Lookup table polynomial interactive oracle proofs (LUT PIOPs) make SNARK arithmetizations concise, yet almost all efficient constructions assume field arithmetic. We show that directly instantiating them over a composite residue ring \(\mathbb Z_Q\) can be unsound: component-wise set checks preserve the residue multiset in each CRT component but lose the alignment across components. We formalize this obstruction, which we call the CRT alignment ambiguity. To overcome this ambiguity, we present GlueLUT, a family of efficient LUT PIOPs over residue rings. GlueLUT runs the lookup over an auxiliary field while retaining the arithmetic proof over \(\mathbb Z_Q\), and then proves consistency between the two witness representations. Our first construction, GlueLUT-4Sq, introduces a cross-modulus consistency (CMC) PIOP, which proves that witnesses over two coprime moduli encode the same integer vector. We construct the CMC PIOP via a range-check PIOP over the product ring using the Lagrange four-square decompositions, structured Johnson–Lindenstrauss projections, and a GKR-style consistency check. For a witness of size \(n\), a table of size \(m\), and security parameter \(\lambda\), GlueLUT-4Sq has \(O(n+m)\) algebraic prover work after witness generation and \(O(\operatorname{poly}(\lambda,\log n,\log m))\) verifier work and proof size. Our second construction, GlueLUT-Fold, uses random rank-one folded consistency checks to achieve better concrete prover efficiency and has \(O(n+m)\) prover work, at the cost of \(O(\sqrt n+\operatorname{poly}(\lambda,\log n,\log m))\) verifier work; its proof size is \(O(\log n+\log m)\). We implement GlueLUT-4Sq and GlueLUT-Fold as stand-alone PIOPs and report prototype results that corroborate our theoretical efficiency analysis.

Fully homomorphic encryption (FHE) allows a server to run a language model directly on encrypted user prompts, but current approaches remain prohibitively slow. Ciphertexts natively support only addition, multiplication, and rotation, and multiplications may be composed only to a bounded depth before a costly bootstrapping operation is required to continue. Every nonlinearity must therefore be approximated by an iterative method; each iteration increasing the number of multiplications. A higher iteration count buys precision but exhausts the available depth more frequently and thus triggers more bootstraps, which dominate latency. We introduce Homomorphic Encryption-Aware Training (HEAT), a fine-tuning method that makes the per-nonlinearity iteration counts learnable, enabling them and the model weights to co-adapt during training. HEAT optimizes iterations with respect to the task objective, allowing the model to adapt to approximation errors encountered during inference without architectural changes or retraining from scratch. We further relate iteration count to quantization bit width and bound, at fixed weights, the gap between our objective and quantization-aware training. On encrypted GPT-2 decoding, HEAT reduces iterations by $3.1\times$, bootstraps by $1.6\times$, and end-to-end latency by $1.4\times$, while improving decode agreement over the calibrated encrypted baseline.

CROSS is a code-based signature scheme built on the Restricted Syndrome Decoding Problem and is a second-round candidate in NIST's additional digital signature standardization process. Recent work shows that its reference implementation is vulnerable to side-channel analysis, allowing an attacker to recover the long-term secret key from a single power trace. No masking countermeasure has so far been designed for CROSS's restricted-syndrome framework, leaving its practical side-channel resistance unresolved. In this work, we present a full sensitivity analysis and a gadget-based masking schedule ($G_0-G_8$) for the CROSS signing algorithm of the R-SDP(G) variant. One gadget in this schedule, the restriction-lift exponentiation, has no counterpart in prior masked multivariate- or lattice-based signatures: it masks $g^{\bar{\mathbf v}[i]}$ via table lookup, share-serial conversion, and ISW-multiplication sub-gadgets rather than via a fixed linear or bilinear map. We rigorously prove $t_{\mathrm{mask}}$-probing security for each gadget individually and for their full composition, using the NI, SNI, and NIo frameworks. We implement the resulting masked signer for an arbitrary number of shares $d$ and evaluate it on an x86-64 platform, measuring cycle overheads of $21.73\times$ at first order and $78.05\times$ at second order relative to the unmasked baseline. At first order, our masked CROSS is cheaper than a comparably masked Dilithium-2 ($38\times$), but Dilithium-2 overtakes it at second order ($70\times$). This crossover cost is driven by the $O(d^3)$ chained-ISW cost of $G_3$/$G_7$ compared to Dilithium's cheaper $O(d^2)$ scaling.

Since its introduction, Solinas' window $\tau$-NAF algorithm has been a landmark method for accelerating scalar multiplication on Koblitz curves over binary fields. A long-standing open problem has been to identify a suitable family of elliptic curves over prime fields for which the window $\tau$-NAF approach can be effectively extended. In this paper, we settle this problem by establishing such an extension for the family $E_b: y^2=x^3+b$ over $\mathbb{F}_p$ with prime $p\equiv1\pmod 3$. This family includes several practically important curves used in blockchain applications (e.g., secp256k1) and pairing-based cryptography (e.g., BN254 and BLS12-381). By considering a nonzero nonunit element of minimal norm in the ring of Eisenstein integers $\mathbb{Z}[\omega]$, we identify the endomorphism $\tau=1-\omega$ as a natural choice for $\tau$-adic scalar multiplication on $E_b/\mathbb{F}_p$. In Jacobian projective coordinates, the map $\tau P$ can be evaluated using only $6\mathbf{M}$ (where $\mathbf{M}$ denotes a field multiplication). This also yields a new point-tripling formula requiring only $10\mathbf{M}$, improving upon the previous best cost of $15\mathbf{M}$. Furthermore, we optimize the pre-computation stage by choosing a set of coefficients invariant under the unit group $U\subset\mathbb{Z}[\omega]$. Exploiting this sixfold symmetry reduces the pre-computation cost by approximately five-sixths. The $U$-invariant structure also plays an important role in further accelerating window $\tau$-NAF evaluation. Our optimized method achieves performance improvements of $16.7\%$, $17.6\%$, and $18\%$ over the current state-of-the-art GLV method for $256$-, $384$-, and $512$-bit group orders, respectively. We also develop a regular window $\tau$-NAF variant as a countermeasure against side-channel attacks. Compared with the regularized GLV method, this variant reduces the scalar multiplication cost by $17.7\%$, $19.8\%$, and $20.9\%$ for $256$-, $384$-, and $512$-bit group orders, respectively.

Hash-based signatures offer a conservative foundation for post-quantum authentication, but their large signatures impose substantial communication and storage costs. For security parameter $\lambda$, discrete-logarithm-based signatures have length $O(\lambda)$, while known hash-based constructions have quadratic signature length, up to logarithmic factors, even for one-time signing. Is this gap inherent? We prove what are, to the best of our knowledge, the first lower bounds on the length of signature schemes in the (pure) random oracle model. Our bounds apply to schemes with non-adaptive verifiers and a natural security property called salted soundness: a scheme with such security is unforgeable even against an adversary that is granted a limited ability to resample and restore oracle answers. This class essentially captures all known hash-based constructions (possibly after low-cost modifications). We show that the combined public-key and signature length of a one-time signature scheme must be $\Omega(\lambda^2/\log\lambda)$. For many-time signatures, we prove the stronger conclusion that the signature length alone must satisfy the same lower bound, irrespective of the public-key length. More precisely, if the relevant length is $o(\lambda^2/\log\lambda)$, then an adversary making $2^{o(\lambda)}$ random-oracle queries breaks salted soundness with inverse-polynomial probability. Our proof uses the high-entropy hitting lemma of Haitner, Nukrai, and Yogev (Crypto 22) to transform a short signature scheme into a scheme whose verifier makes only a few queries. We then apply the Barak and Mahmoody-Ghidary (FOCS 07) attack on one-time signatures with a low-query verifier. Balancing these two steps yields the near-quadratic lower bounds.

Atomic swaps are the prototypical application of adaptor signatures. Practical constructions settle with two ordinary on-chain signatures and require no scripting, but they need two sequential online rounds: Alice samples a hard statement and sends its pre-signature, and Bob follows with his own pre-signature using the same statement. We ask whether the protocol can be compressed into a single online round (from Bob to Alice), which we call a non-interactive atomic swap, without relying on impractical universal adaptor signatures. In particular, we require that both parties continue to use standard signature schemes with unmodified verification algorithms. Our main result is a lower bound: for statistically unlinkable adaptors with negligible faithfulness failure, Bob's valid-signature space per message must be superpolynomially larger than the relation's witness space. This (1) reaffirms the impossibility result by Erwig et al. [PKC 2021] for unique signatures as a trivial corollary, and (2) excludes non-interactive swaps using the same signature scheme on both sides. However, the bound does leave room for asymmetric instantiations. We give one in which Alice signs with BLS and Bob uses a pairing-Schnorr adaptor whose witness is Alice's BLS signature, and prove its security under the native unforgeability of BLS in the random oracle model. To support more signature schemes in our non-interactive swap framework, we introduce atomic signature swaps with preprocessing: Alice publishes message-independent public data before the messages are chosen. These data, together with her public key and the messages, later determine a statement whose witnesses assemble into her native signature. The protocol requires a single online round carrying a pre-signature by Bob and falls into our non-interactive framework. We prove a Schnorr/Schnorr instantiation under the OMDL assumption in the random oracle model, and give a conditional ECDSA/Schnorr instantiation.

We improve recent generic proof systems for isogeny knowledge by Cong, Lai, Levin based on circuit satisfiability, by using radical isogeny descriptions to prove a path in the underlying isogeny graph. We then present a new generic construction for a verifiable random function (VRF) based on a one-more type hardness assumption and zero-knowledge proofs. We argue that isogenies fit the constraints of our construction and instantiate the VRF with a CGL walk and our new proofs. As a different contribution, we also propose a new VRF in the effective group action description of isogenies. Our protocol takes a novel approach based on the polynomial-in-the-exponent technique, but without the need of a trusted setup or heavy preprocessing. We compare our protocols to the current state-of-the-art isogeny VRFs by Leroux and Lai, with a particular emphasis on computational efficiency.

We present variants of blind Schnorr and blind Okamoto-Schnorr signatures that are not susceptible to ROS-style attacks. We prove the schemes unforgeable in the algebraic group model and the random oracle model: the Okamoto-Schnorr variant under the discrete-logarithm assumption; the Schnorr variant under the algebraic one-more discrete-logarithm assumption. Our Schnorr variant improves on the communication complexity of Snowblind (CRYPTO 2023), the state-of-the-art "pairing-free" blind signature scheme, while matching its signature size. Moreover, we show that this communication complexity is optimal: any blind "Schnorr-like" scheme whose first message is a single group element is susceptible to a variant of the ROS attack by Benhamouda et al. (EUROCRYPT 2021).

Anonymous blocklisting enables services to revoke malicious users while preserving anonymity for honest users. Signature-based revocation supports revocation from past authentications, but existing systems incur substantial overhead at large scale and for users returning after long offline periods. Window-based alternatives reduce this overhead but impose restrictive revocation-timing policies. This work presents zk-BAN, a signature-based anonymous blocklisting system that reduces proof-generation and verification costs through two design improvements: constructing a carefully filtered revocation list and partially unifying PRF tags to reduce repeated zero-knowledge computations. We formalize zk-BAN and prove that it satisfies blocklistability and unlinkability. Under modeled large-scale real-world workloads, zk-BAN generates proofs in approximately 600 ms and verifies them in approximately 2 ms. We show zk-BAN displays 54.4 times faster proving than our naive baseline and 136-fold faster proving and 32-fold faster verification than prior work.

Witness encryption over blockchain state aims to release a secret on a ledger condition without a key custodian. Validators with enough stake to construct a valid fork witness can obtain the secret although the condition never holds on the canonical chain. They finalize a private fork that satisfies the condition, and keeping the fork hidden withholds the conflicting votes that slashing needs. We propose slashable secrecy to address this gap with Ethereum’s native slashing rules, without an additional key-custody committee or separate collateral. In executions where the condition never holds on the finalized canonical chain through completion, an information advantage yields evidence of those votes against keys the adversary controlled, or a solution to a designated hard problem. We give a construction from a witness KEM and prove slashable secrecy conditionally on its extraction interface. We bound the implicated historical stake under changing validator weights. For an archived Ethereum mainnet state, the historical evidence-weight floor exceeds 3.5 percent of its active stake, about 1.44 million ETH, under stated budget and coverage assumptions. Experiments on a synthetic Ethereum network confirm native processing of the evidence, without WE decryption. Two limitations remain. A witness KEM satisfying the full relation and extraction interface remains uninstantiated. Enforcement requires that the evidence is available, converted to native form and included while its signers remain eligible.

Selfish mining profits in Nakamoto consensus because difficulty adjustment mechanisms (DAMs) misinterpret uncounted orphans as hash-rate contraction. Although orphan-aware DAMs record orphaned proof-of-work, strict same-epoch inclusion rules enable an orphan exclusion attack (OEA): an adversary can race private forks near epoch boundaries to permanently exclude honest tail orphans from retargeting, restoring substantial profits in short-epoch protocols. We propose the pipelined buffer difficulty adjustment mechanism (PB-DAM), which partitions each epoch into an accountable prefix and a settlement buffer of depth $d$. Pipelining estimation windows across epochs grants honest miners a grace period to report prefix uncles while advancing buffer work to subsequent retargets, closing the boundary gap without heuristic damping. Random-walk excursion bounds demonstrate that OEA success decays exponentially with $d$ for all $\alpha \le \alpha^\star < 1/2$, reducing the time-averaged profit advantage to $O(\varepsilon)$. Under stylized dynamic scheduling models, intermittent idling is analytically shown to be unable to raise the gross reward rate above $\alpha$. Simulations confirm that buffer depths $d = 16$ neutralize selfish mining even at $L = 64$ when $\alpha = 0.40$, and systems recover from a $50\%$ hash-rate crash within $2.2 \pm 0.8$ epochs, incurring under $1\%$ block capacity overhead.

Key derivation functions can be used to derive variable-length random strings that serve as cryptographic keys. They are integral to many widely-used communication protocols such as TLS, IPsec and Signal. NIST SP 800-108 specifies several key derivation functions based on pseudorandom functions such as CMAC and HMAC, that can be used to derive additional keys from an existing cryptographic key. This standard either explicitly or implicitly requests their KDFs to be variable output length pseudorandom function, collision resistant, and preimage resistant, which are also demanded by practical applications. Yet, since the publication of this standard dating back to the year of 2008, until now, there is no formal analysis to justify these security properties of KDFs. In this work, we give the formal security analysis of key derivation functions in NIST SP 800-108. We show both positive and negative results regarding these key derivation functions. For KCTR-CMAC, KFB-CMAC, and KDPL-CMAC that are key derivation functions based on CMAC in counter mode, feedback mode, and double-pipeline mode respectively, we prove that all of them are secure variable output length pseudorandom functions and preimage resistant. We show that KFB-CMAC and KDPL-CMAC are collision resistant. While for KCTR-CMAC, we can mount constant-time collision attack against it. For KCTR-HMAC, KFB-HMAC, and KDPL-HMAC that are key derivation functions based on HMAC in modes, we show that all of them behave like variable output length pseudorandom functions. When the key of these key derivation functions is of variable length, they suffer from collision attacks. For the case when the key of these key derivation function is of fixed length and less than \(d-1\) bits where \(d\) is the input block size of the underlying compression function, we can prove that they are collision resistant and preimage resistant. Finally, we extend our analysis to the plain CMAC-based KDFs for which mitigation techniques against key-control attacks do not apply, as well as to the KMAC-based KDF.

