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MATHEMATICS (645 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
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: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
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  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     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: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Applicable Algebra in Engineering, Communication and Computing
  [SJR: 0.354]   [H-I: 27]   [2 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0622 - ISSN (Online) 0938-1279
   Published by Springer-Verlag Homepage  [2329 journals]
  • Predicting the elliptic curve congruential generator
    • Authors: László Mérai
      Pages: 193 - 203
      Abstract: Let p be a prime and let \(\mathbf {E}\) be an elliptic curve defined over the finite field \(\mathbb {F}_p\) of p elements. For a point \(G\in \mathbf {E}(\mathbb {F}_p)\) the elliptic curve congruential generator (with respect to the first coordinate) is a sequence \((x_n)\) defined by the relation \(x_n=x(W_n)=x(W_{n-1}\oplus G)=x(nG\oplus W_0)\) , \(n=1,2,\ldots \) , where \(\oplus \) denotes the group operation in \(\mathbf {E}\) and \(W_0\) is an initial point. In this paper, we show that if some consecutive elements of the sequence \((x_n)\) are given as integers, then one can compute in polynomial time an elliptic curve congruential generator (where the curve possibly defined over the rationals or over a residue ring) such that the generated sequence is identical to \((x_n)\) in the revealed segment. It turns out that in practice, all the secret parameters, and thus the whole sequence \((x_n)\) , can be computed from eight consecutive elements, even if the prime and the elliptic curve are private.
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0303-x
      Issue No: Vol. 28, No. 3 (2017)
  • On the dynamics of endomorphisms of finite groups
    • Authors: Alexander Bors
      Pages: 205 - 214
      Abstract: Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting’s Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed 1-tree whose cycle is a loop with a disjoint union of cycles, generalizing results of Hernández-Toledo on linear finite dynamical systems, and we fully characterize the possible forms of state spaces of nilpotent endomorphisms via their “ramification behavior”. Finally, as an application, we will count the isomorphism types of state spaces of endomorphisms of finite cyclic groups in general, extending results of Hernández-Toledo on primary cyclic groups of odd order.
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0304-9
      Issue No: Vol. 28, No. 3 (2017)
  • More classes of permutation polynomials of the form $$(x^{p^m}-x+\delta
           )^s+L(x)$$ ( x p m - x + δ ) s + L ( x )
    • Authors: Dabin Zheng; Zhen Chen
      Pages: 215 - 223
      Abstract: This note presents two classes of permutation polynomials of the form \((x^{p^m}-x+\delta )^s+L(x)\) over the finite fields \({{\mathbb {F}}}_{p^{2m}}\) as a supplement of the recent works of Zha, Hu and Li, Helleseth and Tang.
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0305-8
      Issue No: Vol. 28, No. 3 (2017)
  • An automatic semigroup of languages
    • Authors: B. Panbehkar; H. Doostie
      Pages: 225 - 235
      Abstract: For a finitely generated automatic semigroup \(S=\langle A\rangle \) we define a semigroup \(L_S\) of languages concerning the automatic structure of S, and study the automaticity of \(L_S\) . Also we investigate the natural question “when S is isomorphic to \(L_S\) ?”. Finally, we attempt to verify the equation \(L_S\cup L_T=L_{S\cup T}\) for two non-monoid semigroups \((S, *)\) and (T, o).
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0306-7
      Issue No: Vol. 28, No. 3 (2017)
  • Polynomial interpolation of the Naor–Reingold pseudo-random function
    • Authors: Thierry Mefenza; Damien Vergnaud
      Pages: 237 - 255
      Abstract: We prove lower bounds on the degree of polynomials interpolating the Naor–Reingold pseudo-random function over a finite field and over the group of points on an elliptic curve over a finite field.
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0309-4
      Issue No: Vol. 28, No. 3 (2017)
  • Affine equivalence and non-linearity of permutations over $$\mathbb Z_n$$
           Z n
    • Authors: Yogesh Kumar; P. R. Mishra; N. Rajesh Pillai; R. K. Sharma
      Pages: 257 - 279
      Abstract: In this paper, we explore further the non-linearity and affine equivalence as proposed by Mishra et al. (Non-linearity and affine equivalence of permutations. 2014. We propose an efficient algorithm in order to compute affine equivalent permutation(s) of a given permutation of length n, of complexity \(O(n^4)\) in worst case and \(O(n^2)\) in best case. Also in the affirmative in a special case \(n = p\) , prime, it is of complexity \(O(n^3)\) . We also propose an upper bound of non-linearity of permutation(s) whose length satisfies a special condition. Further, behaviour of non-linearity on direct sum and skew sum of permutation has been analysed. Also the distance of an affine permutation from the other affine permutations has also been studied. The cryptographic implication of this work is on permutation based stream ciphers like RC4 and its variants. In this paper, we have applied this study on RC4 cipher. The analysis shows that increasing the key size for RC4 does not mean that increase in the security or saturation after a limit but security may falls as key size increases.
