Subjects -> MATHEMATICS (Total: 1028 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (729 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (729 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 2)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 1)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 7)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 3)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 3)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 5)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 10)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Cryptography and Communications
Journal Prestige (SJR): 0.446
Citation Impact (citeScore): 1
Number of Followers: 10  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447
Published by Springer-Verlag Homepage  [2469 journals]
  • Minimal linear codes constructed from functions

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      Abstract: In this paper, we consider minimal linear codes by a general construction of linear codes from q-ary functions. First, we give necessary and sufficient conditions for codewords which are constructed by functions to be minimal. Second, as applications, we present three constructions of minimal linear codes. Constructions on minimal linear codes in this paper generalize some recent results in Ding et al. (IEEE Trans. Inf. Theory 64(10), 6536–6545, 2018); Heng et al. (Finite Fields Appl. 54, 176–196, 2018); Bartoli and Bonini (IEEE Trans. Inf. Theory 65(7), 4152–4155, 2019); Mesnager et al. (IEEE Trans. Inf. Theory 66(9), 5404–5413, 2020); Bonini and Borello (J. Algebraic Comb. 53, 327–341, 2021). In our three constructions, the conditions of functions are much looser than theirs.
      PubDate: 2022-01-18
       
  • Differential uniformity and linearity of S-boxes by multiplicative
           complexity

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      Abstract: A cryptographic primitive with low multiplicative complexity (MC) makes various applications efficient, but it may lead to cryptographic vulnerabilities. To find a trade-off between cryptographic resistance and MC, we propose a new tool called A-box, which is constructed using AND gates. In this paper, we prove several important properties of A-boxes, which provide the theoretical lower bounds of differential uniformity and linearity of corresponding S-boxes by MC. Specifically, we show that the differential uniformity (resp. linearity) of an (n, m)-bit S-box is at least 2n−l, where its MC is \(\lfloor \frac {n-1}{2}\rfloor +l\) (resp. m − 1 + l). Furthermore, we develop an algorithm to find S-boxes with differential uniformity equal to the bounds with respect to their MC. We improve the algorithm previously proposed by Zajac and Jókay (Cryptogr. Commun. 6(3), 255–277, 2014), which is applicable only to S-boxes of size lower than 5 bits, whereas ours can run on larger-sized S-boxes. We found a bijective (8,8)-bit S-box with differential uniformity 16, linearity 128, and 8 nonlinear gates: this has better cryptographic security than the SKINNY S-box with differential uniformity 64, linearity 128, and 8 nonlinear gates. We believe that our results provide a better understanding of the relationship between cryptographic resistance and MC of S-boxes.
      PubDate: 2022-01-13
       
  • On the classification of quaternary optimal Hermitian LCD codes

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      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.
      PubDate: 2022-01-07
       
  • New z-complementary/complementary sequence sets with non-power-of-two
           length and low PAPR

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      Abstract: Sequences with low peak-to-average power ratio (PAPR) and desirable lengths are useful and important for orthogonal frequency division multiplexing (OFDM) systems. In this paper, based on the generalized Boolean functions (GBFs), a class of q-ary Z-complementary sequence sets (ZCSSs) and a class of complementary sequence sets (CSSs) are constructed. The obtained new ZCSSs and CSSs have low PAPR and non-power-of-two lengths.
      PubDate: 2022-01-04
       
  • Survey on recent trends towards generalized differential and boomerang
           uniformities

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      Abstract: Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block and stream ciphers and cryptographic hash functions. The discovery of differential cryptanalysis is generally attributed to Biham and Shamir in the late 1980s, who published several attacks against various block ciphers and hash functions, including a theoretical weakness in the Data Encryption Standard (DES). Boomerang cryptanalysis is a method for the cryptanalysis of block ciphers based on differential cryptanalysis. It was invented by Wagner in (FSE, LNCS 1636, 156–170, 1999) and has allowed new avenues of attack for many ciphers previously deemed safe from differential cryptanalysis. Differential and boomerang uniformities are crucial tools to handle and analyze vectorial functions (designated by substitution boxes, or briefly S-boxes in the context of symmetric cryptography) to resist differential and boomerang attacks, respectively. Ellingsen et al. (IEEE Transactions on Information Theory 66(9), 2020) introduced a new variant of differential uniformity, called c-differential uniformity (where c is a non-zero element of a finite field of characteristic p), of p-ary (n, m)-function for any prime p obtained by extending the well-known derivative of vectorial functions into the (multiplicative) c-derivative. Later, Stănică [Discrete Applied Mathematics, 2021] introduced the notion of c-boomerang uniformity. Both c-differential and c-boomerang uniformities have been extended to the idea of simple differential and boomerang uniformities, respectively, which are recovered when c equals 1.This survey paper combines the known results on this new concept of differential and boomerang uniformities and analyzes their possible cryptographic applications. This survey presents an overview of these significant concepts that might have greater implications for future theoretical research on this subject and applied perspectives in symmetric cryptography and related topics. Along with the paper, we analyze these discoveries and the results provided synthetically. The article intends to help readers explore further avenues in this promising and emerging direction of research. At the end of the article, we present more than nine lines of perspectives and research directions to benefit symmetric cryptography and other related domains such as combinatorial theory (namely, graph theory).
      PubDate: 2021-12-03
       
