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  • Further clarification on Mantin’s Digraph Repetition Bias in RC4
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-19
    Pranab Chakraborty, Subhamoy Maitra

    In this paper we provide a theoretical argument towards an unsolved question related to Mantin’s “Digraph Repetition Bias” (Eurocrypt 2005) that is observed in the key-stream of RC4. The open question, that depends on the observation that arrival of four consecutive same bytes (of the form AAAA) in RC4 key-stream is slightly negatively biased, was posed by Bricout et al (Des. Codes Cryptogr. 86:743–770

    更新日期:2020-10-19
  • The complete hierarchical locality of the punctured Simplex code
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-16
    Matthias Grezet, Camilla Hollanti

    This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality.

    更新日期:2020-10-17
  • Improved upper bounds for parent-identifying set systems and separable codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-15
    Xin Wang

    Parent-identifying set systems and separable codes are useful combinatorial structures which were introduced, respectively, for traitor tracing in broadcast encryption and collusion-resistant fingerprints for copyright protection. Determining the maximum size of such structures is the main research objective. New upper bounds are presented in this paper. Specifically, for parent-identifying set systems

    更新日期:2020-10-16
  • Bent and $${{\mathbb {Z}}}_{2^k}$$ Z 2 k -Bent functions from spread-like partitions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-13
    Wilfried Meidl, Isabel Pirsic

    Bent functions from a vector space \({{\mathbb {V}}}_n\) over \({{\mathbb {F}}}_2\) of even dimension \(n=2m\) into the cyclic group \({{\mathbb {Z}}}_{2^k}\), or equivalently, relative difference sets in \({{\mathbb {V}}}_n\times {{\mathbb {Z}}}_{2^k}\) with forbidden subgroup \({{\mathbb {Z}}}_{2^k}\), can be obtained from spreads of \({{\mathbb {V}}}_n\) for any \(k\le n/2\). In this article, existence

    更新日期:2020-10-13
  • A new rank metric for convolutional codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-08
    P. Almeida, D. Napp

    Let \({\mathbb {F}}[D]\) be the polynomial ring with entries in a finite field \({\mathbb {F}}\). Convolutional codes are submodules of \({\mathbb {F}}[D]^n\) that can be described by left prime polynomial matrices. In the last decade there has been a great interest in convolutional codes equipped with a rank metric, called sum rank metric, due to their wide range of applications in reliable linear

    更新日期:2020-10-08
  • Differentially low uniform permutations from known 4-uniform functions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-07
    Marco Calderini

    Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken–Leander function on a subfield.

    更新日期:2020-10-07
  • Generalized isotopic shift construction for APN functions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-07
    Lilya Budaghyan, Marco Calderini, Claude Carlet, Robert Coulter, Irene Villa

    In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for \(n=8\) and produces fifteen new APN functions for \(n=9\).

    更新日期:2020-10-07
  • A construction method of balanced rotation symmetric Boolean functions on arbitrary even number of variables with optimal algebraic immunity
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-06
    Sihem Mesnager, Sihong Su, Hui Zhang

    Rotation symmetric Boolean functions incorporate a super-class of symmetric functions which represent an attractive corpus for computer investigation. These functions have been investigated from the viewpoints of bentness and correlation immunity and have also played a role in the study of nonlinearity. In the literature, many constructions of balanced odd-variable rotation symmetric Boolean functions

    更新日期:2020-10-07
  • On the inverses of Kasami and Bracken–Leander exponents
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-06
    Lukas Kölsch

    We explicitly determine the binary representation of the inverse of all Kasami exponents \(K_r=2^{2r}-2^r+1\) modulo \(2^n-1\) for all possible values of n and r. This includes as an important special case the APN Kasami exponents with \(\gcd (r,n)=1\). As a corollary, we determine the algebraic degree of the inverses of the Kasami functions. In particular, we show that the inverse of an APN Kasami

    更新日期:2020-10-07
  • Construction of single-deletion-correcting DNA codes using CIS codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-25
    Whan-Hyuk Choi, Hyun Jin Kim, Yoonjin Lee

