of-the-art arithmetic circuits and quantum error-correction protocols, the best sieving algorithms require $\approx 10^{13}$ physical qubits and $\approx 10^{31}$ years to solve SVP on a lattice of dimension 400, which is roughly the dimension for minimally secure post-quantum cryptographic standards currently being proposed by NIST. We estimate that a 6-GHz-clock-rate single-core classical computer would take roughly the same amount of time to solve the same problem. We conclude that there is currently little to no quantum speedup in the dimensions of cryptographic interest and the possibility of realising a considerable quantum speedup using quantum sieving algorithms would require significant breakthroughs in theoretical protocols and hardware development.

We develop a new method for the computation of $(3,3)$-isogenies between principally polarized abelian surfaces. The idea is to work with models in $\mathbb P^8$ induced by a symmetric level-$3$ theta structure. In this setting, the action of three-torsion points is linear, and the isogeny formulas can be described in a simple way as the composition of easy-to-evaluate maps. In the description of these formulas, the relation with the Burkhardt quartic threefold plays an important role. Furthermore, we discuss generalizations of the idea to higher dimensions as well as different isogeny degrees.

We provide a new interpretation of the arithmetic on Hessian Kummer lines using level-3 theta structures. This allows us to break the record for tripling on elliptic curves and their Kummer lines, requiring only 4 multiplications and 4 squarings per tripling for well-chosen curve parameters.

Ensuring rigorous protection against physical attacks that simultaneously combine passive side-channel observations with active fault injections is a recent and rapidly evolving research area. Polynomial masking is a promising countermeasure, as it provides both privacy against leakage and redundancy against faults. At CRYPTO 2023, Berndt et al. introduced the ``LaOla’’ scheme, which protects arbitrary circuits against such attacks. However, their model tolerates only a global threshold of e faults across the entire circuit, which fundamentally limits scalability. In this work, we overcome this restriction by extending fault robustness to the region fault model, where an adversary can inject up to \(e\) faults in each gadget. We present the first gadgets secure against combined leakage and fault attacks in this stronger model. This improvement allows us to tolerate up to \(x \cdot {e}\) faults across a circuit with \(x\) gadgets instead of just a total of \(e\) as in previous works. Consequently, the protection order \(e\) can remain constant. To achieve this, we introduce sufficient and practically attainable security definitions that are strictly stronger than those of Berndt et al. We further apply this principle to the LaOla construction, proving our stronger security notions for the adapted multiplication gadget.

FrodoKEM, a conservative post-quantum key encapsulation mechanism based on the plain Learning with Errors (LWE) problem, has been recommended for use by several government cybersecurity agencies and is currently undergoing standardization by the International Organization for Standardization (ISO). Despite its robust security guarantees, FrodoKEM's performance remains one of the main challenges to its widespread adoption. This work addresses this concern by presenting a fully standard-compliant, high-performance hardware implementation of FrodoKEM targeting both FPGA and ASIC platforms. The design introduces a scalable parallelization architecture that supports run-time configurability across all twelve parameter sets, covering three security levels (L1, L3, L5), two PRNG variants (SHAKE-based and AES-based), and both standard and ephemeral modes, alongside synthesis-time tunability through a configurable performance parameter to balance throughput and resource utilization. For security level L1 on AMD Artix 7 FPGA, the implementation achieves 2,599, 2,338, and 2,147 operations per second for key generation, encapsulation, and decapsulation, respectively, representing the fastest standard-compliant performance reported to date while consuming only 37.6K LUTs, 64 DSPs, and 10.1K flip-flops. The design achieves a 2.3–159$\times$ improvement in the Area–Time Product (ATP) over all prior specification-compliant FPGA implementations. Furthermore, this work presents the first ASIC evaluation of FrodoKEM using the NANGATE45 45 nm technology library, achieving 7,721, 6,946, and 6,378 operations per second for key generation, encapsulation, and decapsulation, respectively, with a logic area of 0.250 mm$^2$. The ASIC implementation exhibits favorable sub-linear area scaling and competitive energy efficiency across different performance parameter configurations, establishing a baseline for future comparative studies. The results validate FrodoKEM's practical viability for deployment in high-throughput, resource-constrained, and power-sensitive cryptographic applications, demonstrating that conservative post-quantum security can be achieved without compromising performance.

