Showing papers in "Cryptography and Communications in 2022"
TL;DR: In this article , the authors presented a construction of near MDS codes with oval polynomials and then determined the locality of the codes, which turns out that the near mDS codes and their duals are both distance and dimension-optimal locally recoverable codes.
Abstract: Locally recoverable codes are widely used in distributed and cloud storage systems. In this paper, we first present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out that the near MDS codes and their duals are both distance-optimal and dimension-optimal locally recoverable codes. The lengths of the locally recoverable codes are different from known ones in the literature.
11 citations
9 citations
TL;DR: In this paper , the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes were investigated in some special cases, and a new systematic approach was proposed to obtain Hermitian self-dual (+)-GTRS codes.
Abstract: Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes in some special cases. Then, a new systematic approach is proposed to obtain Hermitian self-dual (+)-GTRS codes, and furthermore, necessary and sufficient conditions for a (+)-GTRS code to be Hermitian self-dual are presented. Finally, several classes of Hermitian self-dual MDS and NMDS codes are constructed with this method.
7 citations
TL;DR: The comparison to the current literature shows that despite its simplicity, the WPB functions presented in this paper are the best in behavior from the algebraic immunity and the k-weight nonlinearities.
7 citations
TL;DR: In this paper , a general construction of many Hermitian LCD [n, k] codes from a given Hermitians LCD code was introduced, including punctured codes and shortened codes.
Abstract: We introduce a general construction of many Hermitian LCD [n, k] codes from a given Hermitian LCD [n, k] code. Furthermore, we present some results on punctured codes and shortened codes of quaternary Hermitian LCD codes. As an application, we improve some of the previously known lower bounds on the largest minimum weights of quaternary Hermitian LCD codes of length $$26 \le n \le 30$$ .
6 citations
TL;DR: New families of bent functions obtained by adding together indicators typical for the C\documentclass[12pt]{minimal] \usepackage{amsmath} \use package{wasysym} £2,000-£3,000 are specified.
6 citations
TL;DR: In this paper , the authors give a complete description of the c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, using double Weil sums, and generalize a result of Boura and Canteaut (IACR Trans. Symmetric Cryptol. 2018(3) : 290-310, 2018) for the classical boomerang uniformity.
Abstract: Here, we give a complete description of the entire c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, by using double Weil sums. As a by-product, we generalize a result of Boura and Canteaut (IACR Trans. Symmetric Cryptol. 2018(3) : 290–310, 2018) for the classical boomerang uniformity (see also the extended abstract by Eddahmani and Mesnager at the Boolean Functions and their Applications (BFA 2021) conference).
6 citations
TL;DR: This paper gives check matrices of twisted generalized Reed-Solomon codes and construct three classes of new LCD MDS codes from twisted generalized RoS Solomon codes, including LCD NMDS codes.
6 citations
TL;DR: In this article , the inverse, the Gold, and the Bracken-Leander functions are studied for building S-boxes of block ciphers with good cryptographic properties in symmetric cryptography.
Abstract: The inverse, the Gold, and the Bracken-Leander functions are crucial for building S-boxes of block ciphers with good cryptographic properties in symmetric cryptography. These functions have been intensively studied, and various properties related to standard attacks have been investigated. Thanks to novel advances in symmetric cryptography and, more precisely, those pertaining to boomerang cryptanalysis, this article continues to follow this momentum and further examine these functions. More specifically, we revisit and bring new results about their Difference Distribution Table (DDT), their Boomerang Connectivity Table (BCT), their Feistel Boomerang Connectivity Table (FBCT), and their Feistel Boomerang Difference Table (FBDT). For each table, we give explicit values of all entries by solving specific systems of equations over the finite field $$\mathbb {F}_{2^n}$$ of cardinality $$2^n$$ and compute the cardinalities of their corresponding sets of such values. The explicit values of the entries of these tables and their cardinalities are crucial tools to test the resistance of block ciphers based on variants of the inverse, the Gold, and the Bracken-Leander functions against cryptanalytic attacks such as differential and boomerang attacks. The computation of these entries and the cardinalities in each table aimed to facilitate the analysis of differential and boomerang cryptanalysis of S-boxes when studying distinguishers and trails.
6 citations
TL;DR: It is proved that the updated list of quadratic APN functions in dimension 7 is complete up to CCZ-equivalence.
6 citations
TL;DR: Based on the generalized Boolean functions (GBFs), a class of q -ary Z-complementary sequence sets (ZCSSs) and aclass of complementary sequences sets ( CSSs) are constructed that have low PAPR and non-power-of-two lengths.
TL;DR: In this paper , the authors further investigated the quadratic APN permutations in dimension 9 and proved that such a family does not contain any other APN for larger dimensions, using tools from algebraic geometry over finite fields.
Abstract: The single trivariate representation proposed in [C. Beierle, C. Carlet, G. Leander, L. Perrin, A Further Study of Quadratic APN Permutations in Dimension Nine, arXiv: 2104.08008 ] of the two sporadic quadratic APN permutations in dimension 9 found by Beierle and Leander (2020) is further investigated. In particular, using tools from algebraic geometry over finite fields, we prove that such a family does not contain any other APN permutation for larger dimensions.
TL;DR: In this article , the authors explore explicit constructions of families of MDS linear codes with one-dimensional hulls for both Euclidean and Hermitian inner product, respectively, using tools from algebraic function fields in one variable to study such codes.