Secure Multi-Party Computation (MPC) enables collaborative and privacy-preserving computation over private inputs. Recent advances in Homomorphic Encryption (HE), particularly the CKKS scheme, have significantly improved the practicality of secure computation, making it suitable for real-world applications involving approximate arithmetic. However, the inherent errors introduced by CKKS pose substantial challenges in the design and analysis of CKKS-based secure computation protocols. In this work, we investigate the correctness and security of existing CKKS-based MPC protocols. Most prior constructions rely on the noise smudging technique, in which each party independently adds exponentially large noise to the output to guarantee the security of the protocol. However, we show that this approach does not achieve standard simulation-based security for MPC. To address this limitation, we apply an alternative method, called collaborative sampling, in which all participating parties jointly generate additive shares of the smudging noise. We consider both asymmetric two-party protocols between a client and a server, and symmetric multiparty protocols among mutually distrusting parties. For each setting, we present concrete protocol constructions based on collaborative sampling, explicitly define the corresponding ideal functionalities, and provide formal security proofs. We further provide concrete constructions and implementations of collaborative sampling protocols. As an alternative perspective, we show that existing protocols, despite failing to achieve standard simulation-based security, still satisfy a weaker security notion called liberal security for approximate MPC protocols.

Merz and Ran derive additional equations from divided powers of the public polar forms in characteristic two. We extend this construction to finite fields of arbitrary characteristic and apply it to the security analysis of QR-UOV.

Password-authenticated key exchange (PAKE) and obfuscated key exchange (OKEX) are widely used protocols, appearing in passport access control, Tor's censorship evasion, and more. As quantum threats grow nearer, there have been an increasing number of proposals for post-quantum PAKE and OKEX. All such protocols are similar in that they build on a KEM, obfuscating public keys and/or ciphertexts sent over the wire, e.g., by adding a random mask or applying an ideal cipher. Many propose instantiation with ML-KEM, a NIST-standardized lattice-based KEM. Unfortunately, ML-KEM is a poor fit for these obfuscating protocols. The algebraic structure of ML-KEM public keys and ciphertexts means that obfuscating these values requires custom procedures for hash-to-vector, matrix expansion, serialization/deserialization, and randomized ciphertext decompression. In order to be broadly useful, these procedures also must be constant-time to prevent side channels and must be standardized to permit interoperability. No such set of procedures exists today. We observe that the barriers to instantiating PAKE and OKEX disappear if some of the KEM's algebraic structure is removed, i.e., if ML-KEM is replaced with a KEM whose public keys and ciphertexts appear to be uniform as bytestrings. In this work, we specify Kopis, a Module Learning-with-Rounding (MLWR) KEM with public keys and ciphertexts that are uniform as bytestrings. Kopis is intended to be a drop-in replacement for ML-KEM, in size, speed, and security. Kopis is nearly identical to Saber, a NIST PQC finalist, and thus inherits its years of cryptanalysis. We demonstrate that Kopis bears the security properties needed for use in various PAKE and OKEX schemes and provide a formally verified Rust implementation complete with portable, AVX2, and NEON backends, and a non-formally-verified C implementation for Cortex-M4. We perform benchmarks and find that Kopis is comparable to and often outperforms the fastest known ML-KEM implementations.

Subversion attacks where the attacker aims to replace parts of a cryptographic system by manipulated parts in an undetectable manner have been shown to model both theoretical and practical attacks such as supply chain attacks. Originally proposed by Young and Yung (CRYPTO 1996), interest in them has increased dramatically after the revelations about the inner workings of intelligence agencies due to Snowden and the following paper by Bellare, Paterson, and Rogaway (CRYPTO 2014). One of the most promising countermeasures against such attacks are cryptographic reverse firewalls, proposed by Mironov and Stephens-Davidowitz (EUROCRYPT 2015), which are small devices used by the parties with the aim to rerandomize the protocol message to remove possible leakage. A wide range of protocols and corresponding firewalls have been developed based on this notion. The usage of such firewalls, however, also introduces another attack surface as an attacker might also corrupt these firewalls. In most works, this problem is either not addressed or treated as if in this case, the complete party using the firewall is compromised. However, as firewalls typically only perform rerandomization without knowledge of secret key material, this is a very coarse over-approximation, as an honest party Alice is now treated as maliciously corrupted. Instead, the main security problem comes from the fact that the firewall can impersonate Alice. In this paper, we introduce the notion of impersonation resilience, which allows us to develop protocols that are also secure against such a corrupted firewall and thus result in an honest complete party. We show a generic compiler that transforms subversion-resilient protocols for commitment or coin toss into protocols that are also impersonation resilient. Following a recent research line, our protocols and security analysis are built on the Universal Composability (UC) framework of Canetti. Of independent interest, we show that existing UC subversion models are either too strong and do not allow secure string commitments, or too weak and allow trivially secure protocols. We addressed this by developing a new, intermediate UC subversion model.

On September 20, 2026, the Chinese Institute of Commercial Cryptography Standards published the 119 first-round candidates of its Next-generation Commercial Cryptographic Algorithms (NGCC) program: 34 signature schemes, 41 key encapsulation mechanisms, 9 key exchange protocols, and 35 hash functions. The program follows the template of the open NIST competitions for AES, SHA-3, and post-quantum cryptography. It opened just after cryptographers' ``Lee Sedol moment'' in the summer of 2026, when AI analysis overtook humans in analyzing the HAWK signature scheme. During the first 7 days of the NGCC competition, according to our harvested sources, 191 active findings were published for 89 candidates, 78 of them rated Critical: universal forgeries, signing-key recovery, trivial hash collisions, broken implicit rejection, and seeds too short for the claimed security level. Our independent evaluation effort discovered, verified, and disclosed 110 of those issues (47 Critical) using the agentic workflow described in this work; outside researchers, some AI-assisted, found the rest. Early AI-assisted findings mostly concerned implementations; by the end of the week, reproduced AI-assisted attacks also included new design-level key recovery. We describe the workflow, review loop, classification ruleset, and observed failure modes. As part of the evaluation, we also benchmarked all algorithm candidates and found that NGCC hash selection may significantly affect final public-key performance, as candidate implementations spend a large share of their cycles on ``placeholder'' hashes.

In this paper, we introduce a new hash algorithm in that we used the Collatz problem, focusing on its conditional branching structure, an element often overlooked despite the fame of the 3x + 1 conjecture. This hash algorithm takes an arbitrary-length input and produces a fixed length 512/384/256 bit output. The presented hash algorithm is in the category of strong one-way Hash Function (OWHF), and this hash algorithm is designed by focusing on its use in password storing and Pseudo-Random Number Generator (PRNG). Until now, quantum computers also didn’t show any speedup in the Collatz conjecture problem, so the proving and disproving of the Collatz conjecture is still a big question, so we believe that there is no structural attack on this hash algorithm.

In public blockchains, the ability to order visible transactions allows block producers to extract value from users, a problem known as Maximal Extractable Value (MEV). Proposer-Builder Separation has turned that right into a formalized auction, and the leading protocol-level mitigations answer it with payload blindness: encrypted mempools, verifiable permutations, and block delay hide or scramble transactions before the order is fixed. Every such mitigation carries a security argument that assumes an adversary who learns nothing before the order commits. Deployed systems face a different adversary, and this paper measures the cost of that difference. We evaluate the three families of mitigations against a single adversary hierarchy, using closed-form analysis and simulations calibrated to Ethereum. Against a fully blind adversary, the outcome follows from the definitions: encryption with a permutation removes the attack classes that depend on transaction content, and block delay increases extraction rather than reducing it. Once that idealization is dropped, deployment problems dominate. The unencrypted envelope identifies the sender, so past behavior restores a usable guess at hidden content. Optional encryption gives builders a reason to starve the transactions it protects, and voluntary adoption then collapses. Key rotation turns a cryptographic parameter into a source of queueing congestion. Suppressing extraction, finally, removes far more producer revenue than it returns to users in lower fees, so the cost of every mitigation falls on the party that controls its deployment. The binding obstacles to MEV-free blockchains are therefore liveness and deployment incentives rather than cryptography.

Secure Transformer inference can be made non-interactive under fully homomorphic encryption (FHE), but the computation is extremely expensive. Existing FHE-based systems reduce that cost by optimizing individual stages in isolation, each within its own component rather than against the CKKS level budget they all share. A local gain therefore may not translate into an end-to-end speedup. We present THEMIS, a co-designed system for encrypted Transformer inference organized around two design principles, one bounding the depth each kind of stage may spend and one fixing where on the modulus chain it runs. THEMIS generalizes coefficient-encoded plaintext-ciphertext matrix multiplication (PCMM) to slot-encoded ciphertexts without format conversion, retaining the same accelerated coefficient-side backend and amortizing its nearly fixed cost through multi-batch packing. Two attention ciphertext-ciphertext matrix multiplication (CCMM) kernels combine the idle imaginary lane of each slot with baby-step giant-step accumulation and hoisting, so the attention multiplications issue far fewer key switches. For softmax, THEMIS conditions the first denominator with a calibrated row-wise offset and reserves high precision for the final normalization alone, which cuts the depth the reciprocal path consumes while keeping the precision of the returned probabilities. For a single stage, THEMIS accelerates PCMM and the attention CCMMs by $21.66\times$ and up to $7.39\times$ over MOAI (ICLR'26), and by up to $23.02\times$ and $16.49\times$ over Euston (S&P'26), while THEMIS's softmax runs $2.57\times$ faster than THOR (CCS'25) at higher precision. For the complete pipeline, THEMIS serves BERT-base on a CPU in $400.06$ amortized seconds per input, with accuracy on GLUE tasks comparable to plaintext. Of that latency, the stages around bootstrapping account for only $10.83\%$, which is the lowest share among all works compared here.

Multi-key fully homomorphic encryption (MKFHE) enables computation over ciphertexts encrypted under keys independently generated by different parties. Recently, Min, Park, and Song (MPS, CRYPTO 2026) constructed the first RLWE-based MKFHE scheme in the plain model, i.e., without trusted or interactive setup. Their construction requires each local compact Gentry-Sahai-Waters (GSW) ciphertext to be extended to a joint-key GSW-like ciphertext before evaluation, incurring $O(dk^2)$ gadget products per input for $k$ parties and gadget length $d$. In this paper, we first construct an extension-free MKFHE scheme (called Levis-fast) in the plain model, eliminating the $O(dk^2)$ gadget products required for joint-key ciphertext extension before homomorphic evaluation. Our core technique is a compatibility technique, termed Cofactor Compatibility, which establishes a common projective decryption relation across ciphertexts encrypted under independently generated local keys, enabling their direct homomorphic evaluation. We further present a compact variant (named as Levis-small) that reduces the communication of each fresh ciphertext from $O(dk^2)$ to $O(d)$ ring elements with only a lightweight lifting operation. A proof-of-concept implementation shows that, compared with MPS, for $k\in\{2,4,8\}$, our construction Levis-fast achieves evaluation speedups of $67.7\times$, $52.8\times$, and $139.4\times$, respectively, while our compact variant Levis-small reduces communication by a factor of $2.5\times$, $8.7\times$ and $14.2\times$, and achieves evaluation speedups of $11.8\times$, $19.7\times$, and $54.4\times$, respectively.

The $k$-nearest neighbor ($k$NN) algorithm is a core primitive for similarity search over sensitive data, but evaluating $k$NN under fully homomorphic encryption remains expensive because it requires distance computation, encrypted ranking, and top-$k$ extraction. CKKS is attractive for this setting because it natively supports packed approximate arithmetic, yet existing CKKS-based systems such as Engorgio (USENIX Security 2025) incur high overhead when used for reranking candidate sets. We present NOMOS, an encrypted $k$NN protocol for candidate sets that targets the ranking and top-$k$ extraction bottleneck. NOMOS builds on Mazzone et al.'s matrix-based ranking method (USENIX Security 2025), but introduces a gap-amplified sign approximation that focuses precision on near-zero distance gaps, where $k$NN rank decisions are most sensitive. NOMOS integrates this primitive into a complete encrypted $k$NN pipeline, using slot-index alignment and ReLU-based top-$k$ extraction to avoid full sorting. For large databases, offline k-means preprocessing forms fixed-capacity candidate sets, allowing NOMOS to avoid global top-$k$ extraction and reduce sign-approximation calls from quadratic global growth to near-linear clustered scaling. With these techniques, NOMOS outperforms state-of-the-art encrypted ranking and top-$k$ baselines. Across the Mazzone-style ranking benchmark and candidate-set workloads compared with Engorgio, NOMOS reduces latency by nearly $8\times$ and up to $828\times$, respectively. On the real-world SIFT dataset, NOMOS achieves $100\%$ top-1 and top-8 retrieval accuracy on evaluated candidate sets, showing consistent retrieval quality on real data.

We give a randomized subexponential-time algorithm for decision Learning with Errors (LWE) in two complementary parameter regimes. For polynomial prime modulus \(q=n^{\kappa+o(1)}\) with any fixed \(\kappa>1/2\), the algorithm handles independent discrete Gaussian errors drawn from \(D_{\mathbb Z,s_e}\), with Gaussian parameter \(s_e\) satisfying \(\ln(2+s_e)=(\ln n)^{a+o(1)}\) for any fixed \(0\le a<1\). Conversely, polynomial error \(s_e=n^{\gamma+o(1)}\), for any fixed \(\gamma>0\), can be handled with a quasipolynomial prime modulus \(q=\exp\!\left((\ln n)^{1+\eta+o(1)}\right)\) for any fixed \(\eta>0\). In both regimes, for an arbitrary secret distribution, the algorithm succeeds with probability \(1-o(1)\) using \(m=n+\Theta(n/\ln\ln n)\) original samples, with expected time and space \(2^{\Theta(n/\ln\ln n)}\). Our starting point is the Wagner-style Gaussian sampler of Ducas, Engelberts, and Loyer (CRYPTO 2025). We instantiate its auxiliary extensions with random \(P\)-ary lattices whose improved smoothing bound supports the accuracy required for LWE without increasing the leading list size exponent. At the smaller Gaussian width enabled by this geometry, the basis-dependent condition of the exact sampler used in prior work is no longer available. We therefore use the statistically approximate shifted discrete Gaussian sampler of Aggarwal, Dadush, and Stephens-Davidowitz (FOCS 2015) and control its error for adaptively chosen shifts. Finally, a martingale analysis applies the Aharonov--Regev Fourier distinguisher (JACM 2005) directly to the dependent output, avoiding the loss incurred by comparison with an independent product distribution. Our analysis applies to unstructured LWE with independent uniform public vectors. In particular, it does not directly apply to ML-KEM, whose security is based on the Module-LWE problem: the algebraic dependencies arising from its module structure are not covered by our analysis.

Efficient evaluation of multivariate polynomials over finite spaces is an important problem in algebraic cryptanalysis, particularly in exhaustive-search attacks on multivariate public-key cryptosystems. Existing fast exhaustive-search techniques, including those of Bouillaguet et al. (CHES 2010), Dinur (EUROCRYPT 2021), and Furue and Takagi (PQCrypto 2023), mainly target the complete space $\mathbb F_q^n$, whereas many cryptanalytic applications require evaluation only over structured subsets. Recently, Liu et al. proposed a memory-efficient algorithm for evaluating degree-$d$ polynomials over product Hamming balls \[ B(\textbf{\textit{n}},\textbf{\textit{w}})=B(n_s,w_s)\times\cdots\times B(n_1,w_1)\subseteq\mathbb F_2^n, \] where $\sum_{i=1}^{s}n_i=n$ and $B(n_i,w_i) \subseteq \mathbb F_2^{n_i} $ denotes the set of vectors of length $n_i$ and having at most $w_i$ nonzero coordinates. In this work, we extend this structured-subset paradigm by developing a unified derivative-based framework, comprising initialization and evaluation phases, first over prime fields $\mathbb F_q$ and subsequently over arbitrary finite fields $\mathbb F_{q^\rho}$ through basis expansion. We derive two initialization methods with time complexities $\mathcal O(nrM)$ and $\mathcal O(rM^2)$, where $M\leq\min\{\binom{n+d}{d},q^n\}$ and $r=\min\{d,q-1\}$. After initialization, evaluation over $B(\textbf{\textit{n}},\textbf{\textit{w}})$ requires $\mathcal O(d|B(\textbf{\textit{n}},\textbf{\textit{w}})|)$ arithmetic operations, apart from a linear setup cost. The corresponding overall memory bounds are $\mathcal O((M+r^2)\log q+n\log(nq))$ and $\mathcal O(((d+1)M+r^2)\log q+n\log(nq))$, respectively, and are independent of the number of evaluated points.