We review the traditional techniques of message authentication from the perspective of Constructive Cryptography, one of the major composable security frameworks. For each of the 'textbook' means of message authentication, known results are compiled, and various gaps are addressed. We also point out areas of remaining study, and obstacles to demonstrating composability in those cases. The results can be thought of as a toolkit showing how to realise composable authentication with various cryptographic primitives, with precise statements on the security guarantees and set-up requirements.

Verifiable Secret Sharing (VSS) schemes usually consider synchronous communication, which cannot always be the case on real networks where packets can be lost or parties arbitrarily delayed. Allowing asynchrony adds a large overhead complexity cost: the dealer and communication complexity is in $O(n^2\log n)$ in state of the art $n$-parties Asynchronous VSS (AVSS) schemes [ABDM25], whereas there are synchronous schemes with only linear communications. To ensure that all honest parties agree on the same secret and are ready for reconstruction, AVSS schemes essentially perform a protocol similar to Bracha's broadcast [Bra87]. While this immediately bounds the overall communication complexity of the protocol to be at least in $O(n^2)$, this method enables to reach the maximum threshold of malicious parties of $t=n/3$. However, a smaller threshold $t$ may be sufficient for some use cases, and one may want to take advantage of this. We consider a statistical scheme, meaning that the correctness and termination properties are only guaranteed with good probability. We propose a new method to transform any linear VSS scheme into a statistical AVSS. We build a statistical AVSS protocol Bonneval-on-Arc where each party only communicates with $d$ neighbours, a situation that we model by a $d$-regular graph. We obtain quasilinear communication complexity for the dealer, and sublinear complexity for each party, and a corruption threshold $t < n/(d+2)$ as a tradeoff.

During the past decade, Deep Neural Networks (DNNs) have proven their value across a wide variety of applications; however, despite their importance, protecting their intellectual property remains an open issue. Recent work has successfully extracted DNNs using cryptanalytic methods in hard-label settings, showing that it is possible to copy a DNN with high fidelity, i.e., a high degree of similarity in correct/incorrect output predictions which corresponds to the proportion of samples for which the extracted model produces the same prediction as the original model. However, these methods have only been demonstrated on Multi-Layer Perceptrons (MLPs) and are sensitive to non–fully connected layers and special-case neurons. To overcome these limitations, we base our contribution on a divide-and-conquer paradigm. We introduce a new black-box side-channel attack that splits the targeted DNN into several linear components, for which cryptanalytic extraction can be performed. Building on this decomposition, we propose an end-to-end framework specifically designed for hard-label settings, not limited to fully connected layers, and robust to special-case neurons, while improving extraction fidelity. We validate our contribution by successfully extracting all architectures previously targeted in the literature, as well as several new architectures implemented on a microcontroller unit. These include an MLP with $1.7$ million parameters, nearly doubling the previous largest number of extracted weights, and a shortened MobileNetv1, which for the first time includes pooling layers and depthwise separable convolutions. Our framework successfully extracts all of these DNNs with high fidelity ($88.4\%$ for MobileNetv1 and $93.2\%$ for the MLP). Finally, we use the copied model to generate adversarial examples and achieve near white-box performance on the victim model ($95.8\%$ and $96.7\%$ transfer rates).

Hash-based succinct non-interactive arguments (SNARGs) are a widely studied and deployed class of proof systems. The security of practical hash-based SNARGs relies on two combinatorial parameters of its underlying linear code $\mathcal{C}$: a distance-preservation error $\varepsilon(\mathcal{C},\delta)$ and the list size $|\Lambda(\mathcal{C}, \delta)|$ (both parametrized by a proximity parameter $\delta$). Optimistically, one might hope that these parameters are bounded all the way to the capacity regime: when the proximity parameter $\delta$ approaches the minimum distance of the code $\delta(\mathcal{C})$. Perhaps too optimistically, several deployed hash-based SNARGs indeed operate in this regime, and initiatives such as the Ethereum Proximity Prize investigate to which extent soundness is preserved in this setting. We present a minimal toy protocol whose analysis captures most of the complexity of state-of-the-art hash-based SNARGs, and present a generic attack whose success probability depends on the list size $|\Lambda(\mathcal{C}, \delta)|$. Further, we investigate the common settings when the code $\mathcal{C}$ is an extension code over a field $\mathbb{F}$ of a base code $\mathcal{C}_\mathbb{B}$ over a small base field $\mathbb{B}$. In this setting, we show that classical combinatorial lower bounds on the list-size of the code yields strong attacks that affect the regimes in which hash-based SNARGs operate in practice.