  • New constructions of self-dual generalized reed-solomon codes

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      Abstract: A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider new constructions of MDS self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The critical idea of our constructions is to choose suitable evaluation points such that the corresponding (extended) GRS codes are self-dual. The evaluation set of our constructions consists of a subgroup of finite fields and its cosets in a bigger subgroup. Four new families of MDS self-dual codes are then obtained. Moreover, by the Möbius action over finite fields, for any known self-dual GRS codes, we give a systematic way to construct new self-dual GRS codes with flexible evaluation points.
      PubDate: 2021-11-24
       
  • Improving bounds on probabilistic affine tests to estimate the
           nonlinearity of Boolean functions

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      Abstract: In this paper we want to estimate the nonlinearity of Boolean functions, by probabilistic methods, when it is computationally very expensive, or perhaps not feasible to compute the full Walsh transform (which is the case for almost all functions in a larger number of variables, say more than 30). Firstly, we significantly improve upon the bounds of Zhang and Zheng (1999) on the probabilities of failure of affinity tests based on nonhomomorphicity, in particular, we prove a new lower bound that we have previously conjectured. This new lower bound generalizes the one of Bellare et al. (IEEE Trans. Inf. Theory 42(6), 1781–1795 1996) to nonhomomorphicity tests of arbitrary order. Secondly, we prove bounds on the probability of failure of a proposed affinity test that uses the BLR linearity test. All these bounds are expressed in terms of the function’s nonlinearity, and we exploit that to provide probabilistic methods for estimating the nonlinearity based upon these affinity tests. We analyze our estimates and conclude that they have reasonably good accuracy, particularly so when the nonlinearity is low.
      PubDate: 2021-11-19
       
  • Rational complexity of binary sequences, F ℚ $\mathbb {Q}$ SRs, and
           pseudo-ultrametric continued fractions in ℝ $\mathbb {R}$

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      Abstract: We introduce rational complexity, a new complexity measure for binary sequences. The sequence s ∈ Bω is considered as binary expansion of a real fraction \(s \equiv {\sum }_{k\in \mathbb {N}}s_{k}2^{-k}\in [0,1] \subset \mathbb {R}\) . We compute its continued fraction expansion (CFE) by the Binary CFE Algorithm, a bitwise approximation of s by binary search in the encoding space of partial denominators, obtaining rational approximations r of s with r → s. We introduce Feedback in \(\mathbb {Q}\) Shift Registers (F \(\mathbb {Q}\) SRs) as the analogue of Linear Feedback Shift Registers (LFSRs) for the linear complexity L, and Feedback with Carry Shift Registers (FCSRs) for the 2-adic complexity A. We show that there is a substantial subset of prefixes with “typical” linear and 2-adic complexities, around n/2, but low rational complexity. Thus the three complexities sort out different sequences as non-random.
      PubDate: 2021-11-15
       
  • A class of binary cyclic codes with optimal parameters

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      Abstract: For positive integers k ≥ 2 and t, let m = 2kt and α be a primitive element of the finite field \(\mathbb {F}_{2^{m}}\) . In this paper, we study the parameters of a class of cyclic codes \(\mathcal {C}_{(1,v)}\) which has two zeros α and αv with \(v=\frac {2^{m}-1}{2^{t}+1}\) . It is shown that \(\mathcal {C}_{(1,v)}\) is optimal or almost optimal with respect to the sphere packing bound. Based on some results of Kloosterman sums and Gaussian periods, the weight distribution of the dual code of \(\mathcal {C}_{(1,v)}\) is completely determined when t = 5.
      PubDate: 2021-11-12
       
  • The second-order zero differential spectra of almost perfect nonlinear
           functions and the inverse function in odd characteristic