    We find a method for constructing DNA codes with single-deletion-correcting capability. We first present an explicit algorithm for the construction of the q-ary single-deletion-correcting codes (abbreviated as SDC codes) using a class of the complementary information set codes (abbreviated as CIS codes), where q is a power of a prime. We then show that the encoding/decoding scheme of the CIS codes

    更新日期:2020-09-25
  • Rédei permutations with cycles of the same length
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-22
    Juliane Capaverde, Ariane M. Masuda, Virgínia M. Rodrigues

    Let \({\mathbb {F}}_{q}\) be a finite field of odd characteristic. We study Rédei functions that induce permutations over \(\mathbb {P}^1({\mathbb {F}}_{q})\) whose cycle decomposition contains only cycles of length 1 and j, for an integer \(j\ge 2\). When j is 4 or a prime number, we give necessary and sufficient conditions for a Rédei permutation of this type to exist over \(\mathbb {P}^1({\mathbb

    更新日期:2020-09-22
  • Construction of isodual codes from polycirculant matrices
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-20
    Minjia Shi, Li Xu, Patrick Solé

    Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can

    更新日期:2020-09-20
  • A polymatroid approach to generalized weights of rank metric codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-15
    Sudhir R. Ghorpade, Trygve Johnsen

    We consider the notion of a (q, m)-polymatroid, due to Shiromoto, and the more general notion of (q, m)-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martínez-Peñas and Matsumoto

    更新日期:2020-09-15
  • Maximal nonassociativity via fields
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-14
    Petr Lisoněk

    We say that \((x,y,z)\in Q^3\) is an associative triple in a quasigroup \((Q,*)\) if \((x*y)*z=x*(y*z)\). Let a(Q) denote the number of associative triples in Q. It is easy to show that \(a(Q)\ge |Q|\), and we call the quasigroup maximally nonassociative if \(a(Q)= |Q|\). It was conjectured that maximally nonassociative quasigroups do not exist when \(|Q|>1\). Drápal and Lisoněk recently refuted this

    更新日期:2020-09-14
  • Two families of two-weight codes over $$\mathbb {Z}_4$$ Z 4
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-12
    Minjia Shi, Wang Xuan, Patrick Solé

    Two infinite families of \(\mathbb {Z}_4\)-codes with two nonzero Lee weights are constructed by their generator matrices. Their Gray images are nonlinear with the same weight distribution as that of the two-weight binary codes of type SU1 in the sense of (Calderbank, Kantor, 1986).

    更新日期:2020-09-12
  • Wide-sense 2-frameproof codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-12
    Junling Zhou, Wenling Zhou

    Various kinds of fingerprinting codes and their related combinatorial structures are extensively studied for protecting copyrighted materials. This paper concentrates on one specialised fingerprinting code named wide-sense frameproof codes in order to prevent innocent users from being framed. Let Q be a finite alphabet of size q. Given a t-subset \(X=\{ x ^1,\ldots , x ^t \}\subseteq Q^n\), a position

    更新日期:2020-09-12
  • Optimal minimal linear codes from posets
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-11
    Jong Yoon Hyun, Hyun Kwang Kim, Yansheng Wu, Qin Yue

    Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. In this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight

    更新日期:2020-09-12
  • Binary primitive LCD BCH codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-03
    Xinmei Huang, Qin Yue, Yansheng Wu, Xiaoping Shi, Jerod Michel

    Linear complementary dual (LCD) codes have attracted much attention in recent years due to their applications in implementations against side-channel attacks and fault injection attacks. Comparing coset leaders, we introduce the new concept of absolute coset leaders, which provides advantages for constructing LCD BCH codes. We then give explicit presentations for the largest, second largest and third

    更新日期:2020-09-03
  • Fast computation of linear approximation over certain composition functions and applications to SNOW 2.0 and SNOW 3G
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-02
    Xinxin Gong, Bin Zhang

    In this paper, we study the linear approximation of certain composition functions, with applications to SNOW 2.0 and SNOW 3G. We first propose an efficient algorithm to compute the linear approximation of certain composition functions with parallel operations, which has a linear-time complexity for any given mask tuple, and thus allows for a wide range of search for linear approximations. Naturally