Delay- and Disruption-tolerant Networks (DTNs) enable communication in challenging environments like space and underwater. Despite the need for secure communication, key management remains an unresolved challenge in DTNs. Both DTN security protocols, BSP and BPSec, explicitly exclude key management from their scope, and research in this area remains limited. Traditional Internet-based key management methods are largely unsuitable due to the unique constraints of DTNs. In this paper, we present BERMUDA, a BPSec-compatible key management framework for unicast messaging. Our approach combines established building blocks, including a hierarchical PKI and ECDH, with an adapted version of NOVOMODO for certificate revocation. To evaluate its applicability, we implement a DTN chat application as an example use case and analyze the system's scalability. While our findings demonstrate the feasibility of BERMUDA for DTNs, we also show limitations related to scalability and computational load in resource-constrained scenarios. By bridging the gap between conceptual designs and practical deployment, this work advances key management research in DTNs, contributing to secure communication in these demanding networks.

Deduplication for encrypted data reduces the storage costs of server while keeping the sensitive data secure. Fuzzy deduplication is developing for the multimedia data for its similarity not exact equality, hence it has better storage space saving capabilities than exact deduplication. However, the most of existing works face the security threat such as brute-force guessing attacks, key recovery attacks and so on. We conduct research on fuzzy deduplication from the fundamental layer for these security goals. In this work, the data similarity is novelty defined based on information entropy theory so that the similarity verification by cloud is without online clients assistance. Moreover, the parameter robustness verification is firstly proposed to be against the key recovery attacks and guessing attacks fundamentally. The simulation experiments show that our scheme can save approximately 87% of storage space while maintaining a tamper detection success rate of no less than 97%.

Ring signatures are cryptographic primitives that enable a user to sign a message on behalf of a group of users in an anonymous manner. The anonymity of the signer is the fundamental security property of ring signatures. However, unrestricted anonymity can be misused, as a malicious signer could use it to send spam or excessive messages. To address this issue, a controlled restriction on signer anonymity is required, which makes such schemes more practical. In this paper, we propose a k-times traceable ring signature scheme that allows the public key of the signer to be traced publicly if the signer exceeds a predetermined signing limit k. The novelty of our construction lies in its reliance on lattice-based assumptions, which ensure post-quantum security. Consequently, the proposed scheme is well-suited for practical deployment in the presence of emerging quantum threats. Our approach achieves competitive performance while providing stronger security guarantees, making it an appropriate candidate for modern cryptographic applications. We also present efficiency analysis and compare our scheme with existing constructions.

We study key-schedule design under boundary round-key leakage, namely leakage of the first round key, the last round key, or both end round keys. We propose the nonlinear key-schedule $\mathrm{RK}_i = K \oplus F\bigl(K \oplus T(i)\bigr)$, where $K$ is the master key, $T(i)$ is a public domain separation value, and $F$ is a public SPN-based permutation parameterized by its round count $N_F$. Under the boundary-leakage model considered in this paper, leakage of one end round key yields an instance of the equation $Z=U\oplus F(U)$, whereas leakage of both end round keys yields a differential constraint of the form $F(U)\oplus F(U\oplus\Delta)=\Gamma$, where $\Delta$ is determined by the two end indices and $\Gamma$ is derived from the two leaked round-key values. These reductions clarify the nonlinear systems induced by boundary leakage and the absence of a linear elimination route to the master key. We also evaluate reduced variants of the resulting systems through Gr\"obner basis experiments, and further examine them by SAT-based key-recovery experiments and right-censored runtime analysis via a Weibull AFT model. Within the tested range, we do not observe degree collapse or unusually strong linear bias. These results provide heuristic support for the view that, under the boundary-leakage model considered here, the tested instantiations of the proposed key-schedule family do not admit an obvious efficient inversion route.