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      Abstract: In a prior paper (Boukerrou et al. IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020), Boukerrou et al. introduced the Feistel Boomerang Connectivity Table (FBCT). FBCT is an important cryptanalytic technique on Feistel ciphers. In fact, the coefficients of FBCT are actually related to the second-order zero differential spectra of functions in even characteristic. In this paper, we push further the study initiated in Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020). Almost perfect nonlinear (APN) functions and the inverse function are interesting in cryptography and coding theory. In Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020), Boukerrou et al. determined the second-order zero differential spectra of APN functions and the inverse function in even characteristic. In order to derive further cryptographic properties of APN functions and the inverse function in odd characteristic, we calculate the second-order zero differential spectra of some APN functions and the inverse function in odd characteristic. In addition, these APN functions and the inverse function have low second-order zero differential uniformity.
      PubDate: 2021-11-09
       
  • Some t-designs from BCH codes

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      Abstract: Combinatorial t-designs are closely related to coding theory and finite geometries and have nice applications in some engineering areas. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. In this paper, this approach is further investigated with a class of linear codes related to the extended BCH codes and their duals over finite fields. By determining the parameters of these codes, an infinite family of 3-designs is presented and their parameters are also explicitly determined. In addition, the parameters of some combinatorial 2-designs from the extended codes of certain primitive BCH codes are also determined. Moreover, Research Problem 9.4 proposed by Ding in [Designs from Linear Codes, World Scientific, Singapore, pp: 257, 2018)] is also solved.
      PubDate: 2021-11-04
       
  • Editorial: Special issue on Boolean functions and their applications 2020

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      PubDate: 2021-11-01
       
  • On constructions of weightwise perfectly balanced Boolean functions

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      Abstract: The recent FLIP cipher is an encryption scheme described by Méaux et al. at the conference EUROCRYPT 2016. It is based on a new stream cipher model called the filter permutator and tries to minimize some parameters (including the multiplicative depth). In the filter permutator, the input to the Boolean function has constant Hamming weight equal to the weight of the secret key. As a consequence, Boolean functions satisfying good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the FLIP stream cipher. Carlet et al. have shown that for Boolean functions with restricted input, balancedness and nonlinearity parameters continue to play an important role with respect to the corresponding attacks on the framework of FLIP ciphers. In particular, Boolean functions which are uniformly distributed over \({\mathbb {F}}_{2}\) on \(E_{n,k}=\{x{\in \mathbb {F}_{2}^{n}}\mid \text {wt}(x)=k\}\) for every 0 < k < n are called weightwise perfectly balanced (WPB) functions, where wt(x) denotes the Hamming weight of x. In this paper, we firstly propose two methods of constructing weightwise perfectly balanced Boolean functions in 2k variables (where k is a positive integer) by modifying the support of linear and quadratic functions. Furthermore, we derive a construction of n-variable weightwise almost perfectly balanced Boolean functions for any positive integer n.
      PubDate: 2021-11-01
       
  • Secret sharing schemes based on the dual of Golay codes

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      Abstract: Linear codes are an important class of codes in coding theory and have been extensively studied due to their significant applications (including the design of secret sharing schemes) in practical systems. Interesting linear codes having several different real-world applications are the so-called Golay codes. Secret sharing schemes play a fundamental role in cryptography and have numerous applications in security systems. One approach to constructing secret sharing schemes is based on linear codes, especially for minimal linear codes and self-dual codes. Several minimal linear codes based on Boolean cryptographic functions and vectorial Boolean functions have been found. This paper proposes two secret sharing schemes based on the dual of the [23,12,7]2 and [11,6,5]3 Golay codes, respectively, where these two Golay codes are neither minimal nor self-dual. We determine the minimal access structures of our schemes by using the two Golay codes’ combinatorial properties. To our surprise, our schemes are 3-democratic. This is interesting since our schemes are not threshold secret sharing schemes, and previous works propose some democratic secret sharing schemes that are based on the dual of minimal linear codes. On the other hand, we find that our schemes’ minimal access structures contradict a result of Dougherty et al. (ITW 2008). We then revise the minimal access structures of the secret sharing schemes based on the [24,12,8]2 and [12,6,6]3 extended Golay codes, respectively, and we further discuss the democracies of these two schemes.
      PubDate: 2021-11-01
       
  • The linear codes of t-designs held in the Reed-Muller and Simplex codes

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      Abstract: A fascinating topic of combinatorics is the study of t-designs, which has a very long history. The incidence matrix of a t-design generates a linear code over GF(q) for any prime power q, which is called the linear code of the t-design over GF(q). On the other hand, some linear codes hold t-designs with t ≥ 1. The purpose of this paper is to study the linear codes of t-designs held in the Reed-Muller and Simplex codes. Some general theory for the linear codes of t-designs held in linear codes is presented. Several open problems are also presented.
      PubDate: 2021-11-01
       
