Distributed Oblivious RAM (DORAM) is a promising building block for privacy-preserving cloud databases and outsourced storage systems. However, existing two-server designs often rely on slow linear scans or heavy cryptographic primitives, making them struggle to balance efficiency and bandwidth, and thus hindering their practical deployment. We present DuetORAM, a two-server DORAM that achieves constant-round access with $O(\log N)$ communication while avoiding these computational...

This paper analyzes the bilinear embedding of matrix algebras into commutative cyclotomic rings. We apply the Cohn-Umans method. This establishes that single-multiplication bilinear monomial embeddings require a ring degree of $\widetilde{\Omega}(N^3)$. We circumvent this bound by routing Strassen tensor rank decompositions through orthogonal Chinese Remainder Theorem ideals. This reduces the asymptotic complexity to $\widetilde{\Omega}(N^{\log_2 7})$. We optimize the coprime tensor...

Boolean polynomial multiplication is the primary computational bottleneck of the Hamming Quasi-Cyclic (HQC) key encapsulation mechanism. In this paper, we reframe the Frobenius Additive FFT (FAFFT) in ring-theoretic terms, via quotient-ring homomorphisms and the Chinese Remainder Theorem. This perspective shows that a complete decomposition into evaluation points is unnecessary for multiplication, and naturally yields the Strided FAFFT (SFAFFT), which operates over smaller finite fields with...

We study two central problems in threshold cryptography from lattices: (1)~threshold encryption with silent setup for general thresholds $t \geq 2$, where no post-quantum constructions were previously known, and (2)~threshold fully homomorphic encryption (TFHE) with sublinear parameters, an open problem since the work of Boneh~et~al.\ (CRYPTO~2018). We introduce \emph{$(\alpha,\beta)$-Scaled Linear Secret Sharing Schemes} (LSSS), a relaxation of standard LSSS in which each authorized...

We propose NAIBI-Full, a lattice-based key encapsulation mechanism (KEM) together with its forward-secure ephemeral key-agreement protocols, built on the regular representation 𝜌 of the non-split commutative algebra \cA𝛼 =\Rq⁢[𝑦]/(𝑦𝑘 −𝛼) over \Rq =\Z𝑞⁢[𝑥]/(𝑥𝑛 +1), 𝑘 ∈{2,3}, 𝛼 a non-𝑘 -th power. Each party publishes the full matrix \bft =𝐴⁢𝜌⁡(\bfs) +\bfe ∈\Rq𝑘×𝑘 ; because 𝜌⁡(\cA𝛼) is commutative, the cross-product collapses to small noise and a Peikerthint closes the gap to exact agreement,...

The Sumcheck protocol is a cornerstone of modern proof systems, yet its prover remains a performance bottleneck. Even in the multilinear case, the repeated construction of round polynomials leads to significant overhead, limiting scalability in practice. We take a different approach: instead of modifying the protocol, we rethink the representation of multilinear polynomials. We show that any multilinear polynomial admits a simple and structured binary-tree circuit representation, where...

We derive an explicit exponent \(\Psi_\rho\) that bounds the Reed--Solomon MCA bad-slope numerator at every fixed relative radius between Johnson and capacity. The resulting positive-relative-radius exponential-budget safe-frontier certificate strictly improves the smallest-test MDS exponent and gives a constant post-Johnson radius for every positive usable budget exponent. An all-test-size MDS circuit-incidence envelope gives exact large-field capacity plateaux, improved adjacent...

In reaction to the emerging quantum threat, the National Institute of Standards and Technology (NIST) seeks post-quantum secure digital signature schemes. NIST's ongoing competition recently advanced to the third round, in which the Unbalanced Oil and Vinegar scheme (UOV) is a promising candidate due to UOV's conservative design, small signatures, and performant signing and verification. While these benefits make UOV attractive, the implementation aspects for compact hardware acceleration of...

Range proofs enable a prover to convince a verifier that a committed value lies within a specific interval without revealing additional information. They are fundamental to privacy-preserving systems including anonymous credentials, e-voting, e-cash, and cryptocurrencies like Monero and Grin. A critical challenge is efficiently proving that multiple committed values simultaneously satisfy range constraints while minimizing communication overhead. Vector commitment schemes provide a...

Boolean functions with additional structure play an important role in symmetric cryptography, both for achieving strong cryptographic properties and for enabling efficient implementations. Recent works on homomorphic-friendly symmetric primitives, especially in the context of Hybrid Homomorphic Encryption, highlighted the interest of Boolean functions whose evaluation can be decomposed according to structured partitions of the Boolean cube. A classical example is given by Hamming-weight...

In this work we propose a novel Boolean lookup-table evaluation methodology over binary CKKS when circuit XORs are kept lazy, i.e., evaluated as additions whose least significant bits remain correct. Our method represents a LUT in the Walsh basis, forms the required parity sums by lazy CKKS additions, and packs them into ciphertext slots. We then use CKKS binary bootstrapping as a refresh step: the StC stage maps the packed lazy parities to MSB-encoded bits, removing the overflow; CtS places...

Bitslice implementations are widely adopted in lightweight cryptography (LWC) due to their efficiency and inherent resilience to side-channel attacks. However, this paper reveals that their decomposition of the S-box exposes critical vulnerabilities to the operation skip fault model. Unlike data corruption faults suffering from high-entropy diffusion, we identify that skipping bitwise operations induces strongly restricted differential patterns. To exploit this characteristic, we...