Multi-scalar multiplication (MSM), $MSM(\vec{P},\vec{x})=\sum_{i=1}^n x_i P_i$, is a dominant computational kernel in discrete-logarithm–based cryptography and often becomes a bottleneck for verifiers and other resource-constrained clients. We present 2G2T, a simple protocol for verifiably outsourcing MSM to an untrusted server. 2G2T is efficient for both parties: the server performs only two MSM computations and returns only two group elements to the client, namely the claimed result $A=MSM(\vec{P},\vec{x})$ and an auxiliary group element $B$. Client-side verification consists of a single length-$n$ field inner product and only three group operations (two scalar multiplications and one group addition). In our Ristretto255 implementation, verification is up to $\sim 300\times$ faster than computing the MSM locally using a highly optimized MSM routine (for $n$ up to $2^{18}$). Moreover, 2G2T enables latency-hiding verification: nearly all verifier work can be performed while waiting for the server's response, so once $(A,B)$ arrives the verifier completes the check with only one scalar multiplication and one group addition (both independent of $n$). Finally, despite its simplicity and efficiency, we prove that 2G2T achieves statistical soundness: for any (even unbounded) adversarial server, the probability of accepting an incorrect result is at most $1/q$ per query, and at most $e/q$ over $e$ adaptive executions, in a prime-order group of size $q$.

Uncertified DAG-based BFT protocols, such as Mysticeti and Cordial Miners, achieve state-of-the-art latency by eliminating per-block quorum certificates. However, they have lacked rigorous liveness proofs, and recent work has demonstrated explicit desynchronization attacks where honest parties fail to commit leaders after Global Stabilization Time (GST). We present Starfish, an uncertified DAG-based BFT protocol that closes this gap with a new Push pacemaker. This mechanism ensures party synchronization after GST by requiring parties to create their own blocks before advancing rounds and introducing a safe “catch-up” condition for slow parties. To address scalability, Starfish decouples payload from metadata: block headers carry only commitments to Reed-Solomon-encoded fragments, and data availability is certified directly on the DAG via Data Availability Certificates (DACs). This achieves order-optimal worst-case linear payload communication while increasing sequencing latency by only one round. We further propose Starfish-L, combining multi-signatures with a Lazy-Push pacemaker to reduce metadata communication from quartic to cubic in the worst case and quadratic in the happy case. Applying these techniques to Mysticeti yields Mysticeti-L, which matches Mysticeti's low latency while achieving quadratic metadata and linear payload communication costs in the happy case. Finally, we provide full safety and liveness proofs and derive latency bounds in terms of the actual message delay.

In this note we introduce the concept of proximity signatures, where verifiers who can only access a small part of some data would like a guarantee that (a) this data is “close” to a uniquely decodable message (so the message can be decoded from the data via error decoding) and (b) the uniquely decodable message is signed by an associated secret key. This is useful in situations where the message is very large but the verifiers are small devices who only need the guarantee that the message was signed by some specific secret key or set of keys. As a motivating example, we consider the data availability problem. There, users submit large signed pieces of data that together form a larger data matrix. The signatures and integrity of this data must then be checked by nodes who can only download a small proportion of this matrix. We present a construction inspired by linear subspace signatures.

(Partially) blind signatures are foundational cryptographic primitives that enable privacy-preserving authentication in digital systems. Blind signatures allow a user to obtain a signature on a message without revealing its content, while partially blind signatures permit the controlled inclusion of agreed-upon public information into the signed message. These primitives are central to applications such as electronic voting, anonymous credentials, and digital cash. The first isogeny-based construction of (partially) blind signatures, CSIOtter, were proposed by Katsumata et al. at CRYPTO'23. However, its concurrent security was later broken by Katsumata et al. (CRYPTO'24) and Do et al. (EUROCRYPT'24). These findings imply that CSI-Otter is secure only in sequential settings. Recently, Hanzlik et al. (ASIACRYPT'25) has proposed a novel framework for concurrently secure blind signatures which can be instantiated from isogenies with smaller signature size (but larger public key and secret key size). It is not known yet whether their construction can be extended to partially blind signatures. In this paper, we present a new and efficient construction of partially blind signatures based on isogenies with substantially smaller signature and public key sizes than CSI-Otter. This makes our construction the most compact post-quantum partially blind signature scheme known to date. As similar to CSIOtter, our scheme uses small challenge space resulting in only achieving sequential concurrent security. Our design follows the Abe-Okamoto paradigm in the group action setting, building upon the framework introduced by Tessaro and Zhu (EUROCRYPT'22), whose security is based on the Discrete Logarithm Problem. We rigorously prove the security of our scheme in the Algebraic Group Action Model and the Random Oracle Model, under the hardness assumption of the Group Action Discrete Logarithm Problem.