    更新日期:2020-09-03
  • Tightly CCA-secure encryption scheme in a multi-user setting with corruptions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-02
    Youngkyung Lee, Dong Hoon Lee, Jong Hwan Park

    The security of public-key encryption (PKE) schemes in a multi-user setting is aimed at capturing real-world scenarios in which an adversary could attack multiple users and multiple ciphertexts of its choice. However, the fact that a real-world adversary can also mount key-exposure attacks for a set of multiple public keys requires us to consider a more realistic notion of security in multi-user settings

    更新日期:2020-09-03
  • Linear complementary pair of group codes over finite chain rings
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-29
    Cem Güneri, Edgar Martínez-Moro, Selcen Sayıcı

    Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side channel and fault injection attacks. The security parameter for an LCP of codes (C, D) is defined as the minimum of the minimum distances d(C) and \(d(D^\bot )\). It has been recently shown that

    更新日期:2020-08-29
  • An algorithm for decoding skew Reed–Solomon codes with respect to the skew metric
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-20
    Delphine Boucher

    After giving a new interpretation of the skew metric defined in [8], we show that the decoding algorithm of [4] for skew Reed–Solomon codes in the Hamming metric remains valid with respect to the skew metric. This enables us to make a first step towards a list decoding algorithm in the skew metric.

    更新日期:2020-08-20
  • Deletion correcting codes meet the Littlewood–Offord problem
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-18
    Khodakhast Bibak

    In this paper, we make a novel connection between information theory and additive combinatorics; more specifically, between deletion/insertion correcting codes and the celebrated Littlewood–Offord problem. We see how results from one area can have an impact on the other area and vice versa. In particular, a result on the Littlewood–Offord problem gives a nice upper bound for the size of the Levenshtein

    更新日期:2020-08-18
  • Doubly resolvable Steiner quadruple systems of orders $$2^{2n+1}$$ 2 2 n + 1
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-17
    Juanjuan Xu, Jingjun Bao, Lijun Ji

    A t-\((v,k,\lambda )\) design is a pair \((X,\mathcal{B})\), where X is a v-element set and \(\mathcal{B}\) is a set of k-subsets of X, called blocks, with the property that every t-subset of X is contained in exactly \(\lambda \) blocks. A t-\((v,k,\lambda )\) design \((X,\mathcal{B})\) is said to be \((s,\mu )\)-resolvable if \(\mathcal{B}\) can be partitioned into \(\mathcal{B}_1|\cdots |\mathcal{B}_c\)

    更新日期:2020-08-17
  • Access balancing in storage systems by labeling partial Steiner systems
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-14
    Yeow Meng Chee, Charles J. Colbourn, Hoang Dau, Ryan Gabrys, Alan C. H. Ling, Dylan Lusi, Olgica Milenkovic

    Storage architectures ranging from minimum bandwidth regenerating encoded distributed storage systems to declustered-parity RAIDs can employ dense partial Steiner systems to support fast reads, writes, and recovery of failed storage units. To enhance performance, popularities of the data items should be taken into account to make frequencies of accesses to storage units as uniform as possible. A combinatorial

    更新日期:2020-08-14
  • Boomerang uniformity of popular S-box constructions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-14
    Shizhu Tian, Christina Boura, Léo Perrin

    In order to study the resistance of a block cipher against boomerang attacks, a tool called the Boomerang Connectivity Table (BCT) for S-boxes was recently introduced. Very little is known today about the properties of this table especially for bijective S-boxes defined for n variables with \(n\equiv 0 \mod 4\). In this work we study the boomerang uniformity of some popular constructions used for building

    更新日期:2020-08-14
  • Symmetries of biplanes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-07
    Seyed Hassan Alavi, Ashraf Daneshkhah, Cheryl E. Praeger

    In this paper, we first study biplanes \(\mathcal {D}\) with parameters (v, k, 2), where the block size \(k\in \{13,16\}\). These are the smallest parameter values for which a classification is not available. We show that if \(k=13\), then either \(\mathcal {D}\) is the Aschbacher biplane or its dual, or \(\mathbf {Aut}(\mathcal {D})\) is a subgroup of the cyclic group of order 3. In the case where