  • Invariants for EA- and CCZ-equivalence of APN and AB functions

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      Abstract: An (n,m)-function is a mapping from \({\mathbb {F}_{2}^{n}}\) to \({\mathbb {F}_{2}^{m}}\) . Such functions have numerous applications across mathematics and computer science, and in particular are used as building blocks of block ciphers in symmetric cryptography. The classes of APN and AB functions have been identified as cryptographically optimal with respect to the resistance against two of the most powerful known cryptanalytic attacks, namely differential and linear cryptanalysis. The classes of APN and AB functions are directly related to optimal objects in many other branches of mathematics, and have been a subject of intense study since at least the early 90’s. Finding new constructions of these functions is hard; one of the most significant practical issues is that any tentatively new function must be proven inequivalent to all the known ones. Testing equivalence can be significantly simplified by computing invariants, i.e. properties that are preserved by the respective equivalence relation. In this paper, we survey the known invariants for CCZ- and EA-equivalence, with a particular focus on their utility in distinguishing between inequivalent instances of APN and AB functions. We evaluate each invariant with respect to how easy it is to implement in practice, how efficiently it can be calculated on a computer, and how well it can distinguish between distinct EA- and CCZ-equivalence classes.
      PubDate: 2021-11-01
       
  • Characters, Weil sums and c-differential uniformity with an application to
           the perturbed Gold function

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      Abstract: Building upon the observation that the newly defined Ellingsen, et al. (2020) concept of c-differential uniformity is not invariant under EA or CCZ-equivalence Hasan et al. (2021), we showed in Stănică and Geary (2021) that adding some appropriate linearized monomials increases the c-differential uniformity of the inverse function, significantly, for some c. We continue that investigation here. First, by analyzing the involved equations, we find bounds for the uniformity of the Gold function perturbed by a single monomial, exhibiting the discrepancy we previously observed on the inverse function. Secondly, to treat the general case of perturbations via any linearized polynomial, we use characters in the finite field to express all entries in the c-Differential Distribution Table (DDT) of an (n, n)-function on the finite field \({\mathbb {F}}_{p^{n}}\) , and further, we use that method to find explicit expressions for all entries of the c-DDT of the perturbed Gold function (via an arbitrary linearized polynomial).
      PubDate: 2021-11-01
       
  • Kim-type APN functions are affine equivalent to Gold functions

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      Abstract: The problem of finding APN permutations of \({\mathbb {F}}_{2^{n}}\) where n is even and n > 6 has been called the Big APN Problem. Li, Li, Helleseth and Qu recently characterized APN functions defined on \({\mathbb {F}}_{q^{2}}\) of the form f(x) = x3q + a1x2q+ 1 + a2xq+ 2 + a3x3, where q = 2m and m ≥ 4. We will call functions of this form Kim-type functions because they generalize the form of the Kim function that was used to construct an APN permutation of \({\mathbb {F}}_{2^{6}}\) . We prove that Kim-type APN functions with m ≥ 4 (previously characterized by Li, Li, Helleseth, and Qu) are affine equivalent to one of two Gold functions G1(x) = x3 or \(G_{2}(x)=x^{2^{m-1}+1}\) . Combined with the recent result of Göloğlu and Langevin who proved that, for even n, Gold APN functions are never CCZ equivalent to permutations, it follows that for m ≥ 4 Kim-type APN functions on \({\mathbb {F}}_{2^{2m}}\) are never CCZ equivalent to permutations.
      PubDate: 2021-11-01
       
  • Some general properties of modified bent functions through addition of
           indicator functions

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      Abstract: Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n variables are obtained. Some results regarding normal and weakly normal bent functions are generalized. An upper bound for the number of generated bent functions is proven. This bound is attained if and only if the given bent function is quadratic. In certain cases, the addition of the indicator of an m-dimensional subspace, for different m, will not generate bent functions. Such examples are presented for any even n ≥ 10. It is proven that there exists an infinite family of Maiorana–McFarland bent functions such that the numbers of generated bent functions differ for the bent function and its dual function.
      PubDate: 2021-11-01
       
  • LCD and ACD codes over a noncommutative non-unital ring with four elements

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      Abstract: We study LCD (linear complementary dual) and ACD (additive complementary dual) codes over a noncommutative non-unital ring E with four elements. This is the first attempt to construct LCD codes over a noncommutative non-unital ring. We show that free LCD codes over E are directly related to binary LCD codes. We introduce ACD codes over E. They include free LCD codes over E as a special case. These facts imply that LCD and ACD codes over E are worth studying. In particular, we characterize a free LCD E-code C in terms of a binary generator matrix G. We also define an ACD code over E, called a left-ACD code. We give several conditions for the existence of left-ACD codes.
      PubDate: 2021-10-30
       
 
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