Vector retrieval increasingly runs over sensitive embedding databases. Backend-compatible protections are desirable in such settings in that they transform the plaintext vectors while leaving the search algorithm itself unchanged. However, the protected database then leaks some geometry, that is, information about the distances between the stored vectors. We study membership-inference attacks on such leakage given a single database snapshot and known plaintexts. Our central finding is that...

An inherent challenge in cryptography is finding realistic and meaningful models and assumptions. Such assumptions must be fal- sifiable. For symmetric-key cryptography in the standard model (i.e., black-box without leakage), it is conjectured that we have identified the right assumptions: pseudorandom functions and permutations (PRFs and PRPs). However, when considering side-channel attacks (SCAs) that exploit physical side-channel leakage, the answer is less clear. Moreover, the...

Eevee's Umbreon and Espeon modes claim online authenticated-encryption security under nonce reuse. We give an independent analysis of associated-data correlations that yield probability-one non-empty-message forgeries with three encryption queries and one verification query. Two AD-only tags reveal a mask difference that translates a ciphertext to another AD value. The basic attacks and their proof diagnosis overlap with independent and concurrent work by Mao et al. Our complementary...

Eevee is a family of three AEAD modes, Umbreon, Jolteon, and Espeon, proposed at CCS 2023 for IoT-to-cloud secure computation. We analyze structural flaws in the algorithms of the supplied full-version specification and the proof steps underlying their online authenticated-encryption claims. An AD-free, two-encryption prefix distinguisher has advantage $1-2^{-n}$ in the ideal-forkcipher model, contradicting the specified online ideal object. Independently, the separable associated-data...

Choosing a hardware S-box means balancing cryptanalytic strength (differential uniformity δ, linearity L, and algebraic degree) against circuit cost (AND count and AND depth D). Under masking, non-linear gates dominate silicon area, registers, and fresh randomness, while D sets pipeline latency. As a result, automated searches have largely retreated to quadratic permutations (D = 1), whose slow degree growth forces high cipher round counts. We present Yoshan, a co-synthesis engine that...

Authenticated Encryption with Associated Data (AEAD) provides confidentiality and integrity, but traditional security notions do not prevent ciphertexts from decrypting correctly under multiple keys. This motivates committing security, which requires ciphertexts to bind to their encryption inputs uniquely. Recent analyses revealed commitment failures in several forkcipher-based AEAD schemes, leaving open the question of whether these failures are inherent to forkciphers or design specific....

Integral distinguishers can reveal more than a zero-sum property: the number of ones in an output component may be divisible by a high power of $2$, rather than merely being even. To exploit this divisibility, we relate linear, integral, differential-linear, and restricted differential sums through two-way conversions with explicit divisibility guarantees and data complexity, recovering established links as special cases. We derive exact random-permutation probabilities and rigorous bounds...

In this paper, we present a novel framework for cube attacks named cube attacks with elimination strategy. The core idea is to find specific key conditions and cubes such that their superpolies under these key conditions can be efficiently computed. By recovering these conditional superpolies, we can solve the corresponding equation system and thereby retrieve key information. If a sufficient number of such key conditions can be found, the attack can be extended to a larger key space. To...

Almost perfect nonlinear (APN) functions provide optimal resistance to differential cryptanalysis in characteristic two, and constructing new infinite families inequivalent to the known ones remains an important problem in the study of cryptographic functions. We introduce extended biprojective functions, obtained by augmenting biprojective polynomials with truncated trace terms, and establish a new infinite family of quadratic APN functions. To investigate these constructions, we develop an...

Recently, the Institute of Commercial Cryptography Standards (ICCS) launched the Next Generation Commercial Cryptographic Algorithm Program (NGCC), which includes a standardization process for cryptographic hash functions. In this note, we analyze the mode of operation of Duet, one of the hash-function candidates. Duet is a permutation-based hash function directly inspired by the Alternating Sponge (ASP). Both constructions use two permutations on $b=r+c$ bits, split into an outer part of...

At CRYPTO 2016, Cogliati and Seurin proposed EWCDM as a nonce-based MAC construction making two block cipher calls and one almost-XOR-universal (AXU) hash evaluation and achieving beyond-birthday-bound (BBB) security. They noticed that a simplified variant of EWCDM named Encrypted Wegman--Carter (EWC) admits a birthday distinguishing attack. Later, at CRYPTO 2017, Mennink and Neves proposed EWCDMD, the dual of EWCDM, as a new candidate BBB-secure MAC, but at EUROCRYPT 2020 Nandi proposed a...

We present the first new infinite family of APN functions obtained by applying the switching construction to a known family since the introduction of the Budaghyan-Carlet-Leander family in 2009. Our construction is also the first example of an infinite APN family obtained via the switching construction from an infinite family of non-power functions. More generally, we study families of APN functions that can be obtained from the Budaghyan-Helleseth-Kaleyski family by the addition of...