A basic property of lattice-based homomorphic encryption schemes is that ciphertexts carry an inherent noise that accumulates as computation advances. The key-switching procedure of these schemes allows the homomorphic re-encryption of a ciphertext under a new secret key, but it is a major source of noise growth. Several strategies have been proposed to reduce the amount of noise introduced by key-switching in the CKKS scheme. In this work, we generalize the RNS-based decomposition ...

Let $E$ be an elliptic curve over a perfect field $K$. A function $f\in K(E)$ is a compression of degree 2 on $E$ if $f(-P) = f(P)$ for all $P\in E$, and the field extension $K(f)\subset K(E)$ is of degree 2. For a finite subgroup $G\subset E$ over $K$ a function $w\in K(E)$ we will call a $G$-compression if $w(\pm P +G) = w(P)$ for all $P\in E$, and the field extension $K(w)\subset K(E)$ is of degree $2|G|$. We will show that $w\in K(E)$ is a $G$-compression if and only if $w = f\circ \Phi$...

The CKKS fully homomorphic encryption scheme has traditionally been viewed as suitable only for approximate arithmetic. However, recent work (Alexandru et al., Crypto 2025) has introduced functional bootstrapping techniques that enable accurate lookup tables (LUTs) evaluation in CKKS. Nevertheless, to deal with the high precision problem, the state-of-the-art scheme (Dumezy et al., TCHES 2026) requires reshaping the LUTs into a matrix, which incurs $O(P)$ multiplications for a size-$P$ table...

Although the state-of-the-art neural network model extraction attack in the hard-label setting by Carlini {\em et al.} at EUROCRYPT 2025 has polynomial-time complexity in theory, its dual-point clustering relies on singular value decomposition (SVD) with a time complexity of $\mathcal{O}(n^2 \cdot (d^{(k)})^3)$, resulting in huge runtime in practice. To address this computational bottleneck, this work transforms Carlini {\em et al.}'s geometric-view hard-label attack into an algebraic...

The Lattice Isomorphism Problem (LIP) is a computational problem that has recently been introduced into cryptography and is believed to be hard. Its search version, Search Lattice Isomorphism Problem (SLIP), is considered even harder than the Shortest Vector Problem (SVP), yet its complexity is still not well understood. Haviv and Regev (SODA 2014) showed that the decisional version (DLIP) lies in a statistical zero-knowledge class and is therefore unlikely to be NP-hard. This result does...

Many modern SNARK constructions follow a paradigm that combines a Polynomial Interactive Oracle Proof (PIOP) with an appropriate Polynomial Commitment Scheme (PCS). In this paradigm, the PIOP reduces soundness to the verification of a collection of polynomial relations that are checked though oracle queries, while the PCS enables succinct commitments to the corresponding polynomials. Rather than transmitting the full polynomial representation, the prover commits to the polynomials and later...

We give several examples of families of polynomials $p_1, ... , p_t \in \mathbb R[x_1, ... , x_n]/\langle x_i^d - 1\rangle_i$ on which the Low-Norm Nullstellensatz Hypothesis of [Devadas-Hopkins-Kalai-Kothari-Lombardi-Mathialagan, STOC 2026] fails to hold. That is, we prove the existence of polynomials $f \in \langle p_1, ... , p_t\rangle$ with coefficient $L^1$ norm $||f||_1 = 1$ but such that every decomposition $f = \sum_i p_i \cdot q_i$ has cost $\sum_i ||q_i||_1 = 2^{\Omega(n)}$. Our...

Minimizing round complexity is a central goal in secure Multi-Party Computation (MPC), particularly for deployment on high-latency networks. While constant-round protocols with concrete efficiency have been constructed, they are typically designed for Boolean circuits and each gate incurs a bandwidth cost linear in the security parameter. Moreover, for arithmetic-heavy applications such as privacy-preserving machine learning and statistical analysis, compiling arithmetic operations into...

The recent work [Devadas-Hopkins-Kalai-Kothari-Lombardi-Mathialagan, STOC 2026] proposed a low-norm Nullstellensatz hypothesis for the "AND code": every polynomial $f$ vanishing on the "AND-code ideal'' should admit a Nullstellensatz decomposition over the local AND constraints whose total coefficient \(\ell_1\)-norm is only polynomially larger than the \(\ell_1\)-norm of $f$. We give a counterexample to this conjecture by proving an exponential lower bound on the total coefficient...

We present new techniques for converting secret-shared values between different moduli in arithmetic MPC, without relying on bit decomposition. More concretely, our protocols convert a sharing \([x]_q\) over a source modulus \(q\) into a sharing \([x]_t\) over a target modulus \(t\), under a mild bound on the size of \(x\). We give three variants: a particularly simple protocol for power-of-two moduli, a protocol for arbitrary source modulus and prime target modulus, and a general protocol...

In this note, we study decomposition of the Ate pairing on certain elliptic curves defined over finite fields. As an application, we reduce a generalized pairing inversion to root findings of an element of the affine coordinate ring appearing in the decomposition. For a supersingular curve $E / {\bf F}_q$ satisfying $\sharp E( {\bf F}_q ) = q+1$, heuristic observation suggests that a number of calls to a root finding algorithm seems to $O( N )$ where $N$ is the maximal power of...