      PubDate: 2017-06-01
      DOI: 10.1007/s00200-016-0307-6
      Issue No: Vol. 28, No. 3 (2017)
  • New algorithm for the elliptic curve discrete logarithm problem with
           auxiliary inputs
    • Authors: Jiang Weng; Yunqi Dou; Chuangui Ma
      Pages: 99 - 108
      Abstract: The discrete logarithm problem with auxiliary inputs (DLP-wAI) is a special discrete logarithm problem. Cheon first proposed a novel algorithm to solve the discrete logarithm problem with auxiliary inputs. Given a cyclic group \({\mathbb {G}}=\langle P\rangle \) of order p and some elements \(P,\alpha P,\alpha ^2 P,\ldots , \alpha ^d P\in {\mathbb {G}}\) , an attacker can recover \(\alpha \in {\mathbb {Z}}_p^*\) in the case of \(d (p\pm 1)\) with running time of \({\mathcal {O}}(\sqrt{(p\pm 1)/d}+d^i)\) group operations by using \({\mathcal {O}}(\text {max}\{\sqrt{(p\pm 1)/d}, \sqrt{d}\})\) storage ( \(i=\frac{1}{2}\) or 1 for \(d (p-1)\) case or \(d (p+1)\) case, respectively). In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs (ECDLP-wAI). We show that if some points \(P,\alpha P,\alpha ^k P,\alpha ^{k^2} P,\alpha ^{k^3} P,\ldots ,\alpha ^{k^{\varphi (d)-1}}P\in {\mathbb {G}}\) and multiplicative cyclic group \(K=\langle k \rangle \) are given, where d is a prime, \(\varphi (d)\) is the order of K and \(\varphi \) is the Euler totient function, the secret key \(\alpha \in {\mathbb {Z}}_p^*\) can be solved in \({\mathcal {O}}(\sqrt{(p-1)/d}+d)\) group operations by using \({\mathcal {O}}(\sqrt{(p-1)/d})\) storage.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0301-z
      Issue No: Vol. 28, No. 2 (2017)
  • A simple method for obtaining relations among factor basis elements for
           special hyperelliptic curves
    • Authors: Palash Sarkar; Shashank Singh
      Pages: 109 - 130
      Abstract: Nagao proposed a decomposition method for divisors of hyperelliptic curves defined over a field \({\mathbb {F}}_{q^n}\) with \(n\ge 2\) . Joux and Vitse later proposed a variant which provided relations among the factor basis elements. Both Nagao’s and the Joux–Vitse methods require solving a multi-variate system of polynomial equations. In this work, we revisit Nagao’s approach with the idea of avoiding the requirement of solving a multi-variate system. While this cannot be done in general, we are able to identify special cases for which this is indeed possible. Our main result is for curves \(C:y^2=f(x)\) of genus g defined over \({\mathbb {F}}_{q^2}\) having characteristic >2. If there is no restriction on f(x), we show that it is possible to obtain a relation in \((4g+4)!\) trials. The number of trials, though high, quantifies the computation effort needed to obtain a relation. This is in contrast to the methods of Nagao and Joux–Vitse which are based on solving systems of polynomial equations, for which the computation effort is hard to precisely quantify. The new method combines well with a sieving technique proposed by Joux and Vitse. If f(x) has a special form, then the number of trials can be significantly lower. For example, if f(x) has at most g consecutive coefficients which are in \({\mathbb {F}}_{q^2}\) while the rest are in \({\mathbb {F}}_q\) , then we show that it is possible to obtain a single relation in about \((2g+3)!\) trials. Our implementation of the resulting algorithm provides examples of factor basis relations for \(g=5\) and \(g=6\) . To the best of our knowledge, none of the previous methods known in the literature can provide such relations faster than our method. Other than obtaining such decompositions, we also explore the applicability of our approach for \(n>2\) and for binary characteristic fields.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0299-2
      Issue No: Vol. 28, No. 2 (2017)
  • Some classes of linear codes over $$\mathbb {Z}_4+v\mathbb {Z}_4$$ Z 4 + v
           Z 4 and their applications to construct good and new $$\mathbb {Z}_4$$ Z 4
           -linear codes
    • Authors: Jian Gao; Fang-Wei Fu; Yun Gao
      Pages: 131 - 153
      Abstract: Some classes of linear codes over the ring \(\mathbb {Z}_4+v\mathbb {Z}_4\) with \(v^2=v\) are considered. Construction of Euclidean formally self-dual codes and unimodular complex lattices from self-dual codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) are studied. Structural properties of cyclic codes and quadratic residue codes are also considered. Finally, some good and new \(\mathbb {Z}_4\) -linear codes are constructed from linear codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0300-0
      Issue No: Vol. 28, No. 2 (2017)
  • Several classes of Boolean functions with few Walsh transform values
    • Authors: Guangkui Xu; Xiwang Cao; Shanding Xu
      Pages: 155 - 176
      Abstract: In this paper, several classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions. Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0298-3
      Issue No: Vol. 28, No. 2 (2017)
  • Minimal logarithmic signatures for one type of classical groups
    • Authors: Haibo Hong; Licheng Wang; Haseeb Ahmad; Jun Shao; Yixian Yang
      Pages: 177 - 192
      Abstract: As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like \(MST_1\) , \(MST_2\) and \(MST_3\) . An LS with the shortest length, called a minimal logarithmic signature (MLS), is even desirable for cryptographic applications. The MLS conjecture states that every finite simple group has an MLS. Recently, the conjecture has been shown to be true for general linear