Belkheyar et al. introduced ChiChi as the even-dimensional, low-latency nonlinear core of ChiLow (Eurocrypt 2025), and Andreoli et al. generalized it into the SWAP and 4-cycle families (ToSC 2025/3), conjecturing five bounds on the linear height and component linear nullity of their inverses, supported by experiments in small dimensions. We settle all five conjectures: Conjectures 1–4 hold for every admissible branch length, and Conjecture 5 is false. In addition, we derive consequences for...

The overwhelming majority of the Keccak instances standardized and used in practice today make use of the Keccak-$f$ [1600] permutation or reduced-round versions of it. There are a few use cases where using a smaller permutation width would be beneficial, notably when one has to hash many very short messages. To address this, the present note defines instances that use the Keccak-$p$[800, $n_r = 12$] permutation, collectively under the name MiniSHAKE.

Quantum attacks based on Simon's algorithm rely on Boolean functions with hidden XOR periods. At ASIACRYPT 2025, Liu et al. introduced a symbolic automated search model for periodic functions used in distinguishers. However, for distinguishers on target ciphers, the search mainly works with truncated differences and does not jointly constrain exact differential propagation. A separate modeling gap arises in the key-recovery setting: the model does not cover the key-dependent periodic...

Secure computation often hashes high-entropy fixed-length values in inner loops. A public permutation with terminal Davies--Meyer feed-forward can expose the permutation value when an application applies another feed-forward step. We study an input-fed alternative that injects the input after every AES round. The base construction, $H_{128}:\{0,1\}^{128}\to\{0,1\}^{128}$, uses ten full AESENC-style rounds with keys $x+c_i$ and no AES key expansion. Its concrete analysis adapts...

Almost pairwise independence asks how closely a block cipher reproduces the joint output distribution of a random permutation on two distinct plaintexts. Existing analyses of AES with independent round keys combine bounds on the distribution after the first few rounds with contraction over later rounds. Diffusion makes local output differences dependent, and estimating local responses or successive transitions separately can lose useful information. We preserve these dependencies in two...

GCM is the leading authenticated encryption scheme. With its application in TLS alone, it finds millions of uses every day. However, in the last years, various shortcomings of GCM have been observed: mistakes in earlier proofs, non-optimal security degradation in case of shorter tags, the support for a $96$-bit nonce only (concatenated with a $32$-bit counter) for the most widely implemented variant, but most of all, the brittle resistance against nonce misuse. This latter shortcoming is...

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...

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...

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...

The complexity of fast correlation attack is fundamentally determined by the correlations of the linear approximations used. Conventional fast correlation attacks either rely on a single dominant linear approximation or use the lower bound to evaluate the resulting correlation of multiple linear approximations, which have the same output mask and distinct input masks. How to exploit multiple linear approximations with distinct output masks remains an open problem. In this paper, we propose a...

Distribution-aware encryption seeks guarantees tailored to the probability law of the protected data and the secret key. We study simultaneous message-recovery, key-recovery, and target-distribution semantic security for arbitrary finite joint distributions, without assuming that messages and keys are independent. We represent encryption by a decomposition of the joint probability matrix and construct this decomposition through capacity-controlled randomized rounding. A stepwise...

Wide-block block ciphers have attracted significant interest due to emerging high-throughput encryption requirements and NIST's Accordion Mode Process. The primary choice for such ciphers is Rijndael-256, also known as WAES. At the same time, independent efforts continue to explore more efficient designs and implementations. In this paper, we present LEANY, a 256-bit block cipher with a 256-bit key. LEANY is a nibble-oriented SPN whose state is an 8×8 matrix of 4-bit nibbles. Each round...

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...

We study affine and linear equivalence of functions $F,G:\mathbb{F}_q^n\to\mathbb{F}_q^m$. We present practical equivalence algorithms that handle arbitrary functions (any algebraic degree, permutations and non-permutations) and are particularly effective on structured instances with nontrivial self-equivalences, covering most cryptographically relevant cases. We also give a dedicated algorithm for computing generators for the group of self-equivalences $(A_1,A_2)$ satisfying $A_2\circ F =...

Context-committing security binds an authenticated encryption (AE) ciphertext uniquely to its encryption context. Many conventional AE schemes lack this guarantee, while most generic committing transforms rely on idealized primitives. We develop committing AE from explicit forkcipher collision-resistance properties: $\mathsf{fCR}$ and zero-message collision resistance ($\mathsf{zmCR}$). For an $n$-to-$2n$-bit forkcipher, we establish matching query complexities of order $2^{n/2}$ and...