We give an efficiently computable invariant for the (Signed) Permutation Code Equivalence ((S)PCE) problem we call the square class invariant, that was previously not recognised in coding theory. Our invariant naturally yields a distinguisher for the decision version of (S)PCE as defined at Eurocrypt 2025 by Albrecht, Benčina and Lai [ABL25], breaking the hardness assumption that underpins the security of their updatable public-key encryption scheme. Moreover, we extend a 2023 result by...

In Geelen and Vercauteren~(Eurocrypt 2025), a Generalized BFV~(GBFV) fully homomorphic encryption scheme was proposed. Here, a plaintext space of form $\mathbb{Z}[x]/(\Phi(x),t(x))$ was utilized to reduce the number of Single Instruction Multiple Data (SIMD) slots within the initial BFV plaintext space. This lowered its dimension and thus enabled lower latencies as well as greater flexibility in parameter selection. However, to obtain slots of degree $1$, the methods of Geelen and...

Pairing-based cryptography relies heavily on the efficiency of bilinear pairings, the computation of which is dominated by the final exponentiation step. This paper describes an efficient cubing operation in the cyclotomic subgroup of $\mathbb{F}_{q^6}$ for $q\equiv1\mod{6}$. As an application, we use existing results for computing Frobenius maps to optimize the cost of the optimal Ate pairing final exponentiation over the SG54 curve. Furthermore, we introduce a novel decomposition for the...

The ARIA block cipher is the Korean national standard (KS X 1213) and an IETF standard (RFC 5794). Despite its widespread use, research on efficient implementation for modern ARMv8 processors has remained limited compared to AES, which benefits from dedicated hardware instructions. The best prior ARMv8 result by Eum et al. reported 0.573 cycles per byte (cpb); however, through direct communication with the authors and independent re-evaluation, we confirmed that this published figure...

Many lattice-based encryption schemes admit a negligible but nonzero decryption failure rate (DFR), which is tied to both correctness and security through failure-based attacks. Several module-lattice constructions (e.g., LAC at NIST PQC Round 2 and DAWN at Asiacrypt 2025), as well as average-case noise analyses in FHE, estimate the DFR from one-coordinate marginals combined with an independence approximation across the coefficients of polynomial products. Geometrically, this approximation...

Trapdoor constructions are an active research area in Multivariate Cryptography. The presented work studies trapdoors based on factor decomposition in algebraic structures, with emphasis on polynomial rings over $F_p$. The main contribution is the formulation of a general property: if an algebraic structure admits a hidden factor decomposition then this property can be used as a trapdoor principle. Based on this approach, two constructions are given: one signature scheme and one encryption scheme.

We give a passive attack on the Hecke-KE key-exchange scheme. The scheme proposes using products of Hecke operators on $S_k(\Gamma_0(N))$ as a one-way function. We show that the Hecke algebra acting on any fixed $S_k(\Gamma_0(N))$ is simultaneously diagonalizable over an explicit number field computable from the public parameters alone, and that this diagonalization reduces shared-key recovery to $d$ scalar divisions over that number field, where $d=\dim S_k(\Gamma_0(N))$. Our main theorem...

TFHE is one of the most promising scheme in the literature for an adoption of Fully Homomorphic Encryption (FHE) in practice. The core reason of its good performances is the powerful Programmable Bootstrapping (PBS) operation, that enables to homomorphically evaluate a Look-Up Table (LUT) on a ciphertext while simultaneously reducing its noise. However, the computational cost of running a PBS degrades severely when the size of the plaintext space increases, making it intractable for...

Batch encryption enables a holder of the secret key to publish a succinct pre-decryption key for a set of ciphertexts, such that exactly that set can be decrypted while other ciphertexts remain secret. Existing constructions either rely on epochs or, when epochless, suffer from large public parameters (quadratic in the batch size) and are vulnerable to censorship. In this work, we present an epochless, censorship-resistant batch encryption scheme with linear-sized public parameters,...

We introduce metric-aware code-based cryptography by moving beyond the Hamming metric to the Niederreiter-Rosenbloom-Tsfasman (NRT) and sum-rank metrics and by exploiting their linear isometry groups via Bruhat-Chevalley-Renner decompositions. On the structural side, we give isometry-invariant distance tests: a parity-check prefix-rank test for single-chain NRT, its multi-prefix extension for block-NRT, and a block rank-profile test for sum-rank. We also analyze orbit structure under the...

We present a low-stack implementation of the module-lattice signature scheme \(\mathrm{HAETAE}\), targeting microcontrollers with \(8\,\mathrm{kB}\)–\(16\,\mathrm{kB}\) of available SRAM. On such devices, peak stack usage is often the binding constraint, and \(\mathrm{HAETAE}\)'s hyperball-based sampler, large transient polynomial vectors, and variable-length signature payloads (hint and high-bits arrays) pose a particular challenge. To address this, we introduce (i) rejection-aware pass...

Curve5453 and Curve6071 are Montgomery curves over the primes $2^{545}-3$ and $2^{607}-1$, providing 271- and 302-bit classical security, respectively. Their TMVP-based field multiplication in 10-limb representation costs 77 multiplications. We reduce this to 60 for Curve5453 ($22\%$ fewer) using a 9-limb radix-$2^{61}$ representation, and to 54 for Curve6071 ($30\%$ fewer) using a 12-limb radix-$2^{51}$ representation with hierarchical block-level TMVP. Choosing the limb count to produce...