    更新日期:2020-08-08
  • On post-processing in the quantum algorithm for computing short discrete logarithms
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-06
    Martin Ekerå

    We revisit the quantum algorithm for computing short discrete logarithms that was recently introduced by Ekerå and Håstad. By carefully analyzing the probability distribution induced by the algorithm, we show its success probability to be higher than previously reported. Inspired by our improved understanding of the distribution, we propose an improved post-processing algorithm that is considerably

    更新日期:2020-08-06
  • Relative t -designs in Johnson association schemes for P-polynomial structure
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-31
    Yan Zhu, Naoki Watamura

    Relative t-designs are defined in both P- and Q-polynomial association schemes. In this paper, we investigate relative t-designs in Johnson association schemes J(v, k) for P-polynomial structure. It is known that each nontrivial shell of J(v, k) is identified with the product of two smaller Johnson association schemes. We prove that relative t-designs in J(v, k) supported by one shell are equivalent

    更新日期:2020-08-01
  • High dimensional affine codes whose square has a designed minimum distance
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-03
    Ignacio García-Marco, Irene Márquez-Corbella, Diego Ruano

    Given a linear code \({\mathcal {C}}\), its square code \({\mathcal {C}}^{(2)}\) is the span of all component-wise products of two elements of \({\mathcal {C}}\). Motivated by applications in multi-party computation, our purpose with this work is to answer the following question: which families of affine variety codes have simultaneously high dimension \(k({\mathcal {C}})\) and high minimum distance

    更新日期:2020-07-24
  • Power error locating pairs
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-08
    Alain Couvreur, Isabella Panaccione

    We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed–Solomon or algebraic geometry codes, the algorithm is a reformulation of the so-called power decoding algorithm. Asymptotically, it corrects errors up to Sudan’s radius. In addition, this new framework applies to any code benefiting from an error

    更新日期:2020-07-24
  • Hamming and simplex codes for the sum-rank metric
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-21
    Umberto Martínez-Peñas

    Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least 3 (thus one-error-correcting) for a fixed redundancy r, base-field size q and field-extension degree m (i.e., number of matrix rows). General upper bounds on their code length, number of shots or sublengths and average sublength

    更新日期:2020-07-24
  • The phantom of differential characteristics
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-24
    Yunwen Liu, Wenying Zhang, Bing Sun, Vincent Rijmen, Guoqiang Liu, Chao Li, Shaojing Fu, Meichun Cao

    For differential cryptanalysis under the single-key model, the key schedules hardly need to be exploited in constructing the characteristics, which is based on the hypothesis of stochastic equivalence. In this paper, we study a profound effect of the key schedules on the validity of the differential characteristics. Noticing the sensitivity in the probability of the characteristics to specific keys

    更新日期:2020-07-24
  • On the security of a Loidreau rank metric code based encryption scheme
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-17
    Daniel Coggia, Alain Couvreur

    We present a polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters.

    更新日期:2020-07-24
  • Codes with locality from cyclic extensions of Deligne–Lusztig curves
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-03
    Gretchen L. Matthews, Fernando Piñero

    Recently, Skabelund defined new maximal curves which are cyclic extensions of the Suzuki and Ree curves. Previously, the now well-known GK curves were found as cyclic extensions of the Hermitian curve. In this paper, we consider locally recoverable codes constructed from these new curves, complementing that done for the GK curve. Locally recoverable codes allow for the recovery of a single symbol by

    更新日期:2020-07-24
  • LCD codes and self-orthogonal codes in generalized dihedral group algebras
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-02
    Yanyan Gao, Qin Yue, Yansheng Wu

    Let \(\mathbb {F}_q\) be a finite field with q elements, \(D_{2n,\,r}\) a generalized dihedral group with \(\gcd (2n,q)=1\), and \(\mathbb {F}_q[D_{2n,\,r}]\) a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of \(\mathbb {F}_q[D_{2n,\,r}]\) is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all