We study the regular indifferentiability of the sum of two n-bit permutations. Previous work proved 2n/3-bit security and gave a 5n/6-bit attack against the uniform simulator. We prove 3n/4-bit se curity for the simulator and give a matching attack. Our proof bounds the KL divergence between response distributions by tracking the bias in unrevealed construction values through their conditional distribution, which was not analysed in detail in previous work. To exceed this thresh old, we...

At EUROCRYPT 2025, Carlini {\em et al.} proposed a breakthrough in the cryptanalytic extraction on hard‑label (S1) deep neural networks (DNNs), demonstrating polynomial-time signature and sign recovery. However, Carlini {\em et al.}'s sign‑recovery method ({which we call \em Future Toggle}) suffers only a marginal advantage over random guessing, producing high‑confidence wrong sign predictions in deeper layers. Such errors trigger expensive exponential‑time enumeration. This work...

The meet-in-the-middle (MITM) attack framework is one of the most powerful cryptanalytic techniques with broad influence to preimage, key recovery, and collision attacks. In this paper, we present two generic techniques. First, we observe that the constant space in MITM attacks is an exploitable source of degrees of freedom: its value-independence enables MITM-style partition and acceleration of attack subprocesses. With this intuition in mind, we revisit the single-color initial structure...

The Walsh-Hadamard transform (WHT) computes the correlation of a Boolean function with every linear function at once. Cryptanalytic workflows transform large arrays repeatedly, in batches. However, available tools specialize in particular data types, platforms, or ecosystems. We present LibFWHT, an open-source C library for dense WHTs, with Python bindings and a command-line interface. It includes vectorized, multicore, and graphics processing unit (GPU) backends, batch operations, and...

The alternative mod-$2$/mod-$3$ function is one of the most widely used weak PRF constructions in modern cryptographic protocols. Despite its practical importance, its security has received relatively limited attention, with the main cryptanalytic results consisting of two distinguishing attacks due respectively to Cheon et al. and Johansson et al. In this work, we revisit the cryptanalysis of this primitive by analyzing the output distribution of the weak PRF under fixed Hamming weights for...

When looking at authenticated encryption schemes, we have schemes that process the input data by having serial calls to their underlying building blocks, like duplex-based constructions, and schemes that allow for parallel calls to their underlying building blocks, like the Galois Counter Mode (GCM). Naturally, one can parallelize a serial scheme by distributing the data to encrypt over different calls to the serial scheme. However, there are many different choices to be made, like how to...

MDS matrices are a key structure for providing optimal diffusion in symmetric primitives. However, the theoretical analysis of their cost remains limited. This issue is particularly relevant to arithmetization-oriented permutations, where designs often either use costly MDS matrices or sacrifice the MDS property to reduce the number of constraints. This paper studies the number of fan-in-two additions needed to implement MDS matrices. We represent fan-in-two addition constraints by a...

The AES S-box is constructed from finite field inversion followed by a fixed affine transformation. Since inversion possesses intrinsic Frobenius symmetries among its coordinate realizations, we study how these basis symmetries are altered by outer affine transformations. We first develop a deterministic rigidity criterion for transformed inversion and apply it to the AES S-box. This shows that the linear part of the AES S-box affine transformation alone makes the transformed...

Areion is a family of AES-based permutations designed for fast hashing and authenticated encryption of short messages. We identify errors in how its security analysis converts active S-box counts into differential and linear probability bounds, and give corrected calculations.

Zero-Knowledge (ZK) proof systems have become a cornerstone of privacy-preserving technologies and blockchain scalability. However, traditional hash functions are often inefficient within ZK protocols due to their high constraint complexity in arithmetic circuits. While various ZK-friendly hash functions have been proposed to address this bottleneck, their diverse algebraic structures and varying security margins make it difficult for practitioners to select the optimal primitive. We...

Fuzzy extractors derive stable cryptographic keys from noisy biometric measurements (Dodis et al., EUROCRYPT 2004). Despite nearly three decades of research, existing fuzzy extractor constructions do not provide strong security for the biometric modalities deployed on modern devices, particularly fingerprints and facial recognition. Recent attacks highlight the gap between known analysis of theoretical constructions and the security levels required for practical deployment (Zhu and Wang,...

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...

Minimizing the data complexity required to recover the secret key of reduced-round block ciphers is a fundamental problem in symmetric cryptanalysis. Here, we introduce Polytopic Sieving, a data-efficient key-recovery framework and apply it to reduced-round AES. By characterizing the algebraic dependencies of anchor bytes (the reference state values that govern differential transitions across S-boxes), we show that cross-column and cross-row geometric consistency substantially restricts the...