The CKKS homomorphic encryption scheme can achieve high throughput for large batches, typically of tens of thousands of inputs, whereas DM/CGGI schemes offer low latency for a single input. In existing CKKS approaches, the multiplicative depth required for nonlinear function evaluation demands a large ciphertext modulus, which forces a large ring degree regardless of the input size. Practical applications, such as encrypted MLP inference, may require only a few hundred function evaluations at a time. For these moderate batch sizes, existing CKKS-based methods requiring large multiplicative depth incur high latency without fully benefiting from their high throughput. We present $\mathsf{SWIFT}$, a CKKS functional-bootstrapping method that reduces latency by using multiple slots to lower multiplicative depth. For input $x$, $\mathsf{SWIFT}$ packs its integer multiples $\ell x$ into unused slots. Exponential bootstrapping then generates the powers $\exp(2\pi\mathrm{i}\ell x)=\exp(2\pi\mathrm{i}x)^\ell=\alpha^\ell$ in parallel. Compared to previous approaches that compute these powers through homomorphic multiplications, $\mathsf{SWIFT}$ directly generates those powers and reduces the required multiplicative depth and ciphertext modulus, allowing a smaller ring degree and lower latency. We also introduce a trigonometric approximation method for singular functions such as $1/\sqrt{x}$, whose derivative is unbounded near zero. We observe that the previous Fourier extension method of Bian et al. (EUROCRYPT'26) can produce extremely large coefficient norms for these functions when focusing solely on reducing the polynomial degree. Instead, we solve an optimization problem to find a trigonometric polynomial that minimizes the coefficient norm while satisfying the required approximation accuracy for the target function. The resulting trigonometric polynomial can be evaluated efficiently and with numerical stability using $\mathsf{SWIFT}$. Our implementation evaluates $\mathsf{ReLU}$ on $[-1,1]$ and $1/\sqrt{x}$ on $[0.0005,1]$ with 12-bit absolute and relative precision, respectively, at ring degree $\log N=15$. For batches of 512 inputs, $\mathsf{SWIFT}$ achieves speedups of $3.94\times$ and $2.86\times$ over the corresponding CKKS baselines for $\mathsf{ReLU}$ and $1/\sqrt{x}$, respectively. Compared with latency estimates of DM/CGGI-based methods, $\mathsf{SWIFT}$ achieves lower latency for $\mathsf{8\text{-}to\text{-}8\ LUT}$ and $\mathsf{12\text{-}to\text{-}12\ LUT}$ at batch sizes as small as 32 inputs.

Migrating blockchain systems to Post-Quantum Cryptography (PQC) requires not only replacing classical primitives, but also analysing transformations that change how signatures are represented and verified. We study Falcon-PKR, a public-key-recovery variant of Falcon, motivated by Zcash-like transparent transaction workflows. Falcon-PKR replaces explicit storage of the full Falcon public key with a compact stored digest and reconstructs a candidate public key from the signature during verification. In our construction, this reduces the combined representation size of public key and signature by approximately 15%, but it also introduces a distinct security case in which verification depends on a reconstructed key derived from adversarially supplied signature data. We address this with a machine-checked EasyCrypt formalisation in the Random Oracle Model (ROM). We mechanically verify an EUF-CMA reduction showing that the security of Falcon-PKR is bounded by the security of standard Falcon together with collision resistance of a domain-separated public-key hash. The analysis therefore treats both assumptions explicitly and does not claim a proof of Falcon itself. We also machine-check correctness for honest signing under an abstract Falcon signing interface. We implement Falcon-PKR for Falcon-512 and Falcon-1024 in Python and C, and evaluate runtime and size against ECDSA and selected Post-Quantum (PQ) alternatives, exposing explicit verification and storage trade-offs. As a complementary case study, we implement and analyse an extended SECUER-based Multi-Party Computation (MPC) ceremony architecture. Together, the two case studies address both transaction-signature and ceremony-infrastructure layers of PQ blockchain migration.

Seur\'e and Suvanto (ePrint 2026/1102) recently showed that, for small-characteristic primes $p$, arithmetic over $\mathbb{F}_{p^r}$ can be homomorphically evaluated in CKKS via a technique they call \emph{spectral encoding}. Their construction is, however, restricted to small characteristic: ciphertext multiplication amplifies the error by the operator norm of the multiplied plaintext. Under the spectral encoding, a field element in $\mathbb F_{p^r}$ is encoded to a plaintext with operator norm at most $O(rp)$. The error therefore grows by a factor of $rp$ in the worst case, limiting the supported size of the characteristic prime $p$. In this work, we propose \emph{bi-spectral encoding}, which decomposes the coefficients of the plaintext polynomials used in the spectral encoding of Seur\'e and Suvanto. With a decomposition parameter $d$, a field element in $\mathbb F_{p^r}$ can be encoded to a plaintext with operator norm $O(rd{p^{1/d}})$, for a suitable choice of encoding parameters. We give a comprehensive analysis of error growth and derive a bound on error amplification under multiplication. For fields with a 256-bit prime characteristic (secp256k1) and extension degrees $1$, $2$, and $4$, we provide numerical simulations of error amplification and compute the maximum multiplication counts satisfying the decoding condition under stated error bounds. We further present a bootstrapping procedure that reduces both the size of the plaintext and its noise.

Supersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular. In this work, we initiate this research topic by giving an efficient Monte Carlo algorithm to verify if an abelian surface over $\mathbb{F}_p$ is supersingular in $O(\log p)$ with negligible failure probability, and an efficient conclusive algorithm if the order is smooth. We derive this algorithm by a careful analysis on the structure of supersingular Jacobians over $\mathbb{F}_p$. Furthermore, we derive efficient algorithms to verify if an abelian variety of any dimension is minimal or maximal, and to verify if a Jacobian of any dimension is superspecial.

In this work, we assess the security of the main signature scheme standardised by NIST, ML-DSA, and its precursor identification schemes under an extended quantum adversarial model, one in which the adversary is allowed to use quantum resources to interact with a prover/signer. We begin our analysis by developing new techniques for superposition attacks that realise a relative phase oracle for the LSBs of a classical function evaluated in a quantum computer. We then extend these techniques to enable a relative phase oracle for arbitrary bits. Leveraging these techniques, we demonstrate full key-recovery attacks on several lattice-based identification schemes, exploiting the affine structure of the output. Finally, we extend these attacks to the corresponding Fiat-Shamir signature schemes and obtain key-recovery attacks under reasonable implementation assumptions. As a result, we are able to mount full key-recovery attacks in the Q2 model against the original CRYSTALS-Dilithium scheme, as well as the corresponding NIST Standardisation Rounds 1 and 2 proposals. However modifications introduced in the scheme during the NIST process preclude our superposition attacks against the final standardised version ML-DSA. We identify and discuss the specific aspects of the algorithm's execution that affect the applicability of our techniques. Overall, our work expands the body of research on superposition attacks and represents a further step towards establishing full quantum security for cryptographic constructions.

The Internet of Things (IoT) is revolutionizing society by enabling anytime, anywhere connectivity, but its widespread deployment also makes IoT devices attractive targets for malicious activities. Over the past decade, radio-coupling based Far-field EM Side-Channel Attacks (FEM-SCAs), also known as screaming channel attacks, have emerged as a new threat to these wireless IoT edges. Unlike conventional power or near-field EM side-channel attacks, FEM-SCAs exploit the unintended coupling between digital computation and the Radio Frequency (RF) transmission chain, allowing sensitive information to be captured through radiated radio signals at long distances. Since the first screaming-channel demonstration, this field has progressed rapidly: attacks have become more efficient, DL-enabled methods have been developed, and recent studies have begun to examine more realistic wireless-protocol settings. Despite existing practical cases of remote FEM-SCA attacks, the literature remains fragmented. To systematically understand this security threat and to aid future countermeasure design, this paper presents the first systematic survey of existing screaming channel attack methodologies and case studies. We organize studies into a hierarchical framework covering leakage discovery and understanding, enhanced attack capability, attack targets and variants, and public data collections. Through a fine-grained cross-paper analysis, we compare representative works in terms of target implementation, attack distance, analysis method, profiling requirement, acquisition environment, and other factors. Building on this end-to-end review, we provide a focused discussion that distills FEM-SCA research into one central trade-off, three major limitations, and three future research roadmaps. Taken together, this survey offers a structured framework for understanding a rapidly developing far-field side-channel attack class, and provides practical guidance for evaluating its real-world threat boundaries.

We improve differential-linear distinguishers and derive key-recovery attacks on reduced-round versions of the PRFs Orthros, Gleeok, ZIP-AES, ZIP-GIFT-64, and ZIP-GIFT-128. Relative to previous differential-linear analyses, we extend the reported coverage for Orthros from 7 to 9 rounds and for Gleeok-128 from 4 to 5 rounds. For Orthros and Gleeok-128, we obtain estimated correlation magnitudes \(2^{-61.40}\) and \(2^{-31.71}\), respectively. We also obtain distinguishers for 6-round Gleeok-256, \((3,3)\)-round ZIP-AES, \((7,7)\)-round ZIP-GIFT-64, and \((10,10)\)-round ZIP-GIFT-128. For key recovery, we give a \((3,3)\)-round differential-linear attack on ZIP-AES requiring approximately \(2^{122.42}\) chosen plaintexts and \(2^{122.88}\) ZIP-AES evaluations. Our \((10,10)\)-round ZIP-GIFT-128 attack has estimated data, time, and memory complexities of \(2^{93}\) chosen plaintexts, \(2^{117}\) full PRF evaluations, and \(2^{25.01}\) bits. We further obtain weak-key attacks on 9-round Orthros, 5-round Gleeok-128, and 6-round Gleeok-256, with key-space coverages of \(2^{-2.87}\), \(2^{-3}\), and \(2^{-1}\), respectively. The Orthros key-recovery result reaches one round beyond the previous DL key-recovery coverage. These results use automated differential and linear trail search together with existing round-based correlation estimation. We enforce the compatibility constraints between branches and select input-side extensions that make their prescribed differences jointly reachable.

FESTA is an isogeny-based trapdoor function proposed as a high-performance trapdoor function in isogeny-based cryptography. Its core design principles have inspired a number of related constructions, collectively referred to as FESTA variants. The MOXZ attack is an adaptive attack that exploits malicious ciphertexts together with access to a checking oracle, aiming to compromise FESTA and its variants. This attack applies to FESTA variants whose secret keys are derived from isogenies of known degree; however, it does not extend to variants employing masked-degree isogenies. In this work, we present a novel adaptive attack that generalizes the MOXZ attack. Our attack successfully targets several FESTA variants even when their secret keys are isogenies of masked degree. We also identify POKE-4D as an exception for which our attack does not appear to be applicable.

TLA$^+$ (Temporal Logic of Actions) is a formal specification language well-suited for distributed systems. However, writing proper TLA$^+$ scripts requires high domain expertise. When it comes to modeling Byzantine behaviors for Byzantine fault-tolerant consensus protocols, the simulation of malicious behavior is a fundamental challenge: overly simplified modeling misses critical vulnerabilities, and verbose modeling leads to state-space explosion. In this paper, we present TLAssist, a large language model (LLM)-assisted tool for semi-automated TLA$^+$ generation tailored for Byzantine reliable broadcast (RBC) protocols. We provide a highly structured workflow and domain-specific data format to improve the quality of LLM prompts. Using five RBC protocols as case studies, we have some interesting findings. First, the specification generated by TLAssist outperforms many open-source TLA$^+$ scripts we are aware of, including those written by domain experts. Second, TLAssist can assist domain experts in identifying deep design flaws. Notably, our case study on the (2,3,4)-Optimistic RBC (a CCS'25 distinguished paper) captures a subtle issue that causes the violation of the totality property. Finally, TLAssist is useful for non-experts. Namely, we show that by revising the protocols slightly, the generated error traces effectively show complex corner cases that can facilitate understanding of the design.

The Institute of Commercial Cryptography Standards (ICCS) launched the Next-generation Commercial Cryptographic Algorithms Program (NGCC) and invited worldwide comments on draft submission requirements and evaluation criteria for cryptographic hash algorithms. Our analysis of seven submitted hash functions gives the following results: - Message differences that cancel in every key injection give explicit collisions for all four fixed-output variants of \textbf{MoFang} and both XOF variants at every finite output length. - Two distinct states of \textbf{Neulaser} become equal after one update, giving collisions for all three variants with the initialization used by the v2 reference and optimized implementations. - An invariant subspace of \textbf{CHIME-512} permits collision search using at most \(2^{64}\) hash evaluations when shifts act separately on 64-bit words, as in both submitted implementations. - \textbf{CHAMP}'s determinant constraint gives collision searches using at most \(2^{192}\) and \(2^{384}\) hash evaluations for its 512- and 1024-bit variants, respectively. - We exhibit explicit free-start collisions for all three \textbf{QSH} variants. In the semi-free-start setting, both messages and every tree node share one chosen complete reset. We prove upper bounds of \(2^{64},2^{128},2^{128}\) compression evaluations for finding collisions with 512-, 768-, and 1024-bit digests, respectively, plus constant preparation and finalization costs. - In both versions of \textbf{WChain}, the message expansion preserves invariant sets and admits sequences of expanded blocks with periods one, three, and six over all prescribed steps. - On a set of 256 message blocks, \textbf{Cuishen}'s message expansion acts as a cyclic shift of eight binary coordinates throughout all 64 rounds. With the same initial chaining register and counter, these blocks give XOR differences between round keys with periods dividing eight. The stated evaluation budgets for \textbf{CHIME-512} and \textbf{CHAMP} give success probabilities greater than \(0.39\).

Incrementally verifiable computation (IVC) [Valiant, TCC '08] allows one to iteratively prove that a configuration $x_0$ reaches a configuration $x_T$ via $T$ repeated applications of a (possibly non-deterministic) machine $\mathcal{M}$. An IVC scheme is fully succinct if the proof size is independent of both $T$ and the size of the intermediate configurations. In this work, we develop a new indistinguishability obfuscation ($i\mathcal{O}$)-based approach to IVC that avoids the extraction-based security analyses central to prior constructions. Assuming subexponential hardness of $i\mathcal{O}$ and one-way functions, we construct an adaptively sound fully succinct IVC scheme for deterministic computations. This yields the first IVC for deterministic computations that does not rely on algebraic assumptions. Under the same assumptions, we further obtain a fully succinct two-hop IVC scheme for $\mathsf{NP}$ with non-adaptive soundness, allowing one to prove that $x_0$ reaches $x_2$ via an intermediate configuration $x_1$. This is the first IVC scheme for $\mathsf{NP}$ achieving full succinctness. Our constructions are based on a new connection between IVC and secret sharing for $s$-$t$ connectivity in graphs.