    更新日期:2020-07-24
  • Enumerating extensions of mutually orthogonal Latin squares
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-30
    Simona Boyadzhiyska, Shagnik Das, Tibor Szabó

    Two \(n \times n\) Latin squares \(L_1, L_2\) are said to be orthogonal if, for every ordered pair (x, y) of symbols, there are coordinates (i, j) such that \(L_1(i,j) = x\) and \(L_2(i,j) = y\). A k-MOLS is a sequence of k pairwise-orthogonal Latin squares, and the existence and enumeration of these objects has attracted a great deal of attention. Recent work of Keevash and Luria provides, for all

    更新日期:2020-06-30
  • The geometric approach to the existence of some quaternary Griesmer codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-30
    Assia Rousseva, Ivan Landjev

    In this paper we prove the nonexistence of the hypothetical arcs with parameters (395, 100), (396, 100), (448, 113), and (449, 113) in \({{\,\mathrm{PG}\,}}(4,4)\). This rules out the existence of Griesmer codes with parameters \([395,5,295]_4\), \([396,5,296]_4\), \([448,5,335]_4\), \([449,5,336]_4\) and solves four instances of the main problem of coding theory for \(q=4\), \(k=5\). The proof relies

    更新日期:2020-06-30
  • Classification of self-dual cyclic codes over the chain ring $$\mathbb Z_p[u]/\langle u^3 \rangle $$ Z p [ u ] / ⟨ u 3 ⟩
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-27
    Boran Kim, Yoonjin Lee

    We classify all the cyclic self-dual codes of length \(p^k\) over the finite chain ring \(\mathcal R:=\mathbb Z_p[u]/\langle u^3 \rangle \), which is not a Galois ring, where p is a prime number and k is a positive integer. First, we find all the dual codes of cyclic codes over \({\mathcal R}\) of length \(p^k\) for every prime p. We then prove that if a cyclic code over \({\mathcal R}\) of length

    更新日期:2020-06-27
  • Characterizations and constructions of triple-cycle permutations of the form $$x^rh(x^s)$$ x r h ( x s )
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-23
    Mengna Wu, Chengju Li, Zilong Wang

    Let \({\mathbb {F}}_q\) be the finite field with q elements and let f be a permutation polynomial over \({\mathbb {F}}_q\). Let \(S_q\) denote the symmetric group on \({\mathbb {F}}_q\). In this paper, we mainly investigate some characterizations on the elements \(f \in S_q\) of order 3, i.e., \(f\circ f\circ f=I\), where f is also called a triple-cycle permutation in the literature. Some explicit

    更新日期:2020-06-23
  • Linearly equivalent S-boxes and the division property
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-23
    Baptiste Lambin, Patrick Derbez, Pierre-Alain Fouque

    Division property is a cryptanalysis method that proves to be very efficient on block ciphers. Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property. Nonetheless, we claim that the previous techniques do not consider the full search space. We show that even if the previous

    更新日期:2020-06-23
  • On the boomerang uniformity of quadratic permutations
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-18
    Sihem Mesnager, Chunming Tang, Maosheng Xiong

    At Eurocrypt’18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new tool called Boomerang Connectivity Table (BCT) for measuring the resistance of a block cipher against the boomerang attack which is an important cryptanalysis technique introduced by Wagner in 1999 against block ciphers. Next, Boura and Canteaut introduced an important parameter related to the BCT for cryptographic S-boxes called

    更新日期:2020-06-18
  • On constructions and properties of ( n , m )-functions with maximal number of bent components
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-18
    Lijing Zheng, Jie Peng, Haibin Kan, Yanjun Li, Juan Luo

    For any positive integers \(n=2k\) and m such that \(m\ge k,\) in this paper we show that the maximal number of bent components of any (n, m)-function is equal to \(2^{m}-2^{m-k},\) and for those attaining the equality, their algebraic degree is at most k. It is easily seen that all (n, m)-functions of the form \(G(x)=(F(x),0),\) with F(x) being any vectorial bent (n, k)-function, have the maximal