The Wrong-Key Randomization (WKR) hypothesis governs data-complexity estimates in differential cryptanalysis: wrong-key guesses are assumed to behave as a random permutation would. Exact computation of fixed-key differential probabilities was, until recently, infeasible. We use quasidifferential trails to compute the exact wrong-key distribution for the key-recovery map \(G_{k,k'} = F_{k'}^{-1}\!\circ F_k\) in PRESENT-like SPNs. A mask-first reformulation exposes a...

ARX-based cryptographic primitives have received considerable attention for their efficient software implementations. For a long time, however, constructing ARX primitives with provable resistance against single-trail differential and linear cryptanalysis remained an open problem. Dinu et al. addressed this problem by introducing the Long Trail Strategy (LTS), the first general design strategy for establishing such bounds for ARX symmetric-key primitives. A remaining challenge in applying...

We propose the arithmetization-oriented (AO) hash function Arion, following a permutation-based design approach. We first define the permutation Arion-π over the finite field F_p, where (p > 2) is prime. The design of Arion-π is based on the recently introduced generalized triangular polynomial system, a novel algebraic framework for constructing cryptographic permutations using polynomials over finite fields. Using this permutation, we define the hash function Arion in two modes: the...

White-box security settings assume an extremely powerful adversary having full visibility and control of the software implementation and internal computations. Leakage-based attacks extract secret information via a local passive attacker (e.g., malware) and transmit it to a remote server. However, an active adversary, who can perform fault injections in a white box setting, has received limited attention, especially in the symmetric-key setting. In this paper, we initiate a formal...

MERIDIAN is a 128-bit blockcipher proposed as a lightweight AES alternative. We show that its “Directional Substitution” layer is not injective by giving an explicit collision. This yields a full 12-round collision for every key. Consequently, no keyed instance of MERIDIAN is a permutation, so no decryption function can invert encryption on all plaintexts, and its blockcipher and PRP security claims fail. We additionally identify a one-round differential that exceeds the claimed bound by a...

Message authentication codes (MAC) are ubiquitous and are considered to be the most important tool employed to ensure authenticity of messages in the symmetric key setting. In this work, we aim to empower MACs with a newly added functionality of updatablility, i.e., the goal is to construct a MAC scheme where the authentication tag for a message can be updated with every update to the message without recomputing the tag for the entire message. Such a functionality can be useful in several...

Linear cryptanalysis measures the correlation of a cipher with the characters of the group used to define differences. If that group is replaced by a second elementary abelian group structure on the same set, here the one coming from a binary bibrace, then the admissible masks are no longer the ordinary scalar products: exactly half of them survive, and the other half are forced to be quadratic. Beyne's geometric approach develops linear cryptanalysis over an arbitrary finite abelian group,...

When two S-box layers of a round are separated by no key addition, the round correlation is a signed sum over all compatible intermediate masks, not a product of layer correlations, so the product rule can fail in either direction. Our central finding is that evaluating this intra-round sum exactly changes the assessment of the published linear cryptanalysis of SPEEDY, whose two S-box layers are separated only by ShiftColumns. We first develop the linear cryptanalysis of this setting:...

This paper studies the post-quantum multi-key security of Galois/Counter Mode (GCM) in the Quantum Ideal Cipher Model (QICM). GCM is one of the most widely used AEAD schemes. In practice, widely deployed cryptosystems are often instantiated under many independent keys, making the multi-key setting practically relevant. A trivial reduction from the multi-key setting to the single-key setting incurs a security loss proportional to the number of keys. In particular, in the post-quantum...

We present the Pilot--Sailor Framework, an LLM-guided system for studying theoretical open problems in symmetric cryptography. Pilot proposes intermediate statements and proof plans. Sailor attempts formal proofs, and the proof assistant admits only checked declarations to the verified context. We apply this methodology to Boolean-function theory and symmetric cryptanalysis through fourteen mathematical case studies, comprising complete resolutions, corrected formulations, counterexamples,...

Large-state ARX-based S-boxes have become a key component of modern lightweight cryptographic designs, yet deriving tight security bounds for their differential and linear properties remains challenging. In this paper, we study the security of Alzette, the 64-bit ARX-based S-box used in the SPARKLE permutation, and present a general framework for the analysis and design of large-state ARX S-boxes. We introduce SMCS, a hybrid search strategy that combines MILP-based optimization with...

Subspace differential uniformity (SDU) measures the concentration of a differential distribution table (DDT) on affine subspaces. We determine the exact optima of the two axial affine-SDU coordinates in dimension five and establish a strict gap between locally admissible support designs and supports realizable by almost perfect nonlinear (APN) permutations. We first prove that every $16$-subset of $\mathbb{F}_2^5$ meets some affine $3$-flat in at least six points. Equality holds precisely...