Fully Homomorphic Encryption (FHE) enables arbitrary computation on encrypted data without decryption, providing strong privacy guarantees for secure cloud computing, encrypted analytics, and privacy-preserving machine learning. However, practical deployment of FHE remains limited by the high computational cost of polynomial arithmetic over large modular rings. In particular, Number Theoretic Transform (NTT)–based polynomial multiplication dominates the execution time of modern lattice-based...

Succinct non-interactive arguments of knowledge (SNARKs) enable the verification of complex computations via short proofs. Recursive proof composition allows long-running or distributed computations to be verified incrementally, but existing approaches exhibit a fundamental trade-off. Folding-based schemes achieve highly efficient recursion but require provers to maintain and communicate large private state, while stateless approaches such as full SNARK recursion and atomic accumulation...

Fully homomorphic encryption algorithms enable users to perform computation on encrypted data. Since the first candidate scheme was proposed in 2009 by Gentry, schemes have rapidly improved in all metrics, be it computational complexity or memory efficiency. The class of accumulator based schemes which include FHEW and TFHE are designed to operate on small data, usually ranging between 4 and 5 bits. Yet, schemes can be effectively leveraged in practice and enable lifting of small data to...

Zero-knowledge virtual machine (zkVM) is a powerful infrastructure for proving the correctness of a program execution with a succinct proof, attracting significant interest from researchers, developers, and users. It has been widely used in applications such as blockchain rollups, privacy-preserving machine learning, and off-chain computation. As the field grows, a wide range of zkVMs have been proposed. However, they adopt different choices in instruction formats, trace layouts, and proving...

Garbling schemes are powerful primitives that enable secure computation between a mutually untrusting garbler and evaluator. A projective garbling scheme is one that encodes the evaluator's input in a simple bit-by-bit manner. Projective schemes, such as the seminal scheme of Yao, are versatile, as they are naturally compatible with other simple tools, such as $1$-out-of-$2$ oblivious transfer (OT). There exist garbling schemes that naturally operate over large finite fields, some of which...

Large-size Number Theoretic Transforms (NTTs) are key operations in modern Zero-Knowledge Proofs (ZKPs), where the NTT size often reaches millions of points and the arithmetic is over wide prime fields. To handle such NTTs on hardware, prior designs commonly rely on the decomposition algorithm, which makes large-size NTTs feasible by streaming sub-NTTs through limited on-chip buffers. However, in practical implementations, decomposition alone is insufficient to ensure high efficiency. Since...

Computing cube roots in quadratic extensions of finite fields is a subroutine that arises in elliptic-curve point decompression, hash-to curve and isogeny-based protocols. While the factorization $p^2 −1 = (p−1)(p+ 1)$ suggests a known subgroup decomposition, implementing the cube root via separate operations in the two subgroups does not beat a direct $\mathbb{F}_{p^2}$ exponentiation in practice. We propose a carefully engineered algorithm that reduces the $\mathbb{F}_{p^2}$ cube root to a...

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

Blind rotation is the computational core of GINX, AP, and AP+ bootstrappings, yet its error behavior has not been precisely characterized. Prior analyses rely on heuristic independence assumptions that fail to capture the distinct error accumulation patterns of different algorithmic variants. We prove that no additional assumptions are needed: the (M)LWE assumption guaranteeing ciphertext indistinguishability also implies the independence properties required for an exact second-moment...

Neural network model extraction attacks pose a serious threat to the intellectual property of deep learning models. While most prior work focuses on Fully Connected Networks (FCNs), effective extraction of Convolutional Neural Networks (CNNs) remains underexplored, particularly in the hard-label setting. In this work, we propose the first systematic method for the recovery of complete CNN parameters in such conditions. By reformulating convolutional layers as sparse Block Toeplitz with...

We show how to improve rank-metric solvers when certain side information (hints) about the secret is available. Concretely, we adapt the kernel search algorithm for MinRank and the GRS algorithm for the Rank Syndrome Decoding problem when some entries in the rank decomposition of the error matrix are known. This setting is motivated by side-channel leakage and cryptographic applications: Mirath and RYDE, two signature candidates in the NIST post-quantum competition, rely on these problems...

The Functional Decomposition Problem (FDP) involves expressing a given set of multivariate polynomials as a composition of simpler polynomials. Traditional methods, such as Faugère-Perret’s AlgoFDP and its generalized variant MultiComPoly, rely on Gröbner basis computations on ideals generated from derivatives of composed polynomials h = f ◦ g, where f and g are called left-factor and right-factor of h, respectively. The computational cost of these methods increases significantly with both...

Fully homomorphic encryption (FHE) enables computation on encrypted data. NTRU-based FHE offers compact ciphertexts—a single ring element rather than a tuple—but FINAL, the leading NTRU-based scheme, represents its ciphertexts and decryption in matrix form that hides the polynomial-ring structure on which recent automorphism-based amortized bootstrapping relies. We reformulate FINAL in the standard polynomial-ring setting and express its decryption as coefficient-wise inner products...

