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New results on non-disjoint and classical strong external difference families Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-02-05 Sophie Huczynska, Sophie Hume
Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently, non-disjoint SEDFs were introduced; it was shown that families of these exist with arbitrarily many sets. We present constructions for both classical and non-disjoint
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A new automatic framework for searching rotational-XOR differential characteristics in ARX ciphers Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-02-05 Yuhan Zhang, Lei Zhang, Yafei Zheng, Wenling Wu
In this paper, a security evaluation framework for ARX ciphers, using modular addition as non-linear component, against rotational-XOR differential cryptanalysis is proposed. We first model all the possible propagations for rotational-XOR difference and rotational-XOR differential probability by some conjunctive normal form clauses. Then, acceleration techniques of automatic search are presented to
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The revised boomerang connectivity tables and their connection to the difference distribution table Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-02-01 Kirpa Garg, Sartaj Ul Hasan, Constanza Riera, Pantelimon Stănică
It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables
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Improved Side Channel Attacks on TRIVIUM, GRAIN-128-AEAD, ACORN-128 v3 and ASCON-128a Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-02-01 Soumya Sahoo, Raghavendra Patil, Sandip Kumar Mondal, Santanu Sarkar, Chester Rebeiro
Side Channel Attacks (SCA) exploit physical information leakage from devices performing cryptographic operations, posing significant security threats. While SCA has been extensively studied in the context of block ciphers, similar analyses on stream ciphers and constructions like authenticated encryption are less explored. In this paper, we present a novel enhancement to existing SCA techniques based
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Perturbation-resilient sets for dynamic service balancing Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-31 Jin Sima, Chao Pan, Olgica Milenkovic
A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in Pan et al. (in: 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, pp 2385–2390, 2022) for exchanging blocks of data chunks stored on distributed storage systems in an access-
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Efficient generation of odd order de Bruijn sequence with the same complement and reverse sequences Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-02-01 Zuling Chang, Qiang Wang
Experimental results show that, when the order n is odd, there are de Bruijn sequences such that the corresponding complement sequence and the reverse sequence are the same. In this paper, we propose one efficient method to generate such de Bruijn sequences. This solves an open problem asked by Fredricksen forty years ago for showing the existence of such de Bruijn sequences when the odd order \(n
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A public key encryption algorithm based on multi-dimensional general Chebyshev polynomial Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-30 Rudong Min, Jiale Han, Shouliang Li, Zhen Yang, Yi Yang
Due to the operational efficiency and lower computational costs of the Chebyshev polynomial compared to ECC, this chaotic system has attracted widespread attention in public key cryptography. However, the single recurrence coefficient limitation and inherent short-period flaw, often render the Chebyshev polynomials cryptosystem ineffective against various attacks, such as Exhaustive Attacks and Ciphertext-Only
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Linear complementary pairs of skew constacyclic codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-31 F. J. Lobillo, José Manuel Muñoz
Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters for LCPs of codes are defined as the (Hamming) distance and the dual distance of the codes in the pair. We study the properties of LCPs of skew constacyclic codes
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On vectorial functions with maximal number of bent components Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-31 Xianhong Xie, Yi Ouyang, Honggang Hu
We study vectorial functions with maximal number of bent components in this paper. We first study the Walsh transform and nonlinearity of \(F(x)=x^{2^e}h(\textrm{Tr}_{2^{2m}/2^m}(x))\), where \(e\ge 0\) and h(x) is a permutation over \({\mathbb {F}}_{2^m}\). If h(x) is monomial, the nonlinearity of F(x) is shown to be at most \( 2^{2\,m-1}-2^{\lfloor \frac{3\,m}{2}\rfloor }\) and some non-plateaued
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On polynomials over finite fields that are free of binomials Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-29 Fabio Enrique Brochero Martínez, Lucas Reis, Sávio Ribas