A dominant approach to solving the scalability problem in blockchain systems has been the development of layer 2 protocols and in particular payment channel networks (PCNs) such as the Bitcoin Lightning Network (LN). Routing payments over LN requires the coordination of all path intermediaries in a multi-hop round trip that encumbers the layer 2 solution both in terms of responsiveness as well as privacy. The issue is resolved by virtual channel protocols that, capitalizing on a suitable off-chain setup operation, enable the two endpoints to engage as if they had a direct payment channel between them. Once the channel is not needed anymore, it can be optimistically closed in an off-chain fashion. Apart from communication efficiency, virtual channel constructions have three natural desiderata. A virtual channel constructor is recursive if it can also be applied on pre-existing virtual channels, variadic if it can be applied on any number of pre-existing channels, and symmetric if it imposes equitable costs on all channel participants in every execution scenario. We introduce Elmo, the first Bitcoin-suitable recursive variadic virtual channel construction. Furthermore our virtual channel constructor is symmetric and offers optimal round complexity for payments, optimistic closing and unilateral closing. We express and prove the security of our construction in the universal composition setting, using a novel induction-based proof technique of independent interest. As an additional contribution, we implement a flexible simulation framework for on- and off-chain payments and compare the efficiency of Elmo with previous virtual channel constructors.

Zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) are cryptographic protocols that allow a prover to convince verifiers of the correctness of a statement without revealing any additional information. Recent zk-SNARK constructions have shifted from univariate to multivariate polynomial-based designs, reducing the proving complexity from quasilinear to linear by avoiding costly univariate polynomial interpolation. This shift, however, makes the sumcheck protocol—a core primitive for verifying polynomial relations over the Boolean hypercube—the dominant component in the prover’s workload. Consequently, the iterative nature and intensive intermediate data movement of the sumcheck protocol introduce severe performance bottlenecks in CPU- and GPU-based implementations, especially for large-scale multivariate polynomials. In this paper, we present PipeSC, a resource-efficient, ASIC-based accelerator for sumcheck. PipeSC combines deep pipelining, modular-multiplier reuse, and a finite-state machine-based dependency scheduler to sustain high utilization of computational resources across phases of the protocol. In addition, we introduce an Equality-MLE generation module that employs hierarchical scheduling and multiplier reuse, yielding a unified hardware substrate shared by multiple proving subroutines. Against state-of-the-art CPU, GPU, and ASIC implementations, PipeSC delivers up to \textbf{5.02$\times$} speedup over the GPU implementation and up to \textbf{2756.2$\times$} speedup over the CPU implementation, while improving the area–time product (ATP) by up to \textbf{3.68$\times$} compared with the ASIC design. These results show that careful hardware–algorithm co-design and conflict-free scheduling substantially accelerate sumcheck, paving the way for fully integrated zk-SNARK hardware pipelines.

Adaptor signatures extend digital signatures with conditional disclosure capabilities, enabling atomic swaps, payment channels, and other advanced blockchain protocols. Although post-quantum adaptor signatures have been explored under lattice, isogeny, and coding-theoretic assumptions, no constructions have yet been realised from the multivariate quadratic (MQ) family of signatures. Classical algebraic adaptor techniques rely on embedding the witness into signing randomness, which is natural for discrete-log-based schemes but does not apply to MQ signatures such as UOV and MAYO: to the best of our knowledge, MQ signing randomness lacks the algebraic structure needed for witness embedding, and no such algebraic adaptor construction is currently known. This motivates a different approach. We propose MWAS, the first commitment-based adaptor-style construction for MQ signatures, specifically UOV and MAYO from the NIST PQC process, implemented via the Open Quantum Safe library. Our construction uses a lightweight HMAC-SHA256 commitment and a concatenation-based adaptation, supporting a hash-preimage witness relation. We prove correctness, witness hiding, and witness extractability in the ROM under MQ-hardness and PRF assumptions. A prototype implementation on a Raspberry Pi~5 shows pre-signature generation under 0.4~ms for UOV and 0.5--3.3~ms for MAYO across 128--256-bit security levels, with throughput up to 710~ops/s and public key sizes of 1.4~KB (MAYO) to 1.2~MB (UOV). These results indicate that commitment-based MQ adaptor signatures are a viable post-quantum option for settings where hash-preimage witness relations are appropriate.