Off-chain cryptography enables more expressive smart contracts for Bitcoin. Recent work, including BitVM, use SNARKs to prove arbitrary computation, and garbled circuits to verifiably move proof verification off-chain. We define a new garbling primitive, Argo MAC, that enables over $1000\times$ more efficient garbled SNARK verifiers. Argo MAC efficiently translates from an encoding of the bit decomposition of a curve point to a homomorphic MAC of that point. These homomorphic MACs enable...

Secure TransFormer Inference (STFI) frameworks have been proposed to address privacy concerns over user inputs and model parameters in Transformer-based LLMs. While most existing solutions rely on interactive protocols that incur substantial user-server communication overhead, non-interactive STFI variants have recently emerged to eliminate such dependencies. Nevertheless, state-of-the-art non-interactive STFI frameworks still suffer from critical limitations. (i) Large ciphertext sizes and...

We present a deterministic framework for navigating $p$-isogeny graphs of genus $g \ge 2$, addressing the lack of canonical and auditable primitives in higher dimensions. The framework integrates two components: the Certified $p$-Isogeny Step (PICS) and a Non-Decomposition Certificate (ND). PICS constructs the unique Frobenius-compatible inseparable isogeny by extracting kernel directions from Hasse--Witt invariants and differential subresultant profiles, thereby eliminating randomized...

With the rapid development of quantum computing, traditional public-key cryptosystems are increasingly vulnerable, making post-quantum cryptography (PQC) a critical area for securing future information systems. As a prominent code-based key encapsulation mechanism (KEM), Classic McEliece offers strong quantum security. However, its large public key size and complex decoding process introduce significant performance bottlenecks, hindering its practical deployment on mobile and edge devices....

In many secure multiparty computation (MPC) applications, the data to be processed are much smaller than the underlying field or ring size. The encoding domain is typically chosen to be large enough to guarantee security (e.g., a 128-bit prime field for 128-bit security), whereas the actual data may consist of only a few bits, such as 4-bit values in a 16-category classification task. This mismatch can lead to substantial communication and computation overhead in existing MPC protocols,...

The growth of advanced cryptographic applications has driven the development of arithmetization-oriented (AO) ciphers over large finite fields, which are designed to minimize multiplicative complexity. However, this design advantage of AO ciphers could also serve as an attack vector. For instance, the \textsf{AIM} one-way function in the post-quantum signature \AIMer proposed at CCS 2023 has been broken by several works soon after its publication. The designers then promptly developed secure...

We study a new variant of the $k$-sum problem. In the classical formulation, one is given $k$ lists of binary vectors and must find one vector from each list such that their sum is the zero vector. In our variant, vectors are instead chosen from the set $\{-1,1\}^m$. First, we analyse how the complexity of the original problem changes when one use $\pm 1$ vectors. We show that this variant achieves better than square-root complexity when using more than two lists, although its overall...

We present an optimized implementation of the GHASH and POLYVAL authentication algorithms used in AES-GCM and AES-GCM-SIV that eliminates the computational overhead of bit-reversal operations. Our approach computes these universal hash functions directly in bit-reversed representation, matching the native format used by carry-less multiplication instructions available on modern processors. The algorithm exploits 64-bit polynomial primitives and parallel execution on superscalar...

Partial fraction decomposition is a fundamental technique in mathematics where products of rational functions can be expressed as sums of fractions. While rational functions have been used in various cryptographic constructions, their rich algebraic structure has not been systematically explored as a direct foundation for building cryptographic primitives. In this work, we describe and exploit two key properties of partial fraction decomposition: (1) the decomposition property itself,...

TFHE bootstrapping is typically limited to a small plaintext space, with an exponential increase in cost for larger plaintext spaces. To bootstrap larger integers, one can use digit decomposition, a procedure that iteratively extracts and bootstraps a part of the larger plaintext space. Conventional state-of-the-art methods typically extract bits starting from the least significant bits (LSBs) and progress to the most significant bits (MSBs). However, we introduce a DirtyMSB extraction...

Lookup arguments have become a central tool in proof systems, powering a range of practical applications. They enable the efficient enforcement of non-native operations, such as bit decomposition, range checks, comparisons, and floating-point arithmetic. They underpin zk-VMs by modelling instruction tables, provide set membership proofs in stateful computations, and strengthen extractors by ensuring witnesses belong to small domains. Despite these broad uses, existing lookup constructions...

In this paper, we provide details on the proofs of the quantum polynomial time algorithm of Biasse and Song (SODA 16) for computing the $S$-unit group of a number field. This algorithm directly implies polynomial time methods to calculate class groups, $S$-class groups, relative class group and unit group, ray class groups, solve the principal ideal problem, solve certain norm equations, and decompose ideal classes in the ideal class group. Additionally, combined with a result of Cramer,...

Polynomial multiplication over $\mathbb{F}_2[x]$ is a fundamental building block in code-based and lattice-based cryptography, particularly on lightweight embedded devices where dedicated carry-less multiply instructions are unavailable. This paper presents a high-speed, constant-time implementation of radix-16 polynomial multiplication on the ARM Cortex-M4, combining zero-padding with recursive Karatsuba layers. Building on the radix-16 decomposition proposed by Chen et al. in TCHES’21, we...