Degree-sum-freedom is a local criterion for division-property propagation from affine input spaces. Immediately after defining this criterion, the published chapter asserts invariance under extended-affine (EA) equivalence. We show that this assertion does not hold beyond ordinary sum-freedom and quantify the resulting variation. First, the natural Gold APN pair $x^3$ and $x^3+x$ has exact proper-flat values 3 and 2 on an infinite sequence of dimensions. We then study a known...

The deployment of advanced cryptographic protocols such as zero-knowledge proofs (ZKPs) requires symmetric primitives optimized for fast verification inside proof systems. In frameworks based on Rank-1 Constraint Systems (R1CS), prover performance and proof size are dominated by the cost of arithmetization, specifically, by the number of nonlinear multiplication constraints. Traditional bit-oriented designs are typically inefficient under this metric. In this paper, we introduce Lumora, a...

Rotational-XOR (RX) cryptanalysis extends rotational cryptanalysis by combining rotational relations with XOR translations, enabling the analysis of symmetric-key primitives even in the presence of symmetry-breaking constants. Existing analyses of RX characteristics, however, typically rely on independence assumptions when estimating characteristic probabilities, which may lead to inaccurate probability evaluations and even incompatible characteristics. In this paper, we introduce the...

Universal hash functions (UHFs) are basic building blocks in cryptography, making the topic of designing secure, fast UHFs of longstanding interest. This paper presents an exploration of the design space for multivariate UHFs, that is UHFs that involve the evaluation of a multivariate polynomial over a finite field. We focus on two-level designs, wherein a lower-level hash function produces intermediate values that are consumed by a higher-level one, and where both hash functions are based...

Conditional linear cryptanalysis represents an extension of linear cryptanalysis and has been applied to DES and AES. Notably, it enables the construction of a linear distinguisher for 4-round AES, which is considered unattainable through standard linear cryptanalysis. The underlying principle is that the correlation of a linear approximation can be improved when the data is restricted to a specific subspace or subset, thereby allowing more effective linear cryptanalysis. The critical...

Modern zero-knowledge (ZK), fully homomorphic encryption (FHE) and Multi-party Computation (MPC) protocols have motivated research interest in Arithmetization-Oriented (AO) cryptographic primitives. The use of these protocols on embedded platforms requires consideration for protection against side-channel analysis (SCA), including timing and power attacks. Compared to traditional bit-oriented block ciphers, the design of side-channel countermeasures for AO-based ciphers poses unique...

In this work, we propose three techniques for advancing cryptanalysis of round-reduced AES, two of which exploit the multiplicative inverse, and a third, structural, property that generalizes the S-box switch to multiple quartets. Firstly, we formalize the cross-ratio property for tracing a nonlinear equation over $F_{2^8}$ from the differences of four distinct inputs or their respective outputs through the key-wrapped multiplicative inverse. While the underlying properties of the...

In this paper, we propose several classes of permutation polynomials having the form $\sum\limits_i(x^{2^m}+x+\delta)^{s_i}+ax$ for $i=1$ or $i=2$, where the exponent $s_i$ satisfies $s_i\equiv 2^j\pmod{2^m+1}$ or $s_i \equiv 2^j\pmod{2^m-1}$ for some different integers $j$, $a\in\mathbb{F}_{2^m}^*$ and $\delta\in \mathbb{F}_{2^{2m}}$. More precisely, by applying the AGW criterion and determining the number of solutions to certain equations over $\mathbb{F}_{2^{2m}}$, several classes of...

Boomerang cryptanalysis is inherently a four-point phenomenon, yet its recent geometric formulation relies on a 3-wise representation imposed by a quartet-sum-zero assumption. This simplification makes the transition matrices tractable, but it also removes boomerangs with unequal paired differences and prevents the framework from modeling impossible boomerang distinguishers. We propose an exact 4-wise geometric framework for boomerang cryptanalysis that is a \emph{strict generalization}...

Side-channel analysis (SCA) attacks rely on leakage from a target device. It is common to assume that linear operations implemented by XOR gates produce symmetric leakage and carry negligible side-channel information. In practice, leakage from XOR gates produces complex, non-independent, and time-varying asymmetric behavior. The paper introduces Feature Estimation based Attacks (FEbA) -- a dedicated profiling attack that exploits these asymmetries. The attack is versatile; it was...

Zero-knowledge (ZK) proof systems have developed rapidly in recent years, with hash functions as one of their central building blocks. Since these often dominate the prover cost, circuit-friendly hash function design has become an active research area. Most hash proposals target prime fields, although recent protocols such as Binius and VOLE-based ZK operate natively over binary extension fields \(\mathbb{F}_{2^n}\). These binary field protocols reduce the cost of proving widely used binary...