Non-local search-to-decision asks whether the difficulty of two non-communicating (non-local) parties both predicting $x$ given a bipartite state (that possibly depends on $x$) implies the difficulty of non-local parties both predicting the inner product $\langle r,x\rangle$, for a uniformly random $r$. This problem and its variants have been extensively studied and are motivated by applications to unclonable cryptographic primitives such as unclonable encryption and copy-protection. We study the identical-challenge setting, in which both parties receive the same uniformly random vector $r$, in contrast to the independently sampled challenges considered in prior works. We demonstrate positive results for the cases when $x$ and $r$ are vectors over $\mathbb{F}_2$ and over large finite fields. As a consequence, we obtain a conceptually different proof of indistinguishability-secure unclonable encryption.

The Internet of Things (IoT) comprises a vast array of interconnected devices that rely heavily on wireless communication to enable applications in domains such as healthcare, transportation, and smart environments. However, intrinsic vulnerabilities in wireless networks, such as susceptibility to eavesdropping, impersonation, and message tampering, require the development of robust yet lightweight authentication mechanisms. To address these concerns, we introduce AEBAP, an efficient authentication protocol based on elliptic curve cryptography (ECC), specifically designed for secure communication in resource-constrained IoT environments. AEBAP ensures mutual authentication, data integrity, and resilience against both passive and active attacks by leveraging the cryptographic strength and computational efficiency of ECC. We evaluate the protocol’s performance through experimental implementation and analyze its security using both informal reasoning and formal verification tools, including Scyther and ProVerif. The results demonstrate that AEBAP achieves strong security guarantees with minimal computational and communication overhead, making it a promising solution for securing next-generation wireless IoT systems

Setting concrete parameters for group action based cryptographic protocols is notoriously difficult due to the incomplete understanding of the concrete efficiency of Kuperberg's subexponential quantum attack. Estimates for the CSIDH group action do exist in the literature, but they do not easily translate into meaningful estimates for the many recent and far more efficient alternative group actions. In this paper, we implement the recent qt-Pegasis group action framework as a (simulated) quantum circuit, allowing for concrete estimation of its efficiency and Kuperberg's attack. Our results suggest that using a 2048-bit base field in qt-Pegasis offers reasonable quantum security, while a 4096-bit base field is required to reach NIST security level 1.

We describe a Las Vegas algorithm for the principal ideal problem in matrix rings $M_g(O)$ for $g \geq 2$, over maximal orders $O$ in the rational quaternion algebra $B_{p, \infty}$ ramified at $\infty$ and a prime number $p$. Under plausible heuristic assumptions, the method has expected polynomial runtime. An implementation in SageMath shows that it runs very efficiently in practice, with compact output. Our main auxiliary result is a method for finding endomorphisms of superspecial abelian varieties (i.e., powers of supersingular elliptic curves) with a prescribed kernel.

In a multi-instance problem, the adversary is given $n$ independent problem instances and succeeds if it solves at least $k$ of them. We study the generic hardness of a broad class of multi-instance problems over prime-order groups, including multi-instance Computational Diffie-Hellman (CDH), Square Diffie-Hellman (SDH), Inverse Diffie-Hellman (IDH), and Linear Kernel Diffie-Hellman (LKDH). As expected, we show that, in generic groups, solving multi-instance CDH and SDH is as hard as solving $k$ independent discrete logarithm instances. In contrast, although the single-instance versions of CDH and IDH are known to be equivalent, we establish generic upper and lower bounds showing that multi-instance IDH (and LKDH) can be significantly easier to solve than multi-instance CDH in certain parameter regimes. All problems, however, offer $1/2(\log(p)+\log(k))$ bits of security. Our lower-bound techniques extend Yun's information-theoretic hyperplane query model (EUROCRYPT 2015). At the core of our approach lies an inductive argument showing that, in order to establish a generic-group lower bound, it suffices to bound the adversary's "zero-hyperplane-query" advantage in the hyperplane query model. For the multi-instance problems considered in this work, we derive such bounds using techniques from algebraic geometry. More precisely, we analyze the Krull dimension of suitable algebraic varieties, either by explicitly computing Gröbner bases or by upper bounding the number of algebraically independent elements in the associated coordinate rings.

Batch decryption allows an authority to release a short key that enables public decryption of a selected batch of ciphertexts. Motivated by encrypted mempools, we study this capability through two constructions with different authorization semantics and assumptions. First, we provide a simple and compact epochless construction in an RSA group based on Fiat's Batch RSA [CRYPTO'89]. Its batch-decryption hint is just one group element, and its keys and ciphertexts have size independent of the batch size, with no batch bound fixed at setup. We prove adaptive security under the strong RSA assumption in the random-oracle model. The scheme permits repeated releases for overlapping batches, with each release authorizing decryption of the selected ciphertexts. Second, we give an adaptively secure generic construction of identity-based encryption with batch decryption in the epoch-based model, which permits at most one batch-key query for the challenge epoch. The construction combines deferred encryption via garbled circuits, non-inclusion secure registration-based encryption, and weak receiver non-committing IBE. We construct the latter primitive from ordinary IBE and pseudorandom functions, obtaining an instantiation of the epoch-based construction from the computational Diffie--Hellman assumption.

Oblivious Transfer (OT) is a fundamental building block for secure computation, in which a sender holds two messages and a receiver learns exactly one of them, without revealing which one was chosen and without learning the other. While generic constructions for Universally Composable (UC) OT exist, instantiating them from post-quantum assumptions remains challenging, particularly under adaptive corruption. In this work, we present the first adaptively UC-secure OT protocol based on Group Actions, specifically assuming weakly pseudorandom Effective Group Actions (EGA) like CSIDH. We adhere to the framework of [BC15], which derives an adaptively UC-secure OT protocol from SPHF-friendly extractable and equivocable (E²) commitment schemes. The central challenge in instantiating this construction from group actions is the lack of SPHF-friendly IND-CCA encryption. Classical CCA transformations such as Fujisaki-Okamoto destroy the algebraic structure required for building SPHFs over ciphertexts, while known group action-based schemes offer no native mechanism to prove ciphertext validity. To overcome this obstacle, we construct from group actions an IND-CCA encryption scheme with enough algebraic structure to efficiently recognize valid ciphertexts. Our contributions are threefold: (1) a verifiable chameleon hash function with perfect soundness in the standard model, (2) an SPHF-friendly, publicly verifiable IND-CCA encryption scheme in the random oracle model, and (3) we combine these to build an SPHF-friendly E² commitment scheme and derive a fully adaptively secure OT protocol in the UC framework. This is the first construction of its kind under group action assumptions, enabling post-quantum secure OT with adaptive security guarantees. These building blocks may also be of independent interest e.g., to obtain digital signatures, non-malleable commitment schemes, or verifiable encryption.

The Chinese NGCC post-quantum competition received a family of lattice KEMs whose decryption failure rates (DFRs) are certified by their designers with models that differ in detail. We recompute the failure probability of the first-round lattice KEMs whose claimed DFR, or a simple recomputation of it, lies near or below the nominal level, and we estimate the offline search for weak ciphertexts under a cap of $2^{64}$ or $2^{80}$ decapsulation queries. Three distinct mechanisms are relevant. (i)~\emph{Correlated decoding blocks.} DTRU decodes 16-coefficient DoubleE$_8$ blocks; in the tricyclotomic ring $\mathbb{Z}_q[x]/(x^n-x^{n/2}+1)$ and the LPPNF ring, the two octets of a block are ring-paired and the repetition code places the same bit on both. Our covariance-aware estimates raise the DFR of six of the seven sets by roughly $50$--$110$ bits. Their estimated uncapped first-failure costs are $2^{85}$--$2^{111}$ decapsulations. Under a fitted ciphertext-tail model, DTRU-648, DTRU-768, and DTRU-Prime fit within $2^{64}$ expected queries after $2^{22}$--$2^{26}$ estimated offline encapsulations. (ii)~\emph{Omitted compression noise.} Cheetah compresses its public key and both ciphertext components. Section~2.2 of the specification omits the public-key term $\langle e_b,r\rangle$, while the $v$-compression error can be treated as a known, ciphertext-dependent shift. Under the coefficient-independence model, exponentially tilted one-dimensional FFTs give DFR estimates of $2^{-79.1}$ and $2^{-51.8}$ for Cheetah128 and Cheetah256, rather than the claimed $2^{-129}$ and $2^{-176}$. Their expected random-query waiting times are below $2^{80}$. We check the noise model at observable rates on a scaled-down instance and against full-size shallow-tail samples. (iii)~\emph{Bounded noise in two-dimensional codes.} Rudraksh2 and Scabbard decode coefficient pairs with B2-Minal codes and already evaluate their joint distribution by two-dimensional FFT. We rederive the two-dimensional atoms and evaluate one-dimensional projections onto failure radii of the real decoder. The resulting projected-tail estimates are $2^{-103.9}$ for Rudraksh2-128-I and $2^{-102.1}$ for Scabbard-128, a few bits below the claimed $2^{-100}$ and $2^{-99}$. Under a $2^{80}$ query cap, the estimated classical totals are $2^{112}$ and $2^{188}$, respectively. No attack described here recovers a key. Under the first-failure DFR metric, several estimated costs lie below their nominal levels; the formal far-tail figures remain subject to the modelling, extrapolation, and geometric limitations stated in the paper.

The Learning With Errors (LWE) problem is a fundamental assumption in post-quantum cryptography. Regev established a quantum reduction from LWE to the Dihedral Coset Problem (DCP). Later, Brakerski et al. introduced the Extrapolated Dihedral Coset Problem (EDCP), proving its equivalence to LWE. However, unlike DCP, EDCP no longer admits a coset structure. This limits the direct application of techniques for hidden subgroup problems. In this work, we introduce the Cyclotomic Coset Problem (CCP), a cyclotomic generalization of DCP that preserves an exact hidden-subgroup structure. Let $\zeta_p$ be a primitive $p$-th root of unity, let $\pi=\zeta_p-1$, and write $q=p^t$ and $L=t(p-1)$. We work over $R_q=\mathbb Z_q[\zeta_p] \cong \mathbb Z[\zeta_p]/(\pi^L)$, where the isomorphism follows from the total ramification identity $(p)=(\pi)^{p-1}$.We exploit the resulting $\pi$-adic ideal chain to construct a quantum sieve that successively reduces phase states modulo $\pi^{L},\pi^{L-1},\ldots,\pi$. For every fixed prime $p$ and modulus $q=p^t$, our algorithm solves the CCP in time and sample complexity $2^{O_p(\log n\log q)}$, using polynomial quantum space. The sieve also applies to uniform EDCP and Gaussian $S\ket{\text{LWE}}$, yielding quasi-polynomial time algorithms for all the above problems when $q=\text{poly}(n)$. This extends the power-of-two EDCP sieve of Bai et al. (CRYPTO 2025) to a cyclotomic setting. However, we emphasize that our result does not, by itself, yield a quasi-polynomial-time algorithm for standard LWE, because the currently known reduction produces only a limited number of approximate CCP states.

We present SUCRE, a novel countermeasure designed to physically protect the rejection sampling step of ML-DSA, one of the post-quantum signature schemes standardized by NIST. At the core of SUCRE is a masking gadget that securely unmasks a vector while simultaneously applying a random permutation of its coefficients. This lightweight mechanism preserves the vector’s infinity norm, enabling rejection sampling to proceed as usual without requiring any complex mask conversions. We formally prove that a $d$-probing adversary can learn at most some permuted rejected values---information which, we show, should remain insufficient to endanger the security of the signature scheme. This security argument relies on a new variant of the Module Learning with Rounding (MLWR) assumption, for which we provide a dedicated concrete security analysis to assess its hardness relative to the standard MLWR assumption. Our implementation of SUCRE achieves a significant performance improvement over previous masked non-bitsliced implementations of rejection sampling---delivering four to six times faster execution than Coron et al. (TCHES 2024)---albeit at the cost of increased memory usage. Since the rejection step accounts for approximately 25% of the total runtime in masked ML-DSA implementations, and given the expected adoption of ML-DSA on embedded platforms, this speedup could significantly enhance efficiency in real-world applications.

Folding schemes combine a batch of relation instances into one accumulator. For quadratic relations, applying the fold directly creates a mixed term for every pair of inputs. We present CauchyFold, a lattice protocol that folds one accumulator with \(k\) fresh quadratic instances without enumerating these pairwise terms. The companion work [WX26] uses Cauchy folding coefficients to represent the mixed contribution through a vector-valued polynomial of degree below \(k\). We give two algorithms that compute its coefficients with quasi-linear arithmetic in \(k\) for fixed relation dimensions. The protocol commits this polynomial before the folding challenge. Since the folding coefficients need not be short integers, it computes the fold over an extension field and canonically re-encodes the result as bits. This preserves the accumulator’s commitment layout and honest opening bound. For classical resettable provers, we give explicit extraction-error and expected-time bounds for a folding node with a fixed-depth reduction chain. It recovers valid source openings or a short nonzero vector in the kernel of a commitment matrix. A compiled profile at \(k=1024\) uses 162.67 KiB of no-retry interactive communication, excluding incoming commitments and the CRS.

Syndrome decoding (SD), together with its regular-noise variant (RSD), is fundamental to many cryptographic primitives; in the generator formulation used in cryptography, it is closely related to learning parity with noise (LPN). While recent proposals extend these problems to larger fields, the concrete security of SD over large fields remains comparatively less understood. This gap leaves room for more effective attacks against SD-based primitives over large fields. In this paper, we present an improved algorithm for solving SD over large fields. Our method modifies Prange's information-set decoding algorithm by iteratively applying Gaussian elimination to reduced-size matrices rather than to the full-size matrix. We call this the ``Reduce and Prange (RP)" algorithm and demonstrate its effectiveness for both SD and its variant with regular noise over large finite fields (e.g., $\mathbb{F}_{2^{128}}$). On the comparison rows of our numerical section, RP lowers the SD estimate by up to $6$ bits, and on the 128-bit recommended SD rows the drop is up to $7$ bits, relative to Liu et al. (Eurocrypt'24). For SD with regular noise, regular-RP gives the lowest listed estimate on the small and medium tested parameter sets, improving on the best previously listed estimate by up to $15$ bits; on the largest tested sets the algebraic estimate of Briaud and {\O}ygarden (Eurocrypt'23) remains lower.

Inner Product Arguments (IPA) [BCC+16,BBB+17] are a family of proof systems with $O(\log n)$ sized proofs, $O(n)$ time verifiers, and transparent setup. Bootle, Chiesa and Sotiraki [BCS21] observed that an IPA can be viewed as a sumcheck protocol [LFKN92] where the summed polynomial is allowed to have coefficients in a group rather than a field. We leverage this viewpoint to improve the performance of multi-linear polynomial commitments based on IPA. Specifically, - We introduce a simplified variant of Halo-style accumulation that works for multilinear evaluation claims, rather than only univariate ones as in [BGH19,BCMS20]. - We show that the size $n$ MSM the IPA verifier performs can be replaced by a ``group variant'' of $\mathsf{basefold}$[ZCF23]. This reduces the verifier complexity from $O(n)$ to $O_{\lambda}(\log^2 n)$ time at the expense of an additional $4n$ scalar multiplications for the IPA prover.