Let \(\mathbb {F}_q\) be the finite field with q elements, where q is a power of a prime p. Given a monic polynomial \(f \in \mathbb {F}_q[x]\) that is not divisible by x, there exists a positive integer \(e=e(f)\) such that f(x) divides the binomial \(x^e-1\) and e is minimal with this property. The integer e is commonly known as the order of f and we write \(\textrm{ord}(f)=e\). Motivated by a recent
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Polynomial reduction from syndrome decoding problem to regular decoding problem Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-28 Pavol Zajac
The regular decoding problem asks for (the existence of) regular solutions to a syndrome decoding problem (SDP). This problem has increased applications in post-quantum cryptography and cryptanalysis. Recently, Esser and Santini explored in depth the connection between the regular (RSD) and classical syndrome decoding problems. They have observed that while RSD to SDP reductions are known (in any parametric
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Symmetric (15, 8, 4)-designs in terms of the geometry of binary simplex codes of dimension 4 Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-24 Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel
Let \(n=2^k-1\) and \(m=2^{k-2}\) for a certain \(k\ge 3\). Consider the point-line geometry of 2m-element subsets of an n-element set. Maximal singular subspaces of this geometry correspond to binary simplex codes of dimension k. For \(k\ge 4\) the associated collinearity graph contains maximal cliques different from maximal singular subspaces. We investigate maximal cliques corresponding to symmetric
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Efficient information-theoretic distributed point functions with general output groups Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-16 Junru Li, Pengzhen Ke, Liang Feng Zhang
An n-server information-theoretic Distributed Point Function (DPF) allows a client to secret-share a point function \(f_{\alpha ,\beta }(x)\) with domain [N] and output group \(\mathbb {G}\) among n servers such that each server learns no information about the function from its share (called a key) but can compute an additive share of \(f_{\alpha ,\beta }(x)\) for any x. DPFs with small key sizes and
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Additive twisted codes: new distance bounds and infinite families of quantum codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-16 Reza Dastbasteh, Petr Lisoněk
We provide a new construction of quantum codes that enables integration of a broader class of classical codes into the mathematical framework of quantum stabilizer codes. Next, we present new connections between twisted codes and linear cyclic codes and provide novel bounds for the minimum distance of twisted codes. We show that classical tools such as the Hartmann–Tzeng minimum distance bound are
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Rate-improved multi-permutation codes for correcting a single burst of stable deletions Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-16 Xiang Wang, Fang-Wei Fu
Permutation and multi-permutation codes have been widely studied due to their potential applications in communications and storage systems, especially in flash memory. In this paper, we consider balanced multi-permutation codes correcting a single burst of stable deletions of length t and length at most t, respectively. Based on the properties of burst stable deletions and stabilizer permutation subgroups
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Blocking sets of secant and tangent lines with respect to a quadric of $$\text{ PG }(n,q)$$ Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-17 Bart De Bruyn, Puspendu Pradhan, Binod Kumar Sahoo
For a set \({\mathcal {L}}\) of lines of \(\text{ PG }(n,q)\), a set X of points of \(\text{ PG }(n,q)\) is called an \({\mathcal {L}}\)-blocking set if each line of \({\mathcal {L}}\) contains at least one point of X. Consider a possibly singular quadric Q of \(\text{ PG }(n,q)\) and denote by \({\mathcal {S}}\) (respectively, \({\mathcal {T}}\)) the set of all lines of \(\text{ PG }(n,q)\) meeting
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On LCD skew group codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-13 Mohammed El Badry, Abdelfattah Haily, Ayoub Mounir
In this paper we study skew group codes as left ideals in some skew group rings. We have constructed a large class of LCD codes and a class of an LCD MDS codes. An important interest is given to the construction of idempotents generators of these codes.
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Designer of codes: a tribute to Jennifer Key Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-12 Vassili C. Mavron, Harold N. Ward
We offer this tribute to our friend and colleague, Jenny Key. After describing her education and career, we comment on her areas of research. The paper concludes with a complete list of her publications.