Integral cryptanalysis analyzes block ciphers using input structures for which the sum of a chosen function of the output bits becomes key-independent. However, most methods still test one output expression at a time, so they can miss distinguishers that emerge only when several outputs are combined, either linearly or nonlinearly. They are also not designed to capture key-dependent integral combinations, which may hold deterministically on part of the key space. In this work, we develop...

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...

Idempotent functions are an important class of Boolean functions, related to cryptography and coding theory.} This paper investigates $k$-idempotent functions, a natural generalization of {idempotent} functions. Based on two classes of Dillon-type bent functions proposed in {the paper ``New characterizations of Dillon-like hyperbent functions via Dickson polynomials", by Z. Tu, C. Li, X. Zeng, T. Helleseth and N. Li, 02 October 2025, Volume 38, article number 35, in Journal of Cryptology}, ...

In this paper, we prove the post-quantum security of the Tweakable Key-Alternating Feistel cipher (TKAF) with a public random function in the Q1 model, under the assumption that the adversary is given quantum access to the internal primitive. Specifically, our target is the TKAF studied in the classical setting by Yan et al. (ACNS 2020), where the tweak is injected into the round-key XOR via a hash function of $\epsilon$-AXU family. Our proof draws on the post-quantum security proof for the...

The main contribution of this paper is to introduce Subspace Differential Uniformity (SDU) for S-boxes and block ciphers. The SDU is essentially a measure of how well any function spreads input differences clustered in affine subspaces away from affine clusters in output differences. We provide some lower bounds for the SDU and describe an efficient algorithm for computing the SDU. Moreover, we provide results for some popular classes of S-boxes up to $n=8$.

A key-independent secret-key distinguisher identifies inherent structural deviations of a block cipher from an ideal random permutation without recovering any information about the secret key. For the Advanced Encryption Standard (AES), various key-independent secret-key distinguishers have been proposed on reduced-round versions. In this paper, we study related-differential distinguishers for 5-round AES that combine a 1-round related differential trail with the 4-round generalized...

The increasing usage of Zero-knowledge proof protocols has raised the need for cryptographic primitives that are efficient in that setting, called Arithmetization-oriented primitives. The security of such permutations is commonly evaluated with the CICO-$k$ problem. The best known CICO-$1$ attack against ZK-Friendly permutations over $\mathbb{F}_q^t$ based on $\alpha$-inversions $x\mapsto x^{1/\alpha}$ exploits resultants (ASIACRYPT 2024, CRYPTO 2025). It starts from one input variable $x$...

Cryptographic compression functions are a core component of vector commitment schemes, including Merkle tree commitments, which are widely used in modern ZK-SNARK and STARK frameworks. Arithmetization-Oriented (AO) compression functions minimize multiplicative complexity over the framework's native field F_p, making them significantly more efficient than bit-oriented designs in algebraic circuits. To date, AO compression functions have been almost exclusively constructed by applying the...

This paper proposes a systematic approach to compute cryptanalytic properties of arbitrary Mealy machines or S-functions. Based on the geometric approach to cryptanalysis, we provide a uniform formula for any cryptanalytic property of such a function, as long as the property is compatible with the way its input and output are split into chunks. Examples include linear, (quasi) differential, (ultrametric) integral, differential-linear, and boomerang properties. To illustrate our results,...

Heterogeneous computing platforms increasingly rely on high-throughput data paths spanning CPUs and accelerators, yet most high-speed software ciphers are optimized primarily for CPU-centric execution models. We present AICE, an arithmetic-oriented stream cipher over \(\mathbb{Z}/2^{16}\mathbb{Z}\) with a 37-word (592-bit) internal state, a nonlinear feedback combining modular addition, multiplication, bitwise OR, and rotation, a 370-round initialization with post-initialization key...

We study generic committing attacks—where ciphertexts decrypt under more than one context, i.e., key, nonce, associated data—for sponge-based authenticated encryption. As our main contribution, we give three new committing attacks which outperform existing attacks. One of our attacks provides a counterexample showing that the previous proof for the committing security of Ascon-like schemes with zero-padding does not extend to all parameter choices: in case of 128-bit tags and 256-bit...

This short note shows that the conventional (2-subset) bit-based division property trail search problem is NP-complete.

Designing a secure symmetric-key cipher over a vector space over a field $\mathbb F_{p^n}^t$ is well known and understood by the cryptographic community. Even if the attacks are continuously improving, our current understanding regarding the design and security of the majority of the symmetric-key primitives has not fundamentally changed in the last 20 years. How does this picture change when we move to an integer ring $\mathbb Z_{p^n}^t$? Although the question is easy to state, it turns...

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...