    更新日期:2020-06-18
  • Caps and progression-free sets in $${{\mathbb {Z}}}_m^n$$ Z m n
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-16
    Christian Elsholtz, Péter Pál Pach

    We study progression-free sets in the abelian groups \(G=({{\mathbb {Z}}}_m^n,+)\). Let \(r_k({{\mathbb {Z}}}_m^n)\) denote the maximal size of a set \(S \subset {{\mathbb {Z}}}_m^n\) that does not contain a proper arithmetic progression of length k. We give lower bound constructions, which e.g. include that \(r_3({{\mathbb {Z}}}_m^n) \ge C_m \frac{((m+2)/2)^n}{\sqrt{n}}\), when m is even. When \(m=4\)

    更新日期:2020-06-16
  • Analysis of DeepBKZ reduction for finding short lattice vectors
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-03
    Masaya Yasuda, Satoshi Nakamura, Junpei Yamaguchi

    Lattice basis reduction is a mandatory tool for solving lattice problems such as the shortest vector problem. The Lenstra–Lenstra–Lovász reduction algorithm (LLL) is the most famous, and its typical improvements are the block Korkine–Zolotarev algorithm and LLL with deep insertions (DeepLLL), both proposed by Schnorr and Euchner. In BKZ with blocksize \(\beta \), LLL is called many times to reduce

    更新日期:2020-06-03
  • On equivalency of zero-divisor codes via classifying their idempotent generator
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-01
    Kai Lin Ong, Miin Huey Ang

    In 2009, Ted and Paul Hurley proposed a code construction method using group rings. These codes with single generator are termed group ring codes and in particular zero-divisor codes when using zero-divisors as generators. In this paper, we mainly study the equivalency of zero-divisor codes in \(F_2G\) having generator from I(G), the set of all idempotents in \(F_2G\). For abelian G, our previous notion

    更新日期:2020-06-01
  • On 2-parent-identifying set systems of block size 4
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-05-18
    Yujie Gu, Shohei Satake

    Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. In this paper we investigate the maximum number of blocks \(I_2(n,4)\) in a 2-parent-identifying set system with ground set size n and block size 4. The previous best-known lower bound states that \(I_2(n,4)=\varOmega (n^{4/3+o(1)})\). We improve this lower bound by showing that \(I_2(n,4)=

    更新日期:2020-05-18
  • A general framework for secondary constructions of bent and plateaued functions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-05-07
    S. Hodžić, E. Pasalic, Y. Wei

    In this work, we employ the concept of composite representation of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying new secondary constructions of bent/plateaued functions. This representation gives a better understanding of the existing secondary constructions and it also allows us to

    更新日期:2020-05-07
  • On q -ary bent and plateaued functions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-05-07
    Vladimir N. Potapov

    We obtain the following results. For any prime p the minimal Hamming distance between distinct regular p-ary bent functions of 2n variables is equal to \(p^n\). The number of p-ary regular bent functions at the distance \(p^n\) from the quadratic bent function \(Q_n=x_1x_2+\cdots +x_{2n-1}x_{2n}\) is equal to \(p^n(p^{n-1}+1)\cdots (p+1)(p-1)\) for \(p>2\). The Hamming distance between distinct binary

    更新日期:2020-05-07
  • Weierstrass semigroup at $$m+1$$ m + 1 rational points in maximal curves which cannot be covered by the Hermitian curve
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-04-27
    Alonso Sepúlveda Castellanos, Maria Bras-Amorós

    We determine the Weierstrass semigroup \(H(P_\infty ,P_1,\ldots ,P_m)\) at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced in Tafazolian et al. (J Pure Appl Algebra 220(3):1122–1132, 2016). Furthermore, we present some conditions to find pure gaps. We use this semigroup to obtain AG codes with better relative parameters than comparable one-point

    更新日期:2020-04-27
  • Affine equivalence for quadratic rotation symmetric Boolean functions
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-28
    Alexandru Chirvasitu, Thomas W. Cusick