The ARX structure plays a crucial role in symmetric-key primitives, with differential-linear (DL) attacks being among the most effective cryptanalysis techniques against ARX ciphers. In this paper, we present a systematic re-decomposition technique for DL distinguishers of ARX ciphers and identify for the first time the hourglass(-like) structural commonalities among optimal DL distinguishers searched out by various deduction techniques, also supported through comprehensive experiments,...

Quantum cryptanalysis of block ciphers with Grover’s search requires synthesis of round function, where the non-linear S-boxes dominate the circuit cost. Efficient quantum implementations of these S-boxes are a bottleneck for cryptanalysis. In this work, we address this problem and present new generic strategy for synthesis of quantum circuit for large S-boxes that reduces the NISQ-era transpiled depth after decomposition into the hardware-oriented universal basis gate set u+cx. We...

Secure multi party computation protocols (MPC) translating between arithmetic and binary data types have recently gained attraction which is introduced by Rotaru and Wood in 2019, called daBit, and improved by Escudero et. al. called edaBits. EdaBits are simply secret shares in arithmetic domain and bit decomposition of the arithmetic share is the binary form the secret shares. These protocols are preprocessing for MPC protocols in order to improve efficiency. Furthermore, fluid MPC setting,...

The problem of finding a minimal circuit to implement a given function is one of the oldest in electronics. It is known to be NP-hard. Still, many tools exist to find sub-optimal circuits to implement a function. In electronics, such tools are known as synthesisers. However, these synthesisers aim to implement very large functions (a whole electronic chip). In cryptography, the focus is on small functions, hence the necessity for new dedicated tools for small functions. Several tools...

FALCON is a NIST-selected post-quantum digital signature scheme whose performance bottleneck lies in the SamplerZ subroutine for discrete Gaussian sampling. We present a throughput-optimized, custom hardware implementation of SamplerZ that introduces several architectural and algorithmic innovations to significantly accelerate signature generation. Our design incorporates a datapath-aware floating-point arithmetic pipeline that strategically balances latency and resource utilization. Our...

Multivariate cryptography is one of the challenging candidates for post-quantum cryptography. There exists a huge variety of proposals, most of them have been broken substantially. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate polynomials $\mathcal{F}$ (often quadratic). The secret polynomials $\mathcal{F}$ possess a trapdoor that allows the legitimate user to find a solution of...

Encrypted matrix-vector multiplication is a fundamental component of a variety of applications that involve data privacy concerns. Current algorithms utilizing fully homomorphic encryption (FHE) generally use batching to enhance computational efficiency while neglecting the sparsity of the matrices, a characteristic that exists naturally in many practical situations. Alternatively, porting plaintext algorithms that address sparsity may fail to utilize batching and introduce additional...

Recent years have witnessed significant progress in composable masked AES designs based on Hardware Private Circuits (HPCs) under the Probe-Isolating Non-Interference (PINI) framework. However, these designs still suffer from substantial randomness requirements and area overhead at higher protection orders. In this work, we revisit Domain-Oriented Masking (DOM), originally proposed by Gross et. al. in 2016, and leverage the DOM-$dep$ and DOM-$indep$ multipliers to construct efficient AES...

This work establishes the CRO Trilemma: no post-quantum proof system can simultaneously satisfy the following three properties beyond negligible failure probability: (i) Confidentiality, quantified by Priv > 1 - negl(lambda); (ii) Reliability, with Rel > 1 - negl(lambda); and (iii) Legal Opposability, measured by contextual entropy H_Opp ≈ log |V_J|, where V_J denotes the validation space of a polynomial-time institutional verifier J. The result formalizes the Invisible Authenticity...

We study the multi-source randomness extraction and generation properties of the monolithic random oracle (RO), whereby one is tasked with extracting or generating uniform random bits from multiple arbitrary unpredictable sources. We formalize this problem according to the query complexities of the involved parties—sources, distinguishers, and predictors, where the latter are used to define unpredictability. We show both positive and negative results. On the negative side, we rule out...

Fully Homomorphic Encryption over the Torus (TFHE) enables efficient evaluation of arbitrary lookup tables (LUT) over encrypted data, allowing complex functions to be computed without decryption. However, in TFHE, only lookup tables with a negacyclic structure can be homomorphically evaluated, which limits the range of functions that can be supported. To overcome this limitation and enable the evaluation of arbitrary functions, the notion of full-domain functional bootstrapping (FDFB) was...

We introduce a novel technique for verifying Schnorr signatures using fast endomorphisms. Traditionally, fast endomorphisms over prime field curves are used to decompose a scalar into two scalars of half of the size. This work shows that the context of the verification of signatures allows for the decomposition into three scalars of a third of the size. We apply our technique to three scenarios: verification of a single Schnorr signature, batch verification, and verification of BLS...

Secure Multi-Party Computation is a privacy-enhancing technology that allows several parties to securely compute on distributed private data. In the line of the well established SPDZ protocol, the by far most expensive task is the generation of Beaver triples in the so called offline phase. Silentium is our implementation of an actively secure offline phase in the form of a Pseudorandom Correlation Generator for Beaver triples (Bt-PCG, Boyle et al. CRYPTO 2020), which, as any PCG, is...