(Multi-branch) Generalized Feistel Network~(GFN) enables the construction of block ciphers from non-linear components with small domains, and has been adopted in various block ciphers. Berger et al. (SAC 2013) introduced the Extended Generalized Feistel Network~(EGFN), which unified and extended existing Feistel-like structures by using a matrix representation. Given an arbitrary matrix, it is typically difficult to determine how many EGFN rounds are sufficient for pseudorandom...

Most symmetric modes of encryption that rely on PRP primitives are limited by the birthday bound over the block size (can’t encrypt more than $2^{n/2}$ blocks). This could be a severe limitation if current block width of 128 is used (can’t encrypt more than $2^{64}$ blocks) for cloud systems that transact a large amount of data. This limitation can be overcome by either realizing a mode of encryption based on a PRF (that doesn’t suffer from the birthday bound) or by using a wider block...

In response to the National Institute of Standards and Technology (NIST)'s 2024 call for wider variants of the Advanced Encryption Standard (AES), this paper presents the first FPGA-based hardware evaluation of Vistrutah, a recently proposed wide-block cipher constructed from AES round primitives. Vistrutah is implemented on a Xilinx Kintex UltraScale+ KCU116 FPGA and evaluated under identical conditions against the published wider Rijndael variant WAES-256. The 256-bit full configuration...

The Kim mapping, which belongs to the only known CCZ-equivalence class in even dimension that contains an APN bijection, and the APN bijections in dimension 9 exhibited by Beierle and Leander, all have a univariate representation corresponding to a cyclotomic mapping (aka Wan-Lidl polynomial), and they are all linearly-equivalent to functions with a highly-structured multivariate representation. In this paper, we show that functions having these properties, which correspond to...

Integral attacks pose a significant threat to block cipher security, yet providing guarantees against such attacks for a target block cipher is difficult. At ASIACRYPT 2021, Hebborn, Lambin, Leander, and Todo proposed the integral resistance property, which offers strong security guarantees for certain SPN and AND-RX block ciphers, assuming independent round keys. However, limitations remain: they proved a security bound for 13-round Present, while the longest known integral...

We propose an algorithm based on the partition refinement framework for testing and recovering CCZ and EA equivalence between a pair of vectorial Boolean functions. In contrast to existing approaches, our method can be used for any pair of functions regardless of their algebraic degree, image size and other properties, and it outperforms all currently known algorithms in terms of time and memory. The algorithm can also compute the automorphism group of the functions efficiently. Our...

The Even-Mansour cipher is a construction of a keyed pseudorandom permutation from a random unkeyed permutation. Its generalization to multiple rounds, known as iterated Even-Mansour or key-alternating cipher, is an important abstraction in block cipher design. Yet, while the security of single-round Even-Mansour is tight in the quantum setting (with attacks matching security proofs), much less is known on multi-round versions. In this paper we study the quantum security of iterated...

Linearization is a cryptanalysis technique in which a nonlinear function (an S-box) is represented by an affine mapping on a certain subset of inputs. Its variants were applied to analyze Keccak, LowMC, RAIN and AIM. In these primitives, the S-boxes are either very small (up to 5 bits) or are very specific monomial functions over a binary field. Linearization of arbitrary S-boxes was never practically explored due to the lack of theoretic, algorithmic, and cryptanalytic understanding. ...

Substitution-permutation networks (SPNs) are the most popular construction method for block ciphers and sponge permutations. Basically, we can divide SPNs into two groups by considering their diffusion layer profiles: bit-wise versus byte-wise (or nibble-wise) diffusion. In this paper, we suitably combine both approaches and present a more efficient and flexible construction that achieves a combination of small S-boxes, linear layers consisting only of XOR operations and bit permutations,...

We address the question of realizing privacy preserving analysis of user data. The abstract scenario considered is that an analyst aims to evaluate a function $f$ on some user data $X$. To achieve comprehensive privacy, it is necessary to protect the input $X$ directly. However, it is known that $f(X)$ may leak too much information about $X$ as well. A common approach to mitigate such risks is to make the computation differentially private. In practice, this is often accomplished by...

The Recording Standard Oracle with Errors (RstOE) technique is a quantum-security proof technique that provides a structured framework for analyzing adversarial capabilities in quantum settings. For example, it can be applied to prove the quantum security of compressing pseudorandom functions. However, against adaptive quantum chosen-plaintext adversaries, traditional RstOE-based proofs may suffer from the ''trivialization of norm'' problem. In the RstOE analyses considered in this paper,...

Existing leakage-resistant AEADs are rarely compatible with {\it single-length key} blockciphers (BCs), i.e., blockciphers with key-length equaling block-length. We present UEDTDM and UEDTMX, two single-length key BC-based leakage-resistant AEAD constructions. Both of them are one-pass with rate $1/4$, use ``partially fixed-key'' BC to maximize {\it practical} efficiency, and gather the strongest level of Grade-3 leakage-resistance (a terminology due to Bellizia et al., CRYPTO 2020)...