    Let \(f_n(x_0, x_1, \ldots , x_{n-1})\) denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree d in \(n \ge d\) variables and let \(wt(f_n)\) denote the Hamming weight of this function. Let \((0, a_1, \ldots , a_{d-1})_n\) denote the function \(f_n\) of degree d in n variables generated by the monomial \(x_0x_{a_1} \ldots x_{a_{d-1}}.\) Such a function

    更新日期:2020-03-28
  • Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-27
    Ryutaroh Matsumoto

    We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert–Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple

    更新日期:2020-03-27
  • A geometric approach to rank metric codes and a classification of constant weight codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-21
    Tovohery Hajatiana Randrianarisoa

    In this work we develop a geometric approach to the study of rank metric codes. Using this method, we introduce a simpler definition for generalized rank weight of linear codes. We give a complete classification of constant rank weight code and we give their generalized rank weights.

    更新日期:2020-03-21
  • On non-binary traceability set systems
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-19
    Elena Egorova, Marcel Fernandez, Grigory Kabatiansky

    We introduce non-binary IPP set systems with traceability properties that have IPP codes and binary IPP set systems with traceability capabilities as particular cases. We prove an analogue of the Gilbert–Varshamov bound for such systems.

    更新日期:2020-03-19
  • Counting Boolean functions with faster points
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-11
    Ana Sălăgean, Ferruh Özbudak

    Duan and Lai introduced the notion of “fast point” for a Boolean function f as being a direction a so that the algebraic degree of the derivative of f in direction a is strictly lower than the expected \(\deg (f)-1\). Their study was motivated by the fact that the existence of fast points makes many cryptographic differential attacks (such as the cube and AIDA attack) more efficient. The number of

    更新日期:2020-03-11
  • Computing sharp recovery structures for locally recoverable codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-03-10
    Irene Márquez-Corbella, Edgar Martínez-Moro, Carlos Munuera

    A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery structure as concise as possible for an arbitrary linear code \({\mathcal {C}}\) and a recovery method that realizes it. This algorithm also provides the locality

    更新日期:2020-03-10
  • Cryptanalysis of a code-based one-time signature
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-02-26
    Jean-Christophe Deneuville, Philippe Gaborit

    In 2012, Lyubashevsky introduced a new framework for building lattice-based signature schemes without resorting to any trapdoor [such as Gentry C, Peikert C, Vaikuntanathan V, in: Ladner and Dwork (eds) 40th ACM STOC, ACM Press, Victoria, pp. 197–206, 2008 or Hoffstein J, Pipher J, Silverman JH in: Pfitzmann (ed) EUROCRYPT 2001. LNCS, vol. 2045, pp 211–228, Springer, Heidelberg, 2001]. The idea is

    更新日期:2020-02-26
  • Construction of self-dual matrix codes
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-02-26
    Lucky Erap Galvez, Jon-Lark Kim

    Matrix codes over a finite field \({\mathbb {F}}_q\) are linear codes defined as subspaces of the vector space of \(m \times n\) matrices over \({\mathbb {F}}_q\). In this paper, we show how to obtain self-dual matrix codes from a self-dual matrix code of smaller size using a method we call the building-up construction. We show that every self-dual matrix code can be constructed using this building-up

    更新日期:2020-02-26
  • Proving the biases of Salsa and ChaCha in differential attack
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-02-20
    Sabyasachi Dey, Santanu Sarkar

    Salsa and ChaCha are two of the most famous stream ciphers in recent times. Most of the attacks available so far against these two ciphers are differential attacks, where a difference is given as an input in the initial state of the cipher and in the output some correlation is investigated. This correlation works as a distinguisher. All the key recovery attacks against these ciphers are based on these

    更新日期:2020-02-20
  • Subspace packings: constructions and bounds
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-02-20
    Tuvi Etzion, Sascha Kurz, Kamil Otal, Ferruh Özbudak

    Grassmannian \({{{\mathcal {G}}}}_q(n,k)\) is the set of all k-dimensional subspaces of the vector space \({\mathbb {F}}_q^n\). Kötter and Kschischang showed that codes in Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are q-analogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian \({{{\mathcal

    更新日期:2020-02-20
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