The LowMC-based post-quantum signature scheme Picnic was selected as a third-round candidate for NIST PQC, attracting wide attention to the design of efficient and secure post-quantum signature schemes using Symmetric Techniques for Advanced Protocols (STAP). Symmetric primitives designed for advanced protocols such as secure multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge (ZK) proof systems, with the goal of reducing the number of multiplication...

Fully Homomorphic Encryption (FHE) allows computations on encrypted data without revealing any information about the data itself. However, FHE ciphertexts include noise for security reasons, which increases during operations and can lead to decryption errors. This paper addresses the noise introduced during bootstrapping in Torus Fully Homomorphic Encryption (TFHE), particularly focusing on approximation errors during modulus switching and gadget decomposition. We propose a mean compensation...

SNAIL (Succinct, Non-interactive, Alon-compressed, Instant argument for Layered circuits) turns any depth-\(d\) arithmetic circuit into a non-interactive argument whose prover runs within \(1 + c(d,k,n)\) of plain circuit execution, where \(c(d,k,n) = \frac{3\,(k+n+1)}{k\,d + n + 1}\). For the representative choice \(k = n = 4\) and \(24 \le d \le 32\) this means only 21–28 % overhead. Core idea: A constant-round zerocheck based on a difference-driven Alon decomposition...

We present a unifying framework for proving the knowledge-soundness of KZG-like polynomial commitment schemes, encompassing both univariate and multivariate variants. By conceptualizing the proof technique of Lipmaa, Parisella, and Siim for the univariate KZG scheme (EUROCRYPT 2024), we present tools and falsifiable hardness assumptions that permit black-box extraction of the multivariate KZG scheme. Central to our approach is the notion of a canonical Proof-of-Knowledge of a Polynomial...

Zero-knowledge (ZK) proofs have been recently explored for the integrity of machine learning (ML) inference. However, these protocols suffer from high computational overhead, with the primary bottleneck stemming from the evaluation of non-linear functions. In this paper, we propose the first systematic ZK proof framework for non-linear mathematical functions in ML using the perspective of table lookup. The key challenge is that table lookup cannot be directly applied to non-linear functions...

Oblivious permutation (OP) enables two parties, a sender with a private data vector $x$ and a receiver with a private permutation π, to securely obtain the shares of π(x). OP has been used to construct many important MPC primitives and applications such as secret shuffle, oblivious sorting, private set operations, secure database analysis, and privacy-preserving machine learning. Due to its high complexity, OP has become a performance bottleneck in several practical applications, and many...

The introduction of shared computation architectures assembled from heterogeneous chiplets introduces new security threats. Due to the shared logical and physical resources, an untrusted chiplet can act maliciously to surreptitiously probe the data communication between chiplets or sense the computation shared between them. This paper presents Garblet, the first framework to leverage the flexibility offered by chiplet technology and Garbled Circuits (GC)-based MPC to enable efficient,...

Efficient anonymous credentials are typically constructed by combining proof-friendly signature schemes with compatible zero-knowledge proof systems. Inspired by pairing-based proof-friendly signatures such as Boneh- Boyen (BB) and Boneh-Boyen-Shacham (BBS), we propose a wide family of lattice-based proof-friendly signatures based on variants of the vanishing short integer solution (vSIS) assumption [Cini-Lai-Malavolta, Crypto'23]. In particular, we obtain natural lattice-based adaptions of...

We revisit the polynomial attack to the $\mathsf{ROS}$ problem modulo $p$ from [BLLOR22]. Our new algorithm achieves a polynomial time solution in dimension $\ell \gtrsim 0.725 \cdot \log_2 p$, extending the range of dimensions for which a polynomial attack is known beyond the previous bound of $\ell > \log_2p$. We also combine our new algorithm with Wagner's attack to improve the general $\mathsf{ROS}$ attack complexity for some of the dimensions where a polynomial solution is still not...

Masking is a commonly used countermeasure against side-channel attacks, encoding secrets into multiple shares such that each share leaks only partial information. A longstanding question is under what noise conditions masking guarantees security, and how this security scales with the number of shares. While sufficient conditions have been known for binary fields and in high-noise regimes, the borderline and low-noise cases have remained poorly understood. In this work, we close this gap...

Folding is a technique for building efficient succinct proof systems. Many existing folding protocols rely on the discrete-log based Pedersen commitment scheme, and are therefore not post-quantum secure and require a large (256-bit) field. Recently, Boneh and Chen constructed LatticeFold, a folding protocol using lattice-based commitments which is plausibly post-quantum secure and can operate with small (64-bit) fields. For knowledge soundness, LatticeFold requires the prover to provide a...

Anamorphic encryption (AE), introduced by Persiano, Phan and Yung at Eurocrypt `22, allows to establish secure communication in scenarios where users might be forced to hand over their decryption keys to some hostile authority. Over the last few years, several works have improved our understanding of the primitive by proposing novel realizations, new security notions and studying inherent limitations. This work makes progress, mainly, on this last line of research. We show concrete...

We present new techniques for garbling mixed arithmetic and boolean circuits, utilizing the homomorphic secret sharing scheme introduced by Roy \& Singh (Crypto 2021), along with the half-tree protocol developed by Guo et al (Eurocrypt 2023). Compared to some two-party interactive protocols, our mixed garbling only requires several times $(<10)$ more communication cost. We construct the bit decomposition/composition gadgets with communication cost $O((\lambda+\lambda_{\text{DCR}}/k)b)$...