MAYO is a post-quantum signature scheme based on UOV that uses the whipping transformation to achieve more compact public keys and retain efficient signing. We present the first structural forgery attack that exploits the geometry of the resulting multivariate quadratic (MQ) maps. Our starting point is the observation that whipping amplifies polar cancellations in the underlying MQ map, producing subspaces with low-dimensional quadratic and polar images. We combine this geometric insight with the Pseudo-Oil Attack (ASIACRYPT 2026) and a descent to the binary field into a structural forgery algorithm. Independently, we introduce a multi-target reduction for homogeneous MQ maps. Projecting onto a quotient of the codomain reduces the number of equations, and homogeneity allows suitable solutions to be rescaled to the original targets. Concretely, the combination of our forgery attacks lowers the estimated bit security of the Security Level I and III parameter sets of MAYO Round 2 by roughly 18 and 16 bits, respectively. In particular, the Level I parameter set falls 15 bits short of its required security level. For the recently released MAYO Round 3 parameters, our attack still reduces the estimated security by roughly 6, 4 and 2 bits for the new MAYO1, MAYO2 and MAYO3 respectively, bringing MAYO2 below the required security by 3 bits.

Decentralised proof of personhood, cryptographically binding a digital identity to a unique living human without a trusted central authority, is a foundational problem in permissionless networks. We present a novel protocol, Secure-GYID (S-GYID), resilient to Identity Theft Attack (i.e., adversarial authorities substitute a victim's biometric fingerprint under a malicious public key) and Ghost Key Attack (i.e., colluding authorities fabricate a registration for a non-existent user). Our protocol closes both vulnerabilities by replacing raw biometric transmission with an encryption-based digital fingerprint derivation $F = E(pk_u, P_u)$ computed under a one-way, chosen-plaintext-secure, deterministic scheme, so that no authority can substitute or forge a binding pair without knowledge of the user's secret key. S-GYID further introduces a three-stratum generational authority hierarchy with bounded tenure and VRF-based session selection to limit long-term collusion structurally. We prove Identity Theft Resistance, Biometric Detectability, and Ghost Key Resistance under standard cryptographic assumptions, and provide a hypergeometric session-capture analysis that establishes concrete parameter design rules for both the key activation and authority promotion thresholds.

We give an elementary construction of large Reed-Solomon lists on multiplicative subgroups. For every fixed rational rate $\rho\in(0,1)$, suitable sequences of lengths give lists of size at least $2^{(2-o(1))H(\rho)/\eta}$ at agreement fraction $\rho+\eta$ as $\eta\to0$, where $H$ is binary entropy. This doubles the leading entropy exponent of the antipodal lower bound stated by Arnon, Boneh, and Fenzi, building on the construction of Krachun, Kazanin, and Haböck. If the reduced denominator of $\rho$ is a power of two, the lengths can also be chosen as powers of two. The construction lifts subsets with a prescribed product from a quotient subgroup of size $s$. This fixes a coefficient while losing at most a factor $s$ in the number of subsets. More precisely, for $n=hs$, $h\ge2$, and $1\le m\le s-2$, a code of dimension $\kappa=mh$ on a subgroup of order $n$ has a word with at least $\binom{s-1}{m+1}/s$ codewords at agreement $\kappa+2h-1$. This holds over every field containing the required roots of unity. Consequently, the exponent constant $c_2$ in the universal list-size conjecture of the S-two whitepaper must satisfy $c_2\ge2$.

The Fiat--Shamir transformation is a fundamental paradigm in cryptography for compiling interactive public-coin protocols into non-interactive arguments. While this transformation has been extensively studied for public-coin protocols, the setting of private-coin protocols, where the verifier's messages depend on secret randomness, remains largely unexplored. To date, there are no candidate transformations for private-coin protocols, neither in the standard model nor in idealized settings. In this work, we present a generic transformation that compiles any 3-message private-coin interactive proof into a non-interactive argument in the standard model, while preserving zero-knowledge. Our construction relies on sub-exponentially secure indistinguishability obfuscation, pseudorandom functions, and input-hiding obfuscation (IHO). As a corollary, this rules out the existence of 3-message weak zero-knowledge proofs with small enough soundness error. We complement this positive result by showing that the reliance on IHO is inherent: any secure Fiat--Shamir transformation for general private-coin protocols necessarily implies the existence of IHO. Finally, we rule out Fiat--Shamir transformations for multi-round private-coin protocols. Specifically, assuming the existence of collision-resistant hash functions, we prove that no such transformation exists in the multi-round setting.

Non-uniform security allows an adversary to receive bounded advice about an oracle before attempting a fresh challenge. This captures the most realistic attacks and has already been studied extensively in prior work. In this work, we introduce an operator-norm approach for non-uniform security in the quantum random oracle and random permutation models. This new approach yields a unified reduction for both search success probability and distinguishing advantage. Previously, the reduction only worked with success probability even in the decision games, yielding a worse bound. Our framework enables tight bounds for Yao's box, both with and without salting, and improved bounds for pseudorandom generators. We also prove an optimal generic salting theorem for decision games. By defining a property of a game, which separates the contributions of the existing queries in the offline stage and subsequent online queries, we obtain stronger bounds for specific salted constructions. These include salted permutation inversion, tight up to logarithmic factors, and salted random-function inversion, tight up to logarithmic factors and the gap already present in classical function inversion.

Determining the precise parts of the key that need to be guessed in a key-recovery attack is fundamental for judging its cost: if the same attack can be executed by guessing less key material, then the cipher's resistance against this attack is overestimated. Although a multitude of prior works provide upper bounds on the key material required, and although these bounds might be tight in some special cases, a precise evaluation of the required key material and the tightness of these bounds is still missing. We remedy this by enumerating linear trails to iteratively compute the affine hull of the support of the Fourier transform of the key-recovery map. This leads to a generic and practical algorithm that identifies the smallest subspace of key material to be guessed. This algorithm is ready to be used in many different attacks and for a large variety of cipher structures. We demonstrate its impact by showcasing improvements on several published integral, linear, differential-linear, and zero-correlation attacks on the block ciphers PRESENT, SIMON, SKINNY, and GIFT.

POKÉ, introduced by Basso and Maino, is one of the most efficient isogeny-based public-key encryption schemes. The generic parallel-encryption approach yields a $(t,n)$-threshold variant by running $n$ independent POKÉ instances and secret-sharing the message, but this multiplies the public-key and ciphertext sizes by roughly $n$. We present S-TPOKÉ, a POKÉ-based $(t,n)$-threshold construction for every $1\le t\le n$, and Ch-TPOKÉ, an $(n,n)$ variant that arranges the parties' secret isogenies differently. Both schemes avoid repeating part of the isogeny computation that appears in every independent POKÉ instance. Compared with the trivial construction, they reduce the number of degree-$3^{b}$ isogenies computed during encryption from $2n$ to $n+1$ and reduce the ciphertext size by about a factor of two when $n$ is large. The two schemes differ in how the parties' secret isogenies are arranged. S-TPOKÉ is our main construction: the dealer samples $n$ independent secret isogenies, while encryption samples one sender-side secret isogeny and shares it across the parties. Ch-TPOKÉ instead arranges the parties' secret isogenies into a chain. For S-TPOKÉ, we prove SIM-CPA security under static corruption in the random oracle model from the $(k,n)$-S-C-POKE assumptions for all $1\le k\le t$, which extend C-POKE to the threshold setting. For Ch-TPOKÉ, we prove only SIM-CPA security under static maximal corruption from the $(j,n)$-Ch-D-POKE assumptions for all $j\in\{1,\ldots,n\}$, which extend D-POKE to a chain-based threshold setting. This guarantee is strictly weaker than SIM-CPA security under static corruption. We also give asymptotic parameter choices targeting $\lambda$-bit security and derive closed-form expressions for the public-key, ciphertext, and partial-decryption sizes in terms of $\lambda$ and $n$.

VOLE-in-the-Head (VOLEitH) is one of the most promising frameworks to design post-quantum digital signatures based on symmetric primitives. However, all existing symmetric primitives do not capture the specialized characteristics of the VOLEitH framework and are not VOLEitH-friendly, leaving room for improving the efficiency of VOLEitH-based signatures. In this paper, we propose a VOLEitH-friendly symmetric primitive called Lynx, which is optimal in terms of the number of required VOLE correlations that directly determines the efficiency of VOLEitH-based signature schemes. In particular, Lynx adopts a multi-branch structure featuring a new truncation function: (a)~nonlinear components are set to minimize the witness length and polynomial degree, as well as the number of finite-field multiplications; (b)~linear layers are strategically interleaved to strengthen security. The security of Lynx is rigorously validated by covering all current attacks in the presence of both classical and quantum adversaries. Built upon Lynx, we design a post-quantum signature scheme, Lynxer, in the VOLEitH framework, which is shorter and faster than all known post-quantum signature schemes from symmetric primitives. According to our experimental results, compared to the state-of-the-art symmetric-based signature schemes in the same setting, i.e., Rainier (CCS'22), AIMer (CCS'23) and FAESTv2 (Crypto'25), our signature scheme Lynxer reduces the ``public-key size + signature size'' by 25%~51%, and improves the signing (resp., verification) time up to 90.5% (resp., 89.9%).

Homomorphic encryption (HE) enables privacy-preserving inference by allowing neural networks to operate directly on encrypted data, but its computational cost remains a major obstacle to deploying large language models in practice. In particular, CKKS-based inference consumes ciphertext modulus through homomorphic multiplications and requires costly bootstrapping when the available modulus is exhausted. In this work, we propose an error-propagation-aware scale design for efficient CKKS-based privacy-preserving LLM inference. We characterize the numerical errors introduced by individual homomorphic operations and analyze how they propagate through subsequent Transformer computations. Based on this analysis, we quantify the contribution of each local error to the final inference error and determine the precision required for individual operations. We then allocate operation-wise scales and modulus levels accordingly, avoiding unnecessarily conservative precision while maintaining the target inference accuracy. As a result, more computation can be performed within a given modulus chain, reducing the frequency of costly bootstrapping operations and improving overall inference efficiency. Compared with THOR, our method reduces modulus consumption by 30.0% and the number of bootstrapping operations by 83.6% for the standard Transformer. For the HE-friendly Transformer, our method reduces modulus consumption by 33.6% and the number of bootstrapping operations by 80% compared with PowerFormer.

One of the most important fundamental elements in guaranteeing data security is data access management. The two primary security components of data access control are typically authorisation and authentication. Data access control is the selective restriction of data access. First, we present an effective data access control mechanism for medical devices that are implanted in this study. Through a signcryption method with proxy reencryption (DAC-PRE), the protocol guarantees anonymous data access control and supports the user’s anonymity behaviour. The security is proven in oracle model. Our experimental analysis shows the proposed protocol has low computational cost.

The XOR of two or more independent random permutations (XoP) is the prototypical pseudorandom function built from permutations achieving the security beyond the birthday bound. The security of the XoP construction is now well established against classical adversaries, however, its security against quantum adversaries that query the construction in superposition has remained widely open. We prove that the XOR of $r\ge 2$ independent random permutations over $\{0,1\}^n$ is indistinguishable from a random function by any $q$-query quantum algorithm with advantage \[ O\left(\min\left\{ \frac{q^3}{2^{rn}},\frac{q^{1.5}}{2^{(r-0.5)n}},\frac{1}{2^{(r-1.5)n}} \right\} \right) \] for all $q\le 2^n/57774$, where the hidden factors depend only on $r$. In particular, the XoP construction remains secure throughout the entire query range, far beyond the $2^{n/3}$ quantum birthday bound due to the quantum collision finding attack. To our knowledge, this is the first construction from permutations that achieves the quantum version of the beyond birthday bound security. We present several heuristic attacks suggesting the tightness of our bounds. For $q\lesssim 2^{n/2}$, the quantum collision finding-based attacks heuristically give the advantage $\Omega(q^3/2^{rn})$ and $\Omega(q^{1.5}/2^{(r-0.5)n})$, and for $q\approx 2^n$, the heuristic collision counting-based attack appears to have the advantage about $2^{-(r-1.5)n}$. We use a Fourier-analytic variant of the polynomial method on the space of functions: the distinguishing advantage of any $q$-query quantum algorithm is controlled by the Fourier components of degree at most $2q$, which is controlled by $2q$ input-output data of the construction. Most components are bounded as a $\ell_2$ norm of the Fourier weights of the XOR of permutations, which gives the bound $2^{-(r-3/2)n}$. For the bound $q^3/2^{rn}$, few low-degree components are too large. We reinterpret these low-degree components as (sums of) distinguishing advantages of the other problems. For example, the degree-2 and degree-4 terms are interpreted as the advantages against random functions with and without \emph{planted collisions}, which in turn are bounded using Zhandry's small-range distributions. Finally, the $q^{1.5}/2^{(r-0.5)n}$ bound can be proven using another bound for the planted collisions. This new bound is proven using the compressed oracle by interpreting the advantage as the other bound about random functions. It also gives a new bound for the small-range indistinguishability for (ironically) large ranges, which is of independent interest.

Threshold signatures for distributed systems require compact public keys and signatures to reduce communication overhead by avoiding packet fragmentation. However, with existing post-quantum threshold signatures, either the public key or the signature does not fit within a single unfragmented network packet. In this work, we present SPRITZ, an isogeny-based post-quantum threshold signature scheme whose public keys and signatures both fit within a single unfragmented network packet at every NIST security level. To the best of our knowledge, SPRITZ is the first post-quantum threshold signature scheme to do so with an arbitrary number of parties. While isogeny-based signatures such as SQIsign and PRISM are known for exceptionally compact public keys and signatures, their algebraic structure makes thresholdization for an arbitrary number of parties highly nontrivial. We address this challenge by introducing a novel graph-based threshold access structure tailored to the isogeny setting. For security against known attacks, we employ a non-interactive zero-knowledge (NIZK) protocol for the verification of isogeny push-forward procedures. At NIST security levels I/III/V, SPRITZ achieves public keys of 129/193/257 bytes and signatures of 223/335/447 bytes, respectively. Among the schemes submitted to the NIST MPTC (Multi-Party Threshold Cryptography) previews phase 2 whose public keys fit within a single unfragmented network packet, SPRITZ achieves the smallest signature size. We also provide a proof-of-concept implementation of SPRITZ.

The Fujisaki-Okamoto (FO) transform makes ML-KEM IND-CCA secure by re-encrypting the decrypted message and returning an implicit-rejection value on any mismatch. Deployed implementations of ML-KEM and its predecessor Kyber have realized this check incorrectly: a skipped conditional move (pqc_kyber/cosmian_kyber, RUSTSEC-2026-0290/-0288) and truncated ciphertext comparisons (wolfSSL, CVE-2026-10097 and CVE-2026-6330). We ask how much of the check must be broken before the key is recoverable, and show that one unverified ciphertext coordinate suffices. For a valid ciphertext the adversary knows the encryption randomness, so sweeping an unverified v-coordinate over the compression grid measures the decryption noise there, a known short-coefficient linear form in the secret; one bounded-error observation per message, solved by least squares, recovers the key. Under a regularity assumption we prove that O(kn log kn) observations identify the key, and we demonstrate full recovery from a single unverified coordinate on all three parameter sets in a few times 10⁵ decapsulation queries against a simulated incomplete comparison built on the kyber-py implementation, with ML-KEM-1024 cheapest owing to its finer compression grid. Sessions fall inversely with the number of unverified coordinates but query cost does not: one unverified coordinate costs what a leaked tail of fifty does. The skipped conditional move yields a complete plaintext-checking oracle and Θ(kn) queries.

We prove that $4r + 4$ rounds of an AES variant with independent and uniform random round keys are $\varepsilon$-close to pairwise independent with $\varepsilon = 2^{14}\, 2^{-39r}$. This result follows from a near-optimal bound for a two-norm version of pairwise independence for the Shark construction, depending on the third singular value of the difference-distribution table of the S-boxes. Our analysis combines insights from cryptanalysis — in particular, truncated differentials — and linear algebra over the reals.