Ensuring ciphertext indistinguishability is fundamental to cryptographic security, but empirically validating this property in real implementations and hybrid settings presents practical challenges. The transition to post-quantum cryptography (PQC), with its hybrid constructions combining classical and quantum-resistant primitives, makes empirical validation approaches increasingly valuable. By modeling indistinguishability under chosen-plaintext attack (IND-CPA) games as binary classification tasks and training on labeled ciphertext data with binary cross-entropy loss, we study deep neural network (DNN) distinguishers for ciphertext indistinguishability. We apply this methodology to PQC key encapsulation mechanisms (KEMs). We specifically test the public-key encryption (PKE) schemes used to construct examples such as ML-KEM, BIKE, and HQC. Moreover, a novel extension of this DNN modeling for empirical distinguishability testing of hybrid KEMs is presented. We implement and test this on combinations of PQC KEMs with unpadded RSA, RSA-OAEP, and plaintext. Finally, methodological generality is illustrated by applying the DNN IND-CPA classification framework to cascade symmetric encryption, where we test combinations of AES-CTR, AES-CBC, AES-ECB, ChaCha20, and DES-ECB. In our experiments on PQC algorithms, KEM combiners, and cascade encryption, no algorithm or combination of algorithms demonstrates a significant advantage (evaluated via two-sided binomial tests with significance level $\alpha = 0.01$), consistent with theoretical guarantees that hybrids including at least one IND-CPA-secure component preserve indistinguishability, and with the absence of exploitable patterns under the considered DNN adversary model. These illustrate the potential of using deep learning as an adaptive, practical, and versatile empirical estimator for indistinguishability in more general IND-CPA settings, allowing data-driven validation of implementations and compositions and complementing the analytical security analysis.

In 2022, Castryck and Decru introduced an attack that broke several isogeny-based schemes, including SIKE, which had advanced to the final round of the NIST Post-Quantum Cryptography Standardization Competition. Despite this attack, research on isogeny-based cryptography has continued, primarily due to the compact key sizes offered by these schemes compared to other post-quantum approaches. There are now many isogeny-based schemes that are resistant to the Castryck-Decru attack. These schemes typically involve advanced mathematical structures that may require significant time and effort to study. In this paper, we provide a structured survey of isogeny-based signature schemes that are resistant to the Castryck-Decru attack, aiming to facilitate an understanding of the current landscape and the most practically relevant schemes in this area. We categorize these signature schemes into two main classes: those based on the CSIDH group action and the SQIsign family. For each class, we discuss their fundamental design principles, security assumptions, and specific constructions. We also compare their performance and compactness. Additionally, we describe one representative scheme from each class that is particularly relevant in practice due to its efficiency or compactness. In conclusion, we compare the performance of the schemes discussed in this work with other post-quantum signature schemes.

Emerging 6G communication systems impose unprecedented requirements on cryptographic primitives, demanding ultra-high throughput, low latency, and strong resistance to implementation-level attacks. LOL2.0 is a recently proposed stream cipher framework that achieves high software efficiency and strong security in post-quantum settings. While several stream ciphers have been proposed to address performance demands, side-channel-protected hardware implementations capable of sustaining 6G-class throughput remain largely unexplored. In this work, we present the first side-channel-protected hardware implementation that meets the 6G-class throughput demand. Focusing on the LOL2.0 stream cipher framework, we leverage Time Sharing Masking to achieve first-order security under the glitch-extended probing model. This design realizes full-phase protection covering initialization, keystream generation, and tag generation. To address diverse deployment requirements, we design two masked architectures: a compact variant optimized for area and randomness efficiency, and a fast variant targeting the maximum achievable throughput. The proposed fast implementations achieve peak throughputs of 183 Gbps and 142 Gbps for the unmasked and masked configurations, respectively. Meanwhile, the compact architecture reduces hardware cost by achieving areas as low as 23.25 kGE and 141.98 kGE in unmasked and masked designs, respectively, while still maintaining competitive throughput. Security is validated through practical side-channel evaluations using Test Vector Leakage Assessment on FPGA platforms. Across up to 100 million measured power traces, no statistically significant first-order leakage is observed for any protected configuration. Overall, this work realizes side-channel-protected stream cipher hardware that sustains ultra-high throughput, providing a concrete path toward secure cryptographic deployment in future 6G communication systems.