Privacy and security have become critical priorities in many scenarios. Privacy-preserving computation (PPC) is a powerful solution that allows functions to be computed directly on encrypted data. Garbled circuit (GC) is a key PPC technology that enables secure, confidential computing. GC comes in two forms: Boolean GC supports all operations by expressing functions as logic circuits; arithmetic GC is a newer technique to efficiently compute a set of arithmetic operations like addition and...

Index Calculus (IC) algorithm is the most effective probabilistic algorithm for solving discrete logarithms over finite fields of prime numbers, and it has been widely applied to cryptosystems based on elliptic curves. Since the IC algorithm was proposed in 1920, the research on it has never stopped, especially discretization of prime numbers on the finite fields, both the algorithm itself and its application have been greatly developed. Of course, there has been some research on elliptic...

Side-channel analysis (SCA) does not aim at the algorithm's weaknesses but rather its implementations. The rise of machine learning (ML) and deep learning (DL) is giving adversaries advanced capabilities to perform stealthy attacks. In this paper, we propose DL-SCADS, a DL-based approach along with signal decomposition techniques to leverage the power of secret key extraction from post-silicon EM/power side-channel traces. We integrate previously proven effective ideas of model ensembling...

In this informal note, we describe how to bypass the characteristic bound in logUp [eprint 2022/1530] by abstracting the notion of (pole) multiplicity. The method applies as well to the GKR-variant from Papini and Haböck [eprint 2023/1284], and it moreover unlocks fractional decomposition lookups over binary fields.

We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers of the form $P^2 Q$ with $\log Q = \Theta(n^a)$ for $a \in (2/3, 1)$ in space and depth sublinear in n (specifically, $\widetilde{O}(\log Q)$) using $\widetilde{O}(n)$ quantum gates; for these integers, no known classical algorithms exploit the relatively...

A proof of solvency (or proof of reserves) is a zero-knowledge proof conducted by centralized cryptocurrency exchange to offer evidence that the exchange owns enough cryptocurrency to settle each of its users' balances. The proof seeks to reveal nothing about the finances of the exchange or its users, only the fact that it is solvent. The literature has already started to explore how to make proof size and verifier time independent of the number of (i) users on the exchange, and (ii)...

This article generalizes the widely-used GLV decomposition for (multi-)scalar multiplication to a much broader range of elliptic curves with moderate CM discriminant \( D < 0 \). Previously, it was commonly believed that this technique can only be applied efficiently for small values of \( D \) (e.g., up to \( 100 \)). In practice, curves with \( j \)-invariant \( 0 \) are most frequently employed, as they have the smallest possible \( D = -3 \). However, $j = 0$ curves are either too...

Lattice-based succinct arguments allow to prove bounded-norm satisfiability of relations, such as $f(\vec{s}) = \vec{t} \bmod q$ and $\|\vec{s}\|\leq \beta$, over specific cyclotomic rings $\mathcal{O}_\mathcal{K}$, with proof size polylogarithmic in the witness size. However, state-of-the-art protocols require either 1) a super-polynomial size modulus $q$ due to a soundness gap in the security argument, or 2) a verifier which runs in time linear in the witness size. Furthermore,...

In 2016,Petit et al. first studied the implementation of the index calculus method on elliptic curves in prime finite fields, and in 2018, Momonari and Kudo et al. improved algorithm of Petit et al. This paper analyzes the research results of Petit, Momonari and Kudo, and points out the existing problems of the algorithm. Therefore, with the help of sum polynomial function and index calculus, a pseudo-index calculus algorithm for elliptic curves discrete logarithm problem over prime finite...

This paper proposes a fast, compact key-size, and hardware-friendly bootstrapping using only 16-bit integer arithmetic and fully homomorphic encryption FHE16, which enables gate operations on ciphertexts using only 16-bit integer arithmetic. The proposed bootstrapping consists of unit operations on ciphertexts, such as (incomplete) number theoretic transform (NTT), inverse NTT, polynomial multiplication, gadget decomposition, and automorphism, under a composite modulus constructed from...

During the past decade, Deep Neural Networks (DNNs) have proven their value across a wide variety of applications; however, despite their importance, protecting their intellectual property remains an open issue. Recent work has successfully extracted DNNs using cryptanalytic methods in hard-label settings, showing that it is possible to copy a DNN with high fidelity, i.e., a high degree of similarity in correct/incorrect output predictions which corresponds to the proportion of samples for...

We present an efficient Publicly Verifiable Fully Homomorphic Encryption scheme that, along with being able to evaluate arbitrary boolean circuits over ciphertexts, also generates a succinct proof of correct homomorphic computation. Our scheme is based on FHEW proposed by Ducas and Micciancio (Eurocrypt'15), and we incorporate the GINX homomorphic accumulator (Eurocrypt'16) for improved bootstrapping efficiency. In order to generate the proof efficiently, we generalize the widely used Rank-1...

This paper explores advancements in the Gentry-Sahai-Waters (GSW) fully homomorphic encryption scheme, addressing challenges related to message data range limitations and ciphertext size constraints. We introduce a novel approach utilizing the Chinese Remainder Theorem (CRT) for message decomposition, significantly expanding the allowable message range to the entire plaintext space. This method enables unrestricted message selection and supports parallel homomorphic operations without...