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Ternary isodual codes and 3-designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-06 Minjia Shi, Ruowen Liu, Dean Crnković, Patrick Solé, Andrea Švob
Ternary isodual codes and their duals are shown to support 3-designs under mild symmetry conditions. These designs are held invariant by a double cover of the permutation part of the automorphism group of the code. Examples of interest include extended quadratic residues (QR) codes of lengths 14 and 38 whose automorphism groups are PSL(2, 13) and PSL(2, 37), respectively. We also consider Generalized
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Somewhat homomorphic encryption based on random codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-06 Carlos Aguilar-Melchor, Victor Dyseryn, Philippe Gaborit
We present a secret-key encryption scheme based on random rank metric ideal linear codes with a simple decryption circuit. It supports unlimited homomorphic additions and plaintext multiplications (i.e. the homomorphic multiplication of a clear plaintext with a ciphertext) as well as a fixed arbitrary number of homomorphic multiplications. We study a candidate bootstrapping algorithm that requires
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RYDE: a digital signature scheme based on rank syndrome decoding problem with MPC-in-the-Head paradigm Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-04 Loïc Bidoux, Jesús-Javier Chi-Domínguez, Thibauld Feneuil, Philippe Gaborit, Antoine Joux, Matthieu Rivain, Adrien Vinçotte
We present a signature scheme based on the syndrome decoding (SD) problem in rank metric. It is a construction from Multi-Party Computation (MPC), using a MPC protocol which is a slight improvement of the linearized polynomial protocol used in Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022), allowing to obtain a zero-knowledge proof thanks to the MPCitH (MPC-in-the-Head) paradigm. We design
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Quantum sieving for code-based cryptanalysis and its limitations for ISD Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-02 Lynn Engelberts, Simona Etinski, Johanna Loyer
Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical and quantum setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, a variant of the information-set decoding (ISD) framework, commonly used for attacking cryptographically
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Fully selective opening secure IBE from LWE Des. Codes Cryptogr. (IF 1.4) Pub Date : 2025-01-03 Dingding Jia, Haiyang Xue, Bao Li
Selective opening security ensures that, when an adversary is given multiple ciphertexts and corrupts a subset of the senders (thereby obtaining the plaintexts and the senders’ randomness), the privacy of the remaining ciphertexts is still preserved. Previous selective opening secure IBE schemes encrypt messages bit-by-bit, or only achieve selective-id security. In this paper, we present the first
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Divisible design graphs from the symplectic graph Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-29 Bart De Bruyn, Sergey Goryainov, Willem H. Haemers, Leonid Shalaginov
A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization of \((v,k,\lambda )\)-graphs. Here we describe four new infinite families that can be obtained from the symplectic strongly regular graph Sp(2e, q) (q odd, \(e\ge 2\)) by modifying the set of edges. To achieve this we need
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The set of pure gaps at several rational places in function fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-28 Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti
In this work, we explore the use of maximal elements in generalized Weierstrass semigroups and their relationship with pure gaps, extending the results in Castellanos et al. [J Pure Appl Algebra 228(4):107513, 2024]. We provide a method to completely determine the set of pure gaps at several rational places in a function field F over a finite field, where the periods of certain places are the same
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Several families of negacyclic BCH codes and their duals Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-27 Zhonghua Sun, Xinyue Liu
Negacyclic BCH codes are a special subclasses of negacyclic codes, and have the best parameters known in many cases. A family of good negacyclic BCH codes are the q-ary narrow-sense negacyclic BCH codes of length \(n=(q^m-1)/2\), where q is an odd prime power. Little is known about the true minimum distance of this family of negacyclic BCH codes and the dimension of this family of negacyclic BCH codes
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The weight hierarchies of three classes of linear codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-27 Wei Lu, Qingyao Wang, Xiaoqiang Wang, Dabin Zheng
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in various applications. However, determining the generalized Hamming weights of linear codes, particularly their weight hierarchy, is generally a challenging task. In this
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Codes from $$A_m$$ -invariant polynomials Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-27 Giacomo Micheli, Vincenzo Pallozzi Lavorante, Phillip Waitkevich
Let q be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on \({\mathbb {F}}_q[x_1,\dots ,x_m]\) combined with the ideas in Datta and Johnsen (Des Codes Cryptogr 91(3):747–761, 2023). Compared with Generalized Reed–Muller codes with analogous parameters, our codes have the same asymptotic relative distance but a better rate. Our results
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On the vector subspaces of $$\mathbb {F}_{2^n}$$ over which the multiplicative inverse function sums to zero Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-27 Claude Carlet
We study the behavior of the multiplicative inverse function (which plays an important role in cryptography and in the study of finite fields), with respect to a recently introduced generalization of almost perfect nonlinearity (APNness), called kth-order sum-freedom, that extends a classic characterization of APN functions, and has also some relationship with integral attacks. This generalization
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Fault attacks on multi-prime RSA signatures Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-27 Chunzhi Zhao, Jinzheng Cao, Junqi Zhang, Qingfeng Cheng
At CHES 2009, Coron et al. proposed a fault attack on standard RSA signatures based on Coppersmith’s method. This work greatly enhances the practicality of fault attacks on RSA signatures. In practice, multi-prime RSA signatures are widely used due to their faster generation speed. In this paper, we propose fault attacks on multi-prime RSA signatures under the PKCS#1 v2.x protocols. We conduct the
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Low-weight codewords in cyclic codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-24 J. G. Coelho, F. E. Brochero Martínez
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that connects their weight distribution to the number of solutions of associated systems of polynomial equations. This relationship allows for the computation of weight
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The support designs of several families of lifted linear codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-25 Cunsheng Ding, Zhonghua Sun, Qianqian Yan
A generator matrix of a linear code \({\mathcal {C}}\) over \({\textrm{GF}}(q)\) is also a matrix of the same rank k over any extension field \({\textrm{GF}}(q^\ell )\) and generates a linear code of the same length, same dimension and same minimum distance over \({\textrm{GF}}(q^\ell )\), denoted by \({\mathcal {C}}(q|q^\ell )\) and called a lifted code of \({\mathcal {C}}\). Although \({\mathcal
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A class of permutations on $${\mathbb {Z}}_{p}$$ with differential uniformity at most 3 Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-22 Prachi Gupta, P. R. Mishra, Atul Gaur
In this paper, we give a class of permutations on \({\mathbb {Z}}_{p}\) having differential uniformity at most 3, where prime p satisfies \(p \equiv 1 \pmod {4}\). Further, we present a sufficient condition for differential uniformity exactly 3 and identify a subclass achieving this value.
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A construction of optimal quasi-cyclic locally recoverable codes using constituent codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-20 Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno
A locally recoverable code of locality r over \(\mathbb {F}_{q}\) is a code where every coordinate of a codeword can be recovered using the values of at most r other coordinates of that codeword. Locally recoverable codes are efficient at restoring corrupted messages and data which make them highly applicable to distributed storage systems. Quasi-cyclic codes of length \(n=m\ell \) and index \(\ell
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On automorphism groups of binary cyclic codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-20 Jicheng Ma, Guiying Yan
Cyclic codes, as a significant subclass of linear codes, can be constructed and analyzed using algebraic methods. Due to its cyclic nature, they have efficient encoding and decoding algorithms. To date, cyclic codes have found applications in various domains, including consumer electronics, data storage systems, and communication systems. In this paper, we investigate the full automorphism groups of
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Guessing less and better: improved attacks on GIFT-64 Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-20 Federico Canale, María Naya-Plasencia
GIFT-64 is a block cipher that has received a lot of attention from the community since its proposal in 2017. The attack on the highest number of rounds is a differential related-key attack on 26 rounds. We studied this attack, in particular with respect to some recent generic frameworks for improving key recovery, and we realised that this framework, combined with an efficient parallel key guessing
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Several new classes of optimal ternary cyclic codes with two or three zeros Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-19 Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let \(\alpha \) be a generator of \(\mathbb F_{3^m}\setminus \{0\}\), where m is a positive integer. Denote by \(\mathcal {C}_{(i_1,i_2,\cdots , i_t)}\) the cyclic code with generator polynomial \(m_{\alpha
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Quantum security of Trojan message attacks on Merkle–Damgård hash construction Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-18 Ying Xu, Xiaoni Du, Jian Zou
In this paper, we promote Trojan message attacks against Merkle–Damgård hash functions and their concatenation combiner in quantum settings for the first time. Two main quantum scenarios are considered, involving the scenarios where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We first discuss the construction of diamond
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Optimal combinatorial neural codes via symmetric designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-18 Xingyu Zheng, Shukai Wang, Cuiling Fan
Combinatorial neural (CN) codes are binary codes introduced firstly by Curto et al. for asymmetric channel, and then are further studied by Cotardo and Ravagnani under the metric \(\delta _r\) (called asymmetric discrepancy) which measures the differentiation of codewords in CN codes. When \(r>1\), CN codes are different from the usual error-correcting codes in symmetric channel (\(r=1\)). In this
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Relating code equivalence to other isomorphism problems Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-16 Huck Bennett, Kaung Myat Htay Win
We study the complexity of the Code Equivalence Problem on linear error-correcting codes by relating its variants to isomorphism problems on other discrete structures—graphs, lattices, and matroids. Our main results are a fine-grained reduction from the Graph Isomorphism Problem to the Linear Code Equivalence Problem over any field \(\mathbb {F}\), and a reduction from the Linear Code Equivalence Problem
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Hulls of projective Reed–Muller codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-14 Nathan Kaplan, Jon-Lark Kim
Projective Reed–Muller codes are constructed from the family of projective hypersurfaces of a fixed degree over a finite field \(\mathbb {F}_q\). We consider the relationship between projective Reed–Muller codes and their duals. We determine when these codes are self-dual, when they are self-orthogonal, and when they are LCD. We then show that when q is sufficiently large, the dimension of the hull
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Codes over $$\mathbb {F}_4$$ and $$\mathbb {F}_2 \times \mathbb {F}_2$$ and theta series of the corresponding lattices in quadratic fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-04 Josline Freed
Using codes defined over \(\mathbb {F}_4\) and \(\mathbb {F}_2 \times \mathbb {F}_2\), we simultaneously define the theta series of corresponding lattices for both real and imaginary quadratic fields \(\mathbb {Q}(\sqrt{d})\) with \(d \equiv 1\mod 4\) a square-free integer. For such a code, we use its weight enumerator to prove which term in the code’s corresponding theta series is the first to depend
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Derivative descendants of cyclic codes and constacyclic codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-04 Li Xu, Cuiling Fan, Chunming Tang, Zhengchun Zhou
Cyclic codes, as a special type of constacyclic codes, have been extensively studied due to their favorable theoretical and mathematical properties. Very recently, by using the derivative of the Mattson-Solomon polynomials, Huang and Zhang (IEEE Trans Inf Theor 70(4):2395–2410, 2024) studied the cyclic derivative descendants (DDs) and linear DDs of binary extended cyclic codes and proposed the corresponding
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A pair of orthogonal orthomorphisms of finite nilpotent groups Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-04 Shikang Yu, Tao Feng, Menglong Zhang
A bijection \(\theta :G\rightarrow G\) of a finite group G is an orthomorphism of G if the mapping \(x\mapsto x^{-1}\theta (x)\) is also a bijection. Two orthomorphisms \(\theta \) and \(\phi \) of a finite group G are orthogonal if the mapping \(x\mapsto \theta (x)^{-1}\phi (x)\) is also bijective. We show that there is a pair of orthogonal orthomorphisms of a finite nilpotent group G if and only
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Factorization and irreducibility of composed products Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-04 Lukas Kölsch, Lucas Krompholz, Gohar Kyureghyan
Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct irreducible polynomials of large composite degrees from irreducible polynomials of lower degrees. We show that the composed product of two irreducible polynomials of degrees m and n is again irreducible if and only if m and
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On translation hyperovals in semifield planes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-04 Kevin Allen, John Sheekey
In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexample is a semifield plane, specifically a Generalised Twisted Field plane, of order 64. We also relate this non-existence to the covering radius of two associated rank-metric codes, and the non-existence of scattered subspaces
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On 3-dimensional MRD codes of type $$\langle X^{q^t},X+\delta X^{q^{2t}},G(X) \rangle $$ Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-05 Daniele Bartoli, Francesco Ghiandoni
In this work we present results on the classification of \(\mathbb {F}_{q^n}\)-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes \(\mathcal {C}=\langle X^{q^t}, F(X), G(X) \rangle \subseteq \mathcal {L}_{n,q}\) of exceptional type, i.e. such that \(\mathcal {C}\) is MRD over infinitely
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On set systems with strongly restricted intersections Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-12-05 Xin Wei, Xiande Zhang, Gennian Ge
Set systems with strongly restricted intersections, called \(\alpha \)-intersecting families for a vector \(\alpha \), were introduced recently as a generalization of several well-studied intersecting families including the classical oddtown and eventown. Given a binary vector \(\alpha =(a_1, \ldots , a_k)\), a collection \({\mathcal {F}}\) of subsets over an n element set is an \(\alpha \)-intersecting
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Quantum rectangle attack and its application on Deoxys-BC Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-21 Yin-Song Xu, Yi-Bo Luo, Zheng Yuan, Xuan Zhou, Qi-di You, Fei Gao, Xiao-Yang Dong
In recent years, it has become a popular trend to propose quantum versions of classical attacks. The rectangle attack as a differential attack is widely used in symmetric cryptanalysis and applied on many block ciphers. To improve its efficiency, we propose a new quantum rectangle attack firstly. In rectangle attack, it counts the number of valid quartets for each guessed subkeys and filters out subkey
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Almost tight security in lattices with polynomial moduli—PRF, IBE, all-but-many LTF, and more Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-19 Zhedong Wang, Qiqi Lai, Feng-Hao Liu
Achieving tight security is a fundamental task in cryptography. While one of the most important purposes of this task is to improve the overall efficiency of a construction (by allowing smaller security parameters), many current lattice-based instantiations do not completely achieve the goal. Particularly, a super-polynomial modulus seems to be necessary in all prior work for (almost) tight schemes
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Breaking the power-of-two barrier: noise estimation for BGV in NTT-friendly rings Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-15 Andrea Di Giusto, Chiara Marcolla
The Brakerski–Gentry–Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. Consequently, the parameters of BGV need to be estimated carefully, with a trade-off between security
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A new method of constructing $$(k+s)$$ -variable bent functions based on a family of s-plateaued functions on k variables Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-13 Sihong Su, Xiaoyan Chen
It is important to study the new construction methods of bent functions. In this paper, we first propose a secondary construction method of \((k+s)\)-variable bent function g through a family of s-plateaued functions \(f_0,f_1,\ldots ,f_{2^s-1}\) on k variables with disjoint Walsh supports, which can be obtained through any given \((k-s)\)-variable bent function f by selecting \(2^s\) disjoint affine
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Further investigation on differential properties of the generalized Ness–Helleseth function Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-10 Yongbo Xia, Chunlei Li, Furong Bao, Shaoping Chen, Tor Helleseth
Let n be an odd positive integer, p be an odd prime with \(p\equiv 3\pmod 4\), \(d_{1} = {{p^{n}-1}\over {2}} -1 \) and \(d_{2} =p^{n}-2\). The function defined by \(f_u(x)=ux^{d_{1}}+x^{d_{2}}\) is called the generalized Ness–Helleseth function over \(\mathbb {F}_{p^n}\), where \(u\in \mathbb {F}_{p^n}\). It was initially studied by Ness and Helleseth in the ternary case. In this paper, for \(p^n
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Parallel construction for constant dimension codes from mixed dimension construction Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-09 Xianmang He, Zusheng Zhang, Si Tian, Jingli Wang, Yindong Chen
The community has been pursuing improvements in the cardinalities for constant dimensional codes (CDC for short) for the past decade. Lao et al. (IEEE Trans Inf Theory 69(7):4333–4344, 2023) has shown that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. The exploration of the CDCs’ construction is transformed into finding mixed dimension/distance subspace
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Improved key recovery attacks on reduced-round Salsa20 Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-09 Sabyasachi Dey, Gregor Leander, Nitin Kumar Sharma
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Generalized bilateral multilevel construction for constant dimension codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-05 Xiaoqin Hong, Xiwang Cao, Gaojun Luo
Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. This paper introduces a new class of codes, namely generalized bilateral Ferrers diagram rank-metric codes, to generalize the bilateral multilevel construction in Etzion and Vardy (Adv Math Commun 16:1165–1183, 2022). Combining our generalized bilateral multilevel construction and the
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Griesmer type bounds for additive codes over finite fields, integral and fractional MDS codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-03 Simeon Ball, Michel Lavrauw, Tabriz Popatia
In this article we prove Griesmer type bounds for additive codes over finite fields. These new bounds give upper bounds on the length of maximum distance separable (MDS) codes, codes which attain the Singleton bound. We will also consider codes to be MDS if they attain the fractional Singleton bound, due to Huffman. We prove that this bound in the fractional case can be obtained by codes whose length
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Simple vs. vectorial: exploiting structural symmetry to beat the ZeroSum distinguisher Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-11-01 Sahiba Suryawanshi, Shibam Ghosh, Dhiman Saha, Prathamesh Ram
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Algebraic hierarchical locally recoverable codes with nested affine subspace recovery Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-10-24 Kathryn Haymaker, Beth Malmskog, Gretchen Matthews
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Association schemes and orthogonality graphs on anisotropic points of polar spaces Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-10-24 Sam Adriaensen, Maarten De Boeck
In this paper, we study association schemes on the anisotropic points of classical polar spaces. Our main result concerns non-degenerate elliptic and hyperbolic quadrics in \({{\,\textrm{PG}\,}}(n,q)\) with q odd. We define relations on the anisotropic points of such a quadric that depend on the type of line spanned by the points and whether or not they are of the same “quadratic type”. This yields