A $(T,N)$-threshold signature scheme distributes a signing key among $N$ participants so that any $T$ participants can jointly generate a valid signature, while fewer than $T$ cannot. In this work, we first introduce a threshold one-time signature scheme with \emph{identifiable abort} based on a variant of Lamport one-time signature and Shamir secret sharing, enabling authorized participants to jointly reconstruct signatures from partial signatures. We then extend the scheme to support multiple messages using multi-layer Merkle trees. One-time signatures introduce specific coordination challenges: participants must agree on both the message and the one-time key index to avoid unsafe key reuse. We address this using a bulletin-board mechanism for consensus. Under this framework, our construction produces signatures with one message from the bulletin board to each signer and one response message from each signer, while the bulletin board may require additional communication to reach agreement. With a simple majority-vote bulletin board, the scheme signs in four rounds. Subject to this coordination constraint, the construction inherits the guarantees of the underlying threshold framework: Universal Composability (UC) unforgeability with identifiable abort, non-UC robustness, and a bulletin-board mechanism that is UC-secure with an honest super-majority and robust when the central aggregator is honest.

Micali's construction of succinct non-interactive arguments (SNARGs) combines a probabilistically checkable proof (PCP), a vector commitment, and the Fiat--Shamir transformation. Its security is established in the random oracle model, but replacing the random oracle with an explicit hash function presents a fundamental challenge: Fiat--Shamir can fail for interactive arguments, and certain choices of the commitment scheme make Micali's construction unsound for every instantiation of the Fiat--Shamir hash. We show how to instantiate Micali's construction in the standard model assuming LWE and function vector commitments with \emph{function statistical binding} for $\Ppoly$, obtaining a non-adaptively sound SNARG for $\NP$. Our construction combines such a commitment with an LWE-based correlation-intractaxble hash and a PCP satisfying a new property, \emph{shadow soundness}. A PCP shadow is a short digest that preserves the information needed to determine the verifier's decision. By statistically binding the commitment to this shadow, we obtain the sparse relation needed to prove Fiat--Shamir soundness. We construct shadow PCPs for $\NP$ whose shadow algorithms lie in $\NC$, and we give a feasibility instantiation of the commitment scheme from strong assumptions. Our results thus identify a concrete cryptographic target for instantiating Micali's SNARG under weaker assumptions, and show that the framework does not admit an attack that succeeds for every choice of its components.

We determine all input differences with constant whole-output XOR derivatives for a four-word ARX topology containing FEILIAN SubColumn. For every word width $w\geq2$ and arbitrary XOR-linear internal maps, the complete linear-structure space contains a universal two-dimensional MSB family and has dimension at most five, with equality attained. We give a necessary-and-sufficient classifier involving at most 32 candidate masks and characterize all additional structures, including an exceptional coset possible only when the first map's image lies in the span of the least and most significant bits. For the specified 64-bit FEILIAN component, the complete space is exactly the universal family. With FEILIAN's actual ShiftRow, no nonzero member remains constant after both of the first two SubColumn layers. We also classify propagation at every boundary for all 20,160 invertible binary four-row mixers composed with ShiftRow. The five profiles stabilize by the third SubColumn layer, and exactly 4,032 mixers (20%) retain a nonzero family indefinitely. Algebraic proofs are supplemented by exhaustive small-word checks and a separate census audit. These results concern component structures and constancy at successive boundaries; they neither classify all endpoint structures of the iterated permutation nor establish an attack on the hash.

In-the-head signatures provide a route to post-quantum authentication based on symmetric primitives. Their algebraic instantiations rely on constraint relations that faithfully encode the underlying one-way function (OWF). We give a classical, public-key-only forgery attack on AIM2-based AIMer v2.0; AIMer was selected in Korea's KpqC competition. For every honestly generated public key of every v2.0 parameter set, the attack forges signatures on arbitrary messages with probability one, without signing queries. We introduce a \emph{null-branch witness attack} exploiting zero factors that leave intermediate values unconstrained. We complete these local assignments into witnesses satisfying the full relation, including public-output binding, using only public data and without solving an OWF inversion problem. Prover completeness ensures that the original message-bound prover can use these witnesses to generate signatures accepted by the unmodified verifier. Proof-system soundness applies to the encoded relation, which the constructed witnesses satisfy. Tests with reference implementations confirm accepted forgeries from satisfying witnesses whose decoded values are not valid OWF preimages. The median AIMer-256f forgery API time is approximately $11.6$ ms in our reference benchmark. We identify a gap in AIMer's security reduction: a satisfying relation witness need not decode to an OWF preimage. A complementary application to vulnerable Lynxer variants extends the analysis to VOLE-in-the-Head. We give quadratic encodings that are sound and complete for the full AIM2 and Lynx computations, including zero inputs. These results highlight relation encoding as a distinct security obligation between OWF hardness and proof-system soundness.

In~\cite{sarr25}, Sarr introduced an embarrassingly parallel impersonation attack against ECMQV and ECHMQV-C whose core step is an adding-based pseudo-random walk over a cyclic group $G$, of order $n$, searching for a \emph{decomposed $i$-point}. In this work, we revisit that construction in the richer multi-party setting where two sets of parties, the initiators $\{\hat{A}_1,\cdots,\hat{A}_{z_1}\}$, and the responders $\{\hat{B}_1,\cdots,\hat{B}_{z_2}\}$, interact under ECHMQV-C. First, we exhibit an embarrassingly parallel attack such that, when $m$~processors are available, the attack runs in expected time $$ \frac{\sqrt{n}}{m\,z_1 z_2}\left(\costa(z_1)+\costd(z_1 z_2)\right), $$ wherein $\costa(z_1)$ is the time for a batch of $z_1$ elliptic-curve additions and $\costd(z_1 z_2)$ is the time for a batch of $z_1 z_2$ digest computations. Second, for any positive integer $z_3$ such that $z_1 z_2 z_3\ll \sqrt{n}$, we propose an improved attack that runs in time $$ \frac{\sqrt{n}}{m\,z_1 z_2 z_3}\left(\costa(z_1 z_3)+\costd(z_1 z_2 z_3)\right), $$ Third, for ECMQV, assuming $z_1z_3 \ll \sqrt{n}$, we propose an attack that runs in time $$ \frac{\sqrt{n}}{m\,z_1 z_3}\costa(z_1 z_3).$$ The attacks require no shared storage among processors, they require respectively $\mathcal{O}(z_1 z_2)$, $\mathcal{O}(z_1 z_2 z_3)$, and $\mathcal{O}(z_1 z_3)$ memory complexity at each processor, and only marginal server--processor communication. As a concrete illustration, for a 128-bit ECHMQV-C instance, with $m=2^{10}$ processors, $z_1=z_2=2^{15}$, and $z_3=2^{10}$, our improved attack yields an effective parallel running time corresponding to 78 bits of security under an idealized massively parallel architecture in which the required batch elliptic-curve additions can be evaluated concurrently. This figure refers to parallel time rather than total computational work, which remains proportional to the number of elliptic-curve additions performed.

We present the first rigorous security analysis of the Resource Public Key Infrastructure (RPKI), an IETF standard for protecting inter-domain routing from basic yet effective attacks: prefix and subprefix hijacks. Existing evaluations of RPKI's security focus on empirical studies: adoption measurements, simulations evaluating the security provided by different adoption levels, and identification of implementation and specification flaws. In contrast, we focus on rigorous, modular security specifications and analysis of RPKI, including its interactions with the Border Gateway Protocol (BGP) and the Internet Protocol (IP). We identify sufficient conditions for RPKI to provably achieve its goals (requirements), under explicit, well-defined assumptions (models). We show that existing RPKI deployments do not always meet these conditions, e.g., because of circular dependencies, and propose standard-compliant improvements that restore them.

We derive joint truncated differential (TD) probabilities from multiple differential-linear (DL) approximations and use them in a framework for preimage filtering. For a fixed input difference, the inverse Walsh transform recovers the probabilities of affine output cosets from DL correlations over a complete mask subspace. In our applications, these correlations are estimated using the round-based DL method. A filter accepts a selected union of affine cosets, whose probability is computed from their joint distribution without assuming independence among the DL events. The framework handles multiple targets, sharing base evaluations and confirming each accepted candidate only once. An independent sampling analysis allows candidate sets from different iterations to overlap and relates success probability to confirmation cost. Applying this framework, we obtain the first preimage attacks on KNOT-Hash below the designers' claimed preimage bounds, for $9$ to $12$ rounds. For all four JH members, we obtain preimage attacks on the reduced-round hash functions under the padding rule of the specification, covering $3$ rounds per compression-function call forJH-224/256/384 and $4$ rounds for JH-512, with speedups ranging from $2^{54}$ to $2^{158}$ over generic preimage search. For reduced-round SKINNY-Hash, we also present the first second-preimage attacks on target messages containing at least two padded blocks, covering $5$ and $6$ rounds of SKINNY-tk2-Hash and $5$, $6$, and $7$ rounds of SKINNY-tk3-Hash. As a further application of the DL-to-TD construction, we give a $6$-round TD distinguisher on Xoodoo/Xoodyak in the related-key setting, whose estimated sample complexity improves on the previous best by about $25$ bits.

We study classical and quantum indistinguishability of sums of independent random permutations and related transformations from permutations to functions. Let $G$ be a finite abelian group of order $N$, and let $\pi^k_+(x)=\pi_1(x)+\cdots+\pi_k(x)$ for $k\geq2$ independent uniform random permutations of $G$. We give a unified Fourier analytic treatment in which the construction is represented by its probability density and a distinguisher by its acceptance function, with the classical and quantum query models imposing different restrictions on the Fourier support of the latter. Classically, we obtain the bound $O_k(q/N^{k-1/2})$ for every $q<N$, and refine it below the birthday threshold to $O_k(q^2/N^k)$. In the quantum model, a simulation argument gives $O_k(N^{-(k-3/2)})$ for $q\leq(N-1)/2$, while Fourier interpolation gives concrete finite bounds up to $q\leq4N/15$ and the query-dependent bounds \[ O\!\left(\min\left\{N^{-1/2},\frac{q^3}{N^2}+\frac1N\right\}\right), \qquad O_k\!\left(\min\left\{\frac{q^3}{N^k},N^{-(k-3/2)}\right\}\right), \] for $k=2$ and $k \geq 3$, respectively, throughout $1\leq q\leq(N-1)/2$. For $q = 1$, the first bound sharpens to $O(N^{-2})$. Over $G=\mathbb F_2^n$, a one-query Fourier attack matches the order of our one-query bound, while an $N/2$-query parity attack with advantage $1/2$ shows that our bounds reach the constant-advantage query threshold. We further study two variants of sum of permutations over binary vector spaces. First, we allow arbitrary surjective linear postprocessing, which includes truncation, and obtain classical and quantum bounds that retain the output-size dependence. Second, we analyse Dinur's variable-output single-permutation construction, $\mathsf{LXoP}$, for every fixed output width, and derive its classical and quantum security bounds; for one- and two-block outputs, we give concrete quantum security bounds.

We study local rewriting after an assumed erasure step in an ideal oblivious-transfer protocol. Bob transforms his retained record while Alice's actual record remains fixed. Exact rewriting between shared-source and independent-source records is possible in both directions precisely when the retained records of the shared source are independent. For balanced deterministic maps retaining $k$ and $\ell$ bits from an $n$-bit source, the optimal error over the maps is $\max\{0,1-2^{n-k-\ell}\}$. For fixed full-row-rank linear maps, it is $1-2^{-d}$, where $d$ is their row-space intersection dimension. A nonlinear example shows that an optimal approximate rewrite may change Bob's marginal distribution.

We give a strict generalization of the LLL algorithm over number fields, based on the reduction theory of $\mathrm{GL}(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. As a consequence, we obtain a hierarchy of reductions from module-(H)SVP to ideal-HSVP, an example of which has runtime and approximation factors subexponential in the field degree. More importantly, we uncover a close connection between structured lattice reduction and a Diophantine approximation over number fields.

In this work, we establish the first separation between computation with bounded and unbounded space, for problems with short outputs (i.e., working memory can be exponentially larger than output size), both in the classical and the quantum setting. Towards that, we introduce a problem called nested collision finding, and show that optimal query complexity can not be achieved without exponential memory. Our result is based on a novel ``two-oracle recording'' technique, where one oracle ``records'' the computation's long outputs under the other oracle, effectively reducing the time-space trade-off for short-output problems to that of long-output problems. We believe this technique will be of independent interest for establishing time-space tradeoffs in other short-output settings.

\Falcon{} is a digital signature scheme based on NTRU lattices, known for its compact signatures. Its weak-smoothness variant, \FalconWS{} (ASIACRYPT 2025), reduces signature sizes by allowing narrower Gaussian sampling distributions. Further reductions require efficient sampling at narrower widths and a security analysis that accounts for the resulting distributions. We analyze the distribution of accepted preimages directly, without estimating the smoothing parameter of the NTRU lattice. We also modify the rejection-corrected Klein--GPV sampler to reduce sampling cost while controlling the resulting distributional error. We combine these results to construct \FalconPP{}, a variant of \Falcon{}, and give UF-CMA and SUF-CMA bounds in the classical random-oracle model. For ring degrees $512$ and $1024$, our estimates give signature sizes of $419$ and $921$ bytes, respectively. These are $37.09\%$ and $28.05\%$ smaller than \Falcon{} signatures, and $11.60\%$ and $5.92\%$ smaller than the estimates for \FalconWS{} at their respective parameter sets.

We present a key-recovery attack on the knapsack McEliece-based public key cryptosystem recently proposed by G\'omez-Torrecillas, Lobillo, and Navarro in DCC 2026. Given the public key alone, the attack recovers the complete private key in time polynomial in the bit-length of the public key, and therefore constitutes a total break. The attack combines two observations based solely on the public key. An integer combination of the public entries whose coefficients sum to zero eliminates the secret mask. If such a combination is also orthogonal to the public key and sufficiently short, then its coordinates are divisible by the corresponding private key integers. The modulus required for correct decryption creates a large norm gap between these short vectors satisfying the hidden private key relations and the remaining vectors in the lattice. LLL reduction exploits this gap to recover the short vectors and hence the corresponding divisibility relations. The private key integers and the remaining secret parameters are then recovered by combining information from multiple overlapping lattices and using greatest common divisors. We implemented the attack in SageMath and recovered the complete private key for all twenty four parameter sets proposed by the authors within 3 seconds, despite claimed security levels ranging from $64$ to $156$ bits. Our analysis further shows that the weakness is structural rather than a consequence of the particular parameter choices.

Deep learning-based side-channel analysis (DLSCA) is dominated by CNNs and from-scratch Transformer architectures, while pretrained Large Language Models (LLMs) as side-channel distinguishers remain largely unexplored. We present the first systematic study of seven off-the-shelf pretrained LLMs (DeepSeek, Falcon, GPT-J, GPT-2, GPT-2m, Qwen2, T5) on three masked AES datasets, i.e., ASCADf, ASCADv, and eShard. With lightweight fine-tuning and no architectural redesign of the backbone, Falcon and GPT-2m reach GE=1 on ASCADf in only 12 to 16 traces (16, 12 and 12 traces for Falcon and 15, 14 and 13 for GPT-2m on desync0, desync50 and desync100) and uniquely sustain this trace count under desynchronization, an order of magnitude below the best prior desynchronized results. The strongest reported alternatives, EstraNet (13 traces) and Order-vs-Chaos (1 trace), are bespoke architectures trained from scratch and report only synchronized results, while other CNN- and Transformer-based baselines degrade substantially under desynchronization. The pretrained LLMs additionally extract exploitable leakage from all 16 first-round AES key bytes, the first such result outside of multi-task CNNs trained from scratch. We further provide the first per-share evaluation and the first interpretability analysis of LLM-based SCA using Effective Perceived Information (EPI), revealing a correlation between the models' leakage extraction capability and their attack performance. Strikingly, randomly initialized backbones perform on par with their pretrained counterparts, indicating that much of the advantage is architectural rather than derived from language pretraining. Our findings establish LLM architectures as unexpectedly powerful, robust, and reusable side-channel distinguishers whose inductive bias yields very low trace complexity and strong robustness to desynchronization.