This paper presents a comprehensive analysis of modular addition from a cryptanalytic perspective, focusing on both linear and differential cryptanalysis techniques. We examine the probability distribution of carry bits in modular addition operations and demonstrate how these probabilities affect linear approximations. The paper provides detailed algorithms for constructing Linear Approximation Tables (LAT) and Difference Distribution Tables (DDT) for modular addition operations, along with...

Masking is a representative side-channel countermeasure that provides provable security. Among masking schemes, Boolean masking (BM) is widely adopted due to its simple sharing structure, while inner product masking (IPM) and code-based masking (CM) have been studied as alternatives that achieve a higher security order with the same number of shares---a property known as security order amplification in the bit-probing model. Recent work by Gaspoz and Dhooghe (TCHES 2025) proposed an IPM...

This paper presents vector-input keyed hashing modes that construct collision-resistant pseudorandom functions (CR PRFs) using a keyed hash function, where a vector refers to a sequence of variable-length strings. The proposed vector-input keyed hashing modes, VIM1 and VIM2, originate from the intuition that a string-input keyed hashing mode using a compression function results in a vector-input keyed hashing mode by replacing the compression function with a hash function. Combined with the...

In this paper, we propose a new widely applicable technique for constructing low-depth S-box circuits, which we call SLICE (Segmented Low‑depth Iterative Circuit Exploration). SLICE reduces circuit depth by partitioning circuits into subcircuits and applying bit-level optimizations. To mitigate the optimization cost of subcircuits with large bit-widths or high AND depth, SLICE temporarily reduces their bit-width during the search, making low-depth circuit construction feasible for various...

Designing cryptographic hash functions that simultaneously achieve high throughput and strong provable security remains a fundamental challenge in symmetric cryptography. Traditional constructions, such as the Merkle-Damg\aa rd (MD) and SPONGE paradigms, inherently suffer from structural limitations: they either expose internal chaining values to length-extension attacks or impose a rigid trade-off between security (capacity) and efficiency (rate), bounding their architectural...

We propose the \emph{Alternating Sponge} (ASP), a permutation-based hashing mode that explores how to obtain beyond-birthday-bound security without duplicating the full capacity state. The main design idea is to replace spatial state duplication by temporal alternation: ASP keeps two \(r\)-bit rate branches but lets them share a single \(c\)-bit capacity chain, and updates the two branches through alternating calls to two independent \((r+c)\)-bit permutations. This yields a state size of...

We study key-schedule design under boundary round-key leakage, namely leakage of the first round key, the last round key, or both end round keys. We propose the nonlinear key-schedule $\mathrm{RK}_i = K \oplus F\bigl(K \oplus T(i)\bigr)$, where $K$ is the master key, $T(i)$ is a public domain separation value, and $F$ is a public SPN-based permutation parameterized by its round count $N_F$. Under the boundary-leakage model considered in this paper, leakage of one end round key yields an...

This paper systematically analyzes the security of the two-branch Unified Feistel Lai Massey (UFLM) structure with independent random round functions under chosen plaintext and chosen ciphertext attacks, focusing on its indistinguishability from a random permutation. UFLM uses an invertible linear layer represented as a $2 \times 2$ block matrix $\varphi$ with blocks $A_{11}, A_{12}, A_{21}, A_{22}$. Previously, Dai et al. proved that when $A_{12}$ is invertible, $4$-round UFLM achieves CCA...

Low-entropy keys such as passwords and biometrics are pervasive, yet classical information-theoretic guarantees, such as perfect secrecy and entropic security, cannot generally be achieved in this regime. Honey encryption (HE) and homophonic ciphers (HC) tailor encryption to the message distribution to provide meaningful security, but their analyses do not establish optimal guarantees for arbitrary distributions. We ask: for messages and keys drawn independently from arbitrary distributions...

Feedback shift registers, such as Linear Feedback Shift Registers (LFSRs), Multi-Recursive Matrix Methods (MRMMs), and Lagged Fibonacci Generators (LFGs), are fundamental components in stream cipher-based cryptographic systems. In this paper, we investigate systems composed of LFSRs under two distinct configurations. First, we study the cascade connection of LFSRs and demonstrate that it represents a special case of the first configuration. Under specific conditions, we derive the exact...

This note describes a weak-key attack on the tweakable block cipher Blink, which was recently introduced at FSE 2026. Specifically, it is shown that two rounds of Blink admit several nonlinear invariants. To illustrate that these invariants indeed lead to attacks, we describe a partial key-recovery attack on Blink-64 with data and time complexity $2^{23}$, for a fraction of $2^{-96}$ weak keys or tweaks. There is a trade-off between the fraction of weak keys and the data complexity, e.g.,...