Abstract: The hull of a linear code C is the intersection of C with its dual C⊥, where the dual is often defined with respect to Euclidean or Hermitian inner product. The Euclidean hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and for checking permutation equivalence of two linear codes. Recently, both Euclidean and Hermitian hulls have found another application to quantum error correcting codes with entanglements. This paper aims to explore explicit constructions of families of MDS linear codes with one-dimensional hull for both cases. We use tools from algebraic function fields in one variable to study such codes. Sufficient conditions for an algebraic geometry code of genus zero to have one-dimensional hull are provided, and some construction methods are presented. We construct many families of MDS linear codes with one-dimensional hull for the Euclidean case and three families for the Hermitian case, respectively.
TL;DR: This paper recalls how to construct new QAMs from a known one and makes two conjectures that the total number of CCZ-inequivalent quadratic APN functions on F28 exceeds 50000, and proposes a new model which can handle the last two columns together and avoid some redundant computation.
TL;DR: A minor variant of nEHtMp construction is proposed and it is shown that it achieves a tight 2n/3 bit security in the multi-user setting and the security bound of the construction also degrades gracefully with the repetition of nonces.
TL;DR: The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls for linear codes and have been studied in this paper , where four general methods of constructing MDS codes with Galois Hulls of arbitrary dimensions by Hermitians or general Galois self-orthogonal (extended) GRS codes are given.
Abstract: The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois hulls of arbitrary dimensions via (extended) GRS codes. Four general methods of constructing MDS codes with Galois hulls of arbitrary dimensions by Hermitian or general Galois self-orthogonal (extended) GRS codes are given. Using these methods, some MDS codes with larger dimensions and Galois hulls of arbitrary dimensions can be obtained. In addition, two new classes of MDS codes with explicit parameters and with Galois hulls of arbitrary dimensions are also constructed. One of the two classes can yield 1-Galois self-orthogonal GRS codes, and more new classes of MDS codes with Galois hulls of arbitrary dimensions can be derived from one of the four general methods we give.
TL;DR: It is shown that erroneous patterns are needed to reconstruct an unknown permutation from an arbitrary unknown permutations for any $n\geq 9$ .
TL;DR: Two randomness tests are proposed including a jump test based on the jump complexity, i.
TL;DR: In this paper , a method for classifying quaternary Hermitian LCD codes having large minimum weights was proposed, where the minimum weights were obtained by classifying optimal Hermitians with dimension 3.
Abstract: We propose a method for classifying quaternary Hermitian LCD codes having large minimum weights. For example, we classify quaternary optimal Hermitian LCD codes of dimension 3.
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TL;DR: In this paper , the authors define the class of triplicate functions as a generalization of 3-to-1 functions over even values of n, and give a lower bound on the Hamming distance between any two quadratic 3-To-1 APN functions.
Abstract: Abstract We define the class of triplicate functions as a generalization of 3-to-1 functions over $$\mathbb {F}_{2^{n}}$$ F 2 n for even values of n . We investigate the properties and behavior of triplicate functions, and of 3-to-1 among triplicate functions, with particular attention to the conditions under which such functions can be APN. We compute the exact number of distinct differential sets of power APN functions and quadratic 3-to-1 functions; we show that, in this sense, quadratic 3-to-1 functions are a generalization of quadratic power APN functions for even dimensions, in the same way that quadratic APN permutations are generalizations of quadratic power APN functions for odd dimensions. We show that quadratic 3-to-1 APN functions cannot be CCZ-equivalent to permutations in the case of doubly-even dimensions. We compute a lower bound on the Hamming distance between any two quadratic 3-to-1 APN functions, and give an upper bound on the number of such functions over $$\mathbb {F}_{2^{n}}$$ F 2 n for any even n . We survey all known infinite families of APN functions with respect to the presence of 3-to-1 functions among them, and conclude that for even n almost all of the known infinite families contain functions that are quadratic 3-to-1 or are EA-equivalent to quadratic 3-to-1 functions. We also give a simpler univariate representation in the case of singly-even dimensions of the family recently introduced by Göloglu than the ones currently available in the literature. We conduct a computational search for quadratic 3-to-1 functions in even dimensions n ≤ 12. We find six new APN instances for n = 10, and the first sporadic APN instance for n = 12 since 2006. We provide a list of all known 3-to-1 APN functions for n ≤ 12.
TL;DR: In this article , the weights wt(fn) of a family of rotation symmetric Boolean functions with the cardinalities of the sets of n-periodic points of a finite-type shift were identified.
Abstract: We identify the weights wt(fn) of a family {fn} of rotation symmetric Boolean functions with the cardinalities of the sets of n-periodic points of a finite-type shift, recovering the second author’s result that said weights satisfy a linear recurrence. Similarly, the weights of idempotent functions fn defined on finite fields can be recovered as the cardinalities of curves over those fields and hence satisfy a linear recurrence as a consequence of the rationality of curves’ zeta functions. Weil’s Riemann hypothesis for curves then provides additional information about wt(fn). We apply our results to the case of quadratic functions and considerably extend the results in an earlier paper of ours.
TL;DR: In this paper , the performance of the Fast Fourier Transform (FFT) distinguisher used in the solving phase of the BKW algorithm has been studied, and it has been shown that it performs much better than previous theory predicts.
Abstract: Abstract The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase. In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt’15 has the same sample complexity as the optimal distinguisher, when making the same number of hypotheses. We also show via simulation that it performs much better than previous theory predicts and develop a sample complexity model that matches the simulations better. We also introduce an improved, pruned version of the FFT distinguisher. Finally, we indicate, via extensive experiments, that the sample dependency due to both LF2 and sample amplification is limited.