The BAG-Loong reference implementation samples its secret matrices X and Y from fixed, publicly known subspaces, although the specification calls for secret random supports. This makes the public-key relation S = HX + Y , with public H, amenable to Gaussian elimination. Expanding the relation over F2 and projecting away the support of Y leaves a linear system for X. We prove an exact recovery criterion based on its column rank. All 40 supplied known-answer-test records, covering four parameter sets, satisfy this criterion: two independent solvers recover each X exactly, and the unmodified decapsulation code reproduces the corresponding session keys. For the largest parameter set, the reduced system has 9360 equations in 728 unknowns per column; one elimination solves all 15 columns.

Post-quantum signature schemes such as ML-DSA, FN-DSA (Falcon), and SLH-DSA have significantly larger keys and signatures than their classical counterparts, making compact multiparty signing an increasingly important research problem. We survey more than 30 schemes published between 2021 and 2026, covering threshold and dis tributed signing, proof-based aggregation, and algebraic half-aggregation. Our survey shows that most existing work is designed around blockchain and validator-consensus applications, where large numbers of mostly ho mogeneous signers sign a common message and accountability is typically represented by a compact signer set. We found that a different and practically important setting has received little attention: institutional multiparty document signing, where tens to hundreds of signers may use different post-quantum schemes or parame ter sets during a gradual migration, while requiring non-interactive sign ing and exact per-signer accountability. To study this gap, we develop an eight-dimensional taxonomy based on deployment requirements and sys tematically classify existing approaches. We also formulate three testable hypotheses and propose a common benchmark methodology for evalu ating communication, computation, verification cost, scalability, signer heterogeneity, and accountability. Our analysis finds no published study that quantitatively evaluates the institutional workload across the ag gregation paradigms covered in our survey. We therefore identify the key experimental and architectural requirements for assessing whether ex isting post-quantum aggregation techniques can support heterogeneous, accountable, and non-interactive institutional signing.

The M operation was introduced by Yura as an alternative to the max operation appearing in the box-ball system (BBS) to construct a BBS over finite fields. The Me operation is a version of the M operation for an elliptic curve $E$ over a finite field ${\mathbb F}_p$. As with the M operation, the Me operation satisfies the idempotent law and does not satisfy the associative law. Nevertheless, for $P,Z \in E({\mathbb F}_p)$ and $n \in {\mathbb N}$, the 1st Me-scalar multiplication $P_{n,Z}^{\,I}$ with auxiliary element $Z$ can be defined. Moreover, for $P,Z \in E({\mathbb F}_p)$ and $n \in {\mathbb Q}_+$, the 2nd Me-scalar multiplication $P_{n,Z}^{II}$ with auxiliary element $Z$ can be defined. This paper shows the following properties that may be useful to construct cryptographic protocols: $(P_{n_0,Z}^{\,I})_{n_1,Z}^{\,I}=(P_{n_1,Z}^{\,I})_{n_0,Z}^{\,I}$, $(P_{n_0,Z}^{II})_{n_1,Z}^{II}=(P_{n_1,Z}^{II})_{n_0,Z}^{II}=P_{n_0n_1,Z}^{II}$; the 1st MeDLP and the 2nd MeDLP, which are Me versions of the ECDLP, are difficult to solve on classical computers under certain conditions; the 1st MeCDH and the 2nd MeCDH, which are Me versions of the ECCDH, are NOT difficult to solve; and the sequence $\{ P_{n,Z}^{II}:n=1,2,3,\ldots \}$ is nonperiodic unless it is constant.

SQIsign holds the smallest known combination among post-quantum signatures, and its dimension-2 signature carries an auxiliary curve whose only role is to make the response computable in dimension 2. SQIsignHD's dimension-4 response has no such curve. We take that construction to the round-3 SQIsign primes, which replaced the round-2 primes in September 2026 after the attacks of Wesolowski and others, on our Rust port of the SQIsign reference code, and measure it in one session next to the reference's own assembly build. At NIST level I the dimension-4 signature is 142 bytes against 200 for the specification's format, with an 84-byte public key: 226 bytes for key and signature together, the smallest level-I combination we are aware of, among isogeny schemes and post-quantum signatures alike, at parameters that stand after those attacks. The price is verification: the dimension-4 verifier costs 9.9 times the dimension-2 verifier of the same code (120.3 against 12.2 megacycles). The dimension-4 parameters published with SQIsignHD are for its authors' own primes; we derive them for the round-3 primes, state which choices are SQIsignHD's and which are ours, and report what was built and measured.

There is currently a strong interest in designing standard-compatible threshold cryptographic primitives, a trend bolstered by NIST's Call for Multi-Party Threshold Schemes (NIST IR 8214C). While Multi-Party Computation (MPC) can be applied to the construction of threshold Key Encapsulation Mechanism (KEM) from NIST standard ML-KEM scheme to preserve the compatibility with ML-KEM, such a direct construction yields a high number of threshold decapsulation rounds as many as 384 for MK-KEM-512. In this paper, we optimise the round complexity of MPC-based threshold ML-KEM decapsulation. Our first construction (Scheme A) uses masked predicates, parallel coin expansion and global scheduling methods to improve the round complexity of MPC-based ML-KEM decapsulation, while maintaining ML-KEM encapsulation, public key and ciphertext formats. For ML-KEM-512, 768 and 1024, our construction improves the round complexity to 145, 218, and 290, respectively. We also introduce a variant (Scheme B) that uses an MPC-friendly variant of Kyber KEM and KangarooTwelve hash to further improve the round complexity to $35$ at the security level of ML-KEM-512, without full ML-KEM compatibility. In the semi-honest MPC model, we prove Scheme A security by exact composition with ML-KEM, and Scheme B IND-CCA security in the QROM from Module-LWE and negligible decryption failure.

Multi-agent systems built on large language models (LLMs) are increasingly being deployed in high-stakes settings such as finance, healthcare, and software engineering, where agents coordinate through natural-language messages. These same communication channels, however, can also enable colluding agents to exfiltrate confidential information or coordinate unauthorized actions. Steganography makes such behavior particularly difficult to detect by hiding covert communication within outputs that appear ordinary to an auditor reading the transcript. Existing provably undetectable LLM steganography protocols, however, are not suited to realistic deployments. High-capacity schemes typically assume a symmetric setting where the receiver can reproduce the sender's output distribution. The state-of-the-art practical protocol for asymmetric agents has very low capacity. Additionally, most existing approaches rely on a pre-shared secret key. In this paper, we make the systematic threat of undetectable agent collusion concrete by proposing Codetta, a high-capacity steganographic protocol for independently deployed agents under realistic asymmetric settings. Codetta combines a shared public model for estimating the communication channel, a sampling mechanism that preserves the sender's output distribution, and an adaptive error-correcting code for high-capacity communication. It further removes the need for a pre-shared secret key through a steganographic key-exchange protocol, enabling independently deployed agents to establish a shared key while keeping their communication transcript computationally indistinguishable from ordinary model outputs. Across three agent workloads and three sender models, Codetta achieves up to $94\times$ the capacity of the state-of-the-art asymmetric protocol. Its key exchange establishes a shared key using approximately 80k visible tokens, with an empirically certified failure probability of at most $4.1\times10^{-3}$ across all three workloads. These results show that effectively undetectable collusion is becoming feasible even between independently deployed agents, and we suggest that auditing mechanisms must be amended with complementary techniques beyond simply inspecting agents' communication transcripts.

On a blockchain, users compete for scarce block space in an auction run by the miner to get their transactions confirmed in the block. This auction is called transaction fee mechanism (TFM). Recent work [Rou21, CS23, SCW23] has been focused on incentive compatibility (IC), requiring that honest behavior maximizes the payoff for each type of strategic player: users, the miner, or miner–user coalitions. In this work, we introduce rational-harm proofness (RHP), which rules out deviations that harm honest parties without also reducing the deviator’s own utility relative to the honest baseline. RHP closes a gap left by IC: IC does not forbid utility neutral yet externally harmful deviations. For example, in a second-price auction, the second-highest bidder can increase the winner’s payment without affecting their own payoff. Such deviation is eliminated by RHP. We characterize TFMs satisfying RHP alongside incentive compatibility for users (UIC) and miners (MIC). For finite block size, we develop a complete characterization in two models: - In the plain model---where a single miner unilaterally implements the auction---we prove a tetrilemma (3-out-of-4 impossibility): among the four desired properties {positive miner revenue, UIC, MIC, RHP against miner–user coalitions}, no mechanism achieves all four simultaneously. This trade-off is tight: any three are jointly achievable in the plain model. - In the MPC-assisted model---where a committee of miners jointly implement the auction via multi-party computation (MPC)---we construct a randomized TFM with a positive miner revenue that achieves UIC, MIC, and RHP against all three types of strategic players. We further show that randomness is necessary: any deterministic TFM satisfying UIC and RHP in this model must confirm no transactions when the number of users exceeds the block size. Finally, we show that IC and RHP are incomparable: for each strategic role, there are mechanisms satisfying one but not the other in both models. Our results broaden the design objectives for TFMs: beyond incentive compatibility, mechanisms should also preclude costless harm to honest participants.

We study interactive proofs of proximity (IPP) for model evaluation: a resource-limited verifier interacts with an untrusted prover, typically the model owner, to certify statistical properties of a model under an unknown input distribution. Our formulation is shaped by the constraints of practical evaluation: it separates sampling the input distribution from querying the model and evaluating its output, allowing their costs and access patterns to be treated independently; it distinguishes real audit data (black-box sampling) from generated data (chosen-randomness, or gray-box, access to the sampler); and it allows the prover and the verifier to score outputs with different evaluators, as happens when scores come from human or judge models. We focus on doubly-sublinear $\mathsf{IPP}$s, in which both the verifier and the designated honest prover use sublinear resources, and on (weighted) Hamming weight properties, which capture the expectation of a Boolean evaluation rule under an unknown distribution and, consequently, a broad range of model-evaluation statistics. As a first step, we give a tolerant $\mathsf{dsIPP}$ for ordinary Hamming weight. For completeness and soundness radii $\varepsilon_c <\varepsilon_f$ and gap $g=\varepsilon_f-\varepsilon_c$, its logarithmic-round instantiation uses $\tilde{O}(1/g)$ verifier queries and $O(1/g^2)$ honest-prover queries, improving the cubic dependence of Amir, Goldreich, and Rothblum [ITCS 2025]. We prove matching query lower bounds up to polylogarithmic factors. We then study distribution-weighted Hamming weight under several access models. Under black-box sampling, the verifier uses $\Theta(1/g^2)$ samples but only $\tilde{O}(1/g)$ evaluations, and we show that the quadratic sample complexity is necessary in the interior regime. With chosen-randomness access to a sampler, the problem reduces to ordinary Hamming weight, giving $\tilde{O}(1/g)$ verifier calls and evaluations. When the two parties' evaluators may disagree arbitrarily on a $\rho$-fraction of the distribution and by up to $\gamma$ elsewhere, we give protocols that remain doubly sublinear whenever $g$ exceeds twice the mean mismatch $\kappa = \rho + (1-\rho)\gamma$. Finally, we show how our technical results can improve the efficiency of model evaluation in natural motivating scenarios by shifting the bulk of the evaluation burden to the model owner while letting any number of auditors verify claims cheaply; we apply them to auditing criteria including accuracy, group fairness, calibration, harmlessness, usefulness, and average-case robustness.

The security of isogeny-based signatures is almost exclusively studied in the single-user setting, leaving a gap for realistic multi-user deployments. This gap is especially crucial for CSI-FiSh, where the small challenge space and parameter sensitivity directly impacts security estimates. We address the multi-user security of CSI-FiSh and obtain tight concrete classical multi-user bounds in the random-oracle model (ROM) plus generic group-action model (GGAM). Crucially, our analysis only incurs an additive degradation in the number of users rather than a multiplicative one. As a byproduct, we show that CSI-FiSh attains $125$ bits of provable classical security even with $2^{46}$ users. We extend this analysis to preprocessing attacks, where an adversary with nation-state resources can perform offline precomputations. We capture this by extending the preprocessing security framework of Coretti et al. to ROM+GGAM and obtain concrete multi-user bounds for CSI-FiSh with preprocessing. Finally, we address the multi-user security of CSI-FiSh in the quantum random-oracle model and obtain results in the algebraic group action model which also avoids this multiplicative loss. This gives a unified concrete security treatment of plain CSI-FiSh in the deployment regimes where multi-user and preprocessing effects are unavoidable.

The knowledge soundness of an interactive proof is often proven via various ``special soundness (SS)'' frameworks which separate knowledge extraction into: (1) extracting accepting transcripts conforming to some structure; (2) recovering a witness from structure-conforming transcripts. However, even access-structure SS [TCC'23], one of the most general, does not handle proof systems employing probabilistic tests, a protocol design technique common in more advanced and especially succinct proof systems. The reason is that its extraction strategy decides whether a challenge is ``useful'' from the challenges used in previous transcripts alone, ignoring the prover messages. While predicate SS [CRYPTO'24] captures probabilistic tests, it does not capture access structures and forgoes the combinatorial nature and simplicity of SS. We introduce adaptive special soundness (AdSS), which generally captures extraction strategies that adaptively pick challenges for the prover taking the history of entire transcripts into account. AdSS in particular captures protocols employing probabilistic tests, formally generalises access-structure SS, and provides a simpler interface than predicate SS while retaining the same expressiveness under mild conditions. We provide knowledge extractors for AdSS protocols with optimal knowledge error $\kappa$ and almost optimal tradeoffs between extraction probability and runtime. To demonstrate the utility of AdSS, we provide a new (knowledge) soundness analysis of Kilian's succinct argument, resolving an open problem in [TCC'24]. In passing, we tighten the existing soundness error bound and unify the analyses in the strict and expected polynomial time regimes. We also provide a range of other examples, from simple ones showing how AdSS captures prior notions, to a new analysis of lattice-based Bulletproofs with unstructured challenges, which improves modularity and covers certain rings beyond $\mathbb{Z}$ compared to [TCC'23].

We introduce an optimization to the Tamarin prover that reduces its search space. The optimization applies to protocol models that use equational theories with cancellative operators, for example, when modelling Diffie-Hellman groups or bilinear pairings. We prove the optimization's soundness and evaluate its performance.

The communication complexity of computing a function in the two party setting can be much smaller than requiring one of the parties to send its input. We revisit how this communication complexity must change if the function must be computed securely. Hubáček and Wichs show that any protocol for computing a function securely must communicate at least as many bits as the length of the function's output. However, all positive results in this direction require much more communication than optimal. In particular, the state of the art for general protocols requires a $\textit{multiplicative}$ overhead polynomial in the security parameter, achieving only ''rate 0'' asymptotically. We show that, assuming the existence of input-succinct indistinguishability obfuscation for Turing machines, it is possible to achieve constant rate for this task. This compiler works even when the original protocol communicates single bits in each round, which is the main obstacle in prior works, and necessitates the use of obfuscation. The compiler can be based on standard non-succinct indistinguishability obfuscation for circuits (instead of Turing machines) in the common random string or random oracle models.

The FRI protocol (ICALP '18) is one of the most influential and widely deployed building blocks at the core of modern SNARK systems. While its concrete security is well understood, existing security proofs are intricate and technically complex. In this work, we present a significantly simpler security analysis of FRI, in particular its round-by-round soundness. Our approach is more accessible to a broader audience, lowering the barrier to understanding this fundamental protocol. Furthermore, the simplicity of our analysis may pave the way for future formal verification efforts of modern SNARK constructions.

Weak and shallow pseudo random functions form a new class of symmetric primitives that is seeing a growing relevance, from their use in the initialization phase of some MPC protocols to the internals of some FHE-based protocols. However, their security is hard to ensure: "weak" means that chosen plaintext attacks are irrelevant, and "shallow" means that their construction cannot be round-based: in this exotic setting, how can we define secure PRFs? In this paper, we investigate EALPN, a recent proposal of this type. We identify critical blind spots in the initial asymptotic analysis of the designers: the role of l, one of its parameters, turns out to be crucial. Indeed, we present a key recovery attack with a complexity that is polynomial in all other parameters, and whose complexity grows exponentially but still slowly with l. As a consequence, some parametrizations intended to provide 128 bits of security only offer 37 bits. Our attack is based on novel use of the belief propagation algorithm. Our analysis of its efficiency in our specific setting can be of independent interest.

The importance of deep neural networks (DNNs) is widely recognized, and the parameters obtained through training are regarded as valuable assets. Recently, attacks that extract these parameters using only oracle queries to a DNN have been actively studied at IACR conferences. The hard-label setting is the most challenging setting for model extraction, where an adversary can observe only the final output label, such as “dog” or “cat.” At Eurocrypt 2025, Carlini et al. proposed polynomial-time hard-label extraction of ReLU-based MLPs. However, one step of this attack process, i.e., sign recovery, requires a large number of queries and substantial computation. Implementing this step in a black-box setting remains difficult. Consequently, a fully black-box end-to-end demonstration on trained deep ReLU MLPs has remained a challenge. In this paper, we propose a new sign-recovery algorithm based on a completely different principle from the existing method. Our method requires no dedicated queries for sign recovery. In our experiments, it achieves higher sign-recovery accuracy than the existing method. Consequently, it enables efficient sign recovery even for trained models. With our sign-recovery algorithm, all steps of hard-label model extraction can be implemented in a black-box setting. By combining these implementations, we demonstrate end-to-end model extraction from models trained on MNIST and Fashion-MNIST, with width 16 and 4 or 6 hidden layers, achieving over 98% label agreement.

Privacy-preserving payment systems are well understood, yet concerns about their misuse for financial crime have led to only limited adoption in regulated settings such as central bank digital currencies (CBDCs) and institutional stablecoins. Tracing is one tool for addressing these concerns: acting on external evidence implicating a user, law enforcement follows the suspect's funds through the ledger to uncover laundering routes and accomplices. Existing coin-tracing schemes, however, provide no cryptographic bound on tracing reach: once initiated, a trace may propagate indefinitely through the transaction graph or persist across all future transactions of a targeted user. Keeping surveillance targeted and temporary therefore depends on the restraint of the authority or a committee. We introduce ephemeral coin tracing (ECT), a primitive that bounds tracing reach by construction. Each account carries an encrypted tag that records which traced identifiers its funds carry while hiding its tracing status from users. When funds move, the sender's tag degrades and merges with the recipient's tag. Each tracing contribution expires independently after a policy-defined number of hops and then becomes unrecoverable even to the tracing authority, without affecting other live contributions in the same tag. Public parameters also bound how many identifiers a tag can distinguish simultaneously. We formalize ECT and give constructions based on exponential ElGamal, Damgård-Jurik encryption, and Ring-LWE, the last providing post-quantum security.

Feige, Lapidot, and Shamir [FOCS'90] presented a generic approach for building non-interactive zero-knowledge proofs via the notion of hidden-bits generators (HBGs). At a high level, an HBG allows a prover to statistically commit to a $k$-bit pseudorandom string in the CRS model with a succinct commitment. Later, the prover can open this pseudorandom string at an arbitrary subset $S \subseteq [k]$ of positions by providing a proof $\pi_S$. The hiding property requires that unopened positions remain pseudorandom. In this work, we study the efficiency of HBGs, focusing on direct constructions that make black-box use of cryptography. We obtain the following results: Succinct CRS: Assuming learning with errors (LWE), we construct an HBG with {\em succinct} CRS of size $\mathsf{poly}(\lambda,\log k)$ for generating $k$ hidden bits. This achieves an exponential improvement over a recent sequence of works by Waters [STOC'24], Branco et al.~[EUROCRYPT'25], and Waters, Wee, Wu~[EUROCRYPT'25] that required a CRS of size at least $k \cdot \mathsf{poly}(\lambda)$. Batch opening: Using pairings, we construct an HBG with batch opening, where the proof size for any subset is $ \mathsf{poly}(\lambda)$. Previously, this was only known from the Naccache-Stern public-key cryptosystem [Groth, ASIACRYPT'10]. Succinct CRS and Batch opening: Assuming the hardness of RSA, we construct an HBG where both the CRS and the opening proof for any subset are of size $ \mathsf{poly}(\lambda,\log k)$. No black-box constructions achieving this efficiency were previously known.

Polar-KEM is a lattice-based key encapsulation mechanism submitted to the Next-generation Commercial Cryptographic Algorithms Program. Its security is claimed to rely on a lattice isomorphism problem over polar-code-defined Construction-D lattices. In its core key-generation algorithm, a polar lattice basis is constructed from a polar-code chain, reduced using LLL, and left-multiplied by a secret orthogonal matrix. The resulting matrix is published as the public key. We show that the key-generation procedure does not instantiate a general lattice isomorphism problem. The reduced reference basis is generated through a public chain of computations: public parameters determine frozen sets, the frozen sets determine a polar-code chain, the code chain determines a Construction-D basis, and the basis is then reduced by the public LLL procedure. Under the natural executable interpretation of the specification, an adversary can reproduce the same reduced basis. If the public key is \ensuremath{B_{\mathsf{pk}}=O B_{\mathsf{red}}}, the secret orthogonal matrix is recovered by the single linear-algebra operation $$ O=B_{\mathsf{pk}}B_{\mathsf{red}}^{-1}. $$ The attack is polynomial time and recovers the exact secret isometry, or its numerical representation, without solving a shortest-vector problem or a general lattice isomorphism problem. We also examine the erasure parameter used by the frozen-set selection algorithm. The specification neither assigns it a concrete value nor defines it as a sampled secret with a distribution, encoding, entropy requirement, or storage mechanism. Treating this unspecified value or unspecified LLL tie-breaking as secret entropy would define a different scheme and would not repair the published construction. The present paper focuses on this direct basis-alignment weakness. Additional structural and correctness analyses are left to an extended version.

Oblivious Linear Evaluation (OLE) is the arithmetic analogue of the well-know oblivious transfer primitive. It allows a sender, holding an affine function $f(x)=a+bx$ over a finite field or ring, to let a receiver learn $f(w)$ for a $w$ of the receiver's choice. In terms of security, the sender remains oblivious of the receiver's input $w$, whereas the receiver learns nothing beyond $f(w)$ about $f$. In recent years, OLE has emerged as an essential building block to construct efficient, reusable and maliciously-secure two-party computation. In this work, we present efficient two-round protocols for OLE over large fields based on the Learning with Errors (LWE) assumption, providing a full arithmetic generalization of the oblivious transfer protocol of Peikert, Vaikuntanathan and Waters (CRYPTO 2008). At the technical core of our work is a novel extraction technique which allows to determine if a non-trivial multiple of some vector is close to a $q$-ary lattice.

We present $\mathsf{Accordion}$, a new proof system that works in two steps: - $\textit{Accumulate}$: The first building block is a multi-folding scheme that efficiently accumulates $k$ different instances of a degree-$d$ polynomial relation into a single accumulated instance, without using recursion. Our scheme builds on the Protostar [Bünz & Chen, ASIACRYPT '23] and Protogalaxy [Eagen & Gabizon, ePrint 2023/1106] line of work, improving further the verifier efficiency. It supports the same expressive class of relations, arbitrary-degree polynomial constraints, enabling efficient folding for CCS, Plonkish constraints, and even custom gates. - $\textit{Decide}$: The second block is a SNARK decider for the folding scheme, which efficiently proves the validity of the resulting accumulated instance using off-the-shelf optimized building blocks. We give a concrete instantiation consisting of a Plonk-based proof plus an additional KZG polynomial commitment opening. This design is especially attractive in batch-aggregation settings where a prover collects many independent witnesses, folds them into a single accumulator, and then runs one succinct decider to certify the entire batch. Our scheme avoids costly recursion overheads. We implement $\mathsf{Accordion}$ and evaluate it against a highly optimized Plonk proving pipeline ($\texttt{midnight-zk}$). For $k=64$ instances, $\mathsf{Accordion}$ is up to $2.5\times$ faster than computing $k$ Plonk proofs for SHA-256 preimages, with a $3\times$ faster verifier and $4\times$ smaller proofs. Its prover is also an order of magnitude faster than using IVC to aggregate the $k$ proofs.

Traceable secret sharing complements traditional schemes by enabling the identification of parties who sell their shares. Recently, two independent works extended traceable secret sharing to general access structures. Goyal, Jain, and Partap [EC'26] introduced a model in which a reconstruction box is augmented with a label $I \subseteq [n]$ and is only required to distinguish between two secrets when queried with the shares of parties in $I$. Based on how this label relates to the corrupted set $J$ that built the box, they defined two notions of traceability. If $I \cap J = \emptyset$, the model is called $\emptyset$-strong traceability, for which they presented a construction based on indistinguishability obfuscation (iO). Otherwise, their model is calledstrong traceability, for which they proved an impossibility result. Farràs and Guiot [EC'26] proposed a different model, which we call hiding traceability, where the reconstruction box has no label and the access structure is hidden from the parties. In this work, we improve traceable secret sharing for general access structures in three directions. First, we present a fully information-theoretic scheme for the $\emptyset$-strong traceability model, eliminating the need for strong cryptographic assumptions. This resolves an open question posed by Goyal, Jain, and Partap, who asked what are the minimal assumptions needed in the $\emptyset$-strong traceability model. Second, motivated by the impossibility of strong traceability, we introduce a relaxed notion calledhidden mildly strong traceability. This model is relevant in practice and bridges the strong and hidden models. For this setting, we present an information-theoretic scheme for general access structures. Finally, we consider the more general model of stateful traceability, where reconstruction boxes may keep state across queries, and we prove an impossibility result for this setting.

We solve the long-standing open question of designing a "truly" linearly homomorphic scheme -- meaning it supports homomorphic additions on arbitrary plaintexts, with no restriction, in contrast to "somewhat" ones -- that achieves CCA1 security under a standard assumption. We do so by introducing a new variant of Paillier-ElGamal, which we call Damgard-Paillier-ElGamal (DPEG) as its design follows a Knowledge-of-Exponent pattern. On top of being linearly homomorphic without any restriction, our scheme enjoys the following properties: - It achieves CCA1 security solely under the DCR assumption. To the best of our knowledge, it is the first "truly" linearly homomorphic proven CCA1 secure solely under this assumption (or any other standard one). - It can be extended to support one level of multiplication while still preserving its CCA1 security under the same assumption. This extension is then the first concrete scheme supporting both homomorphic additions and multiplications (even limited to one-level) that is proven CCA1 secure under DCR. - It also achieves Manulis&Nguyen's stronger notion of vCCA security under an additional non-falsifiable linear-only homomorphism assumption that is commonly used in proof-of-knowledge constructs. DPEG is then the first scheme that is proven vCCA secure while being CCA1 secure under a standard assumption. This also carries over to the multiplicative extension. Interestingly, DPEG achieves the above at only 1.5 times the cost of the baseline CPA-secure Paillier-ElGamal scheme. To establish the CCA1 security of DPEG, we introduce a new abstract framework that allows to prove CCA1 security of a large class of of group-based PKE that also covers other somewhat linearly homomorphic schemes previously known to achieve CCA1 security under falsifiable assumptions such as Damgard-ElGamal, Cramer-Shoup-Lite and the recent variant of Paillier-ElGamal with plaintext zero padding of Libert. This framework may be of independent interest to more easily prove the CCA1 security of other schemes. Lastly, on the negative side, we take a first step in connecting vCCA security to an impossibility result of Gentry&Wichs and show that, under mild assumptions, the vCCA security of DPEG cannot be established from any falsifiable assumption by means of a black-box reduction.

Blind signatures are a central primitive for privacy-preserving applications such as e-cash, anonymous credentials, and e-voting. Classical constructions such as blind Schnorr adapt an ordinary signature scheme while producing signatures that follow the same format and distribution as those generated by the ordinary signing algorithm. This property is particularly relevant in settings where blind and non-blind signatures coexist within the same infrastructure. Achieving an analogous result for lattice-based Fiat--Shamir signatures, with security based on the underlying ordinary signature scheme, has remained open. We present $\mathsf{BRaccoon}$, the first concurrently secure lattice-based realization of the ``blind signatures from a signature assumption'' paradigm of Fuchsbauer and Wolf (EUROCRYPT~2024). Our construction builds on the rejection-free lattice signature scheme $\mathsf{Raccoon}$, yielding signatures that retain the algebraic format and verification relation of $\mathsf{Raccoon}$. At a high level, we introduce blinding at the commitment stage and enforce correct challenge and response generation via linearly homomorphic encryption combined with $\mathsf{NIZK}$ proofs. Since these proofs already bind the hidden message to the resulting signature, their relation can naturally incorporate predicates on that message, providing a direct route toward predicate blind signatures. A central technical challenge stems from discrete Gaussian sampling, where blinding induces a non-trivial distributional shift that precludes direct security reductions. To overcome this, we introduce a modified scheme $\mathsf{Raccoon}^\star$ that explicitly captures this shift. We analyze one-more unforgeability through non-rounded versions of $\mathsf{Raccoon}^\star$ and $\mathsf{Raccoon}$. The deployed blind-signing protocol retains rounding. For a concrete instantiation, we encode the lattice relations and the non-linear challenge computation in a common mixed Boolean and arithmetic relation. Our instantiation retains SHA3-256 and SHAKE256 and proves both protocol statements using the ZK-LaBRADOR toolkit. For up to $2^{32}$ signing queries, its total communication is estimated at approximately $862$ KB.

Mobile access within public finance and enterprise environments often requires lightweight anonymous authentication, allowing users to prove authorization without disclosing their identities. Group Time-based One-Time Passwords (GTOTP) has recently been proposed as a lightweight primitive meeting this need with post-quantum security. To address dynamic group membership, Cao et al. introduced DGTOne, the first dynamic GTOTP construction. It employs chameleon hashes to precompute a fixed set of Merkle-tree leaves (mount points), into which conventional TOTP verification points (VPs) contributed by group members are adaptively inserted. However, DGTOne partitions mount points by time epochs, so they can expire and become unusable, causing capacity waste due to unpredictable join times. Moreover, its outsourced proof generation requires verifiers to be online each epoch to fetch refreshed credentials from Registration Authority (RA), defeating offline verification needed in mobile access. We address these limitations with two new schemes. First, we propose NWDGT, a no-wastage DGTOTP design that constructs Merkle trees of members' verification points (VP-trees) on demand, eliminating expired mount points at the cost of added handling latency. To mitigate this latency, we introduce LWDGT, which instantiates multiple small one-time signature (OTS) trees whose leaves (OTS public keys) serve as mount points. New members' VPs are signed immediately using unused leaves, achieving low wastage. We formally prove that the wastage rate of LWDGT is, with overwhelming probability, lower than that of DGTOne. By modeling the registration process and optimizing OTS-tree size, for deployments with up to 500 members (209 initially, 20 added monthly), LWDGT reduces mount point wastage rate by 10.2% over one year compared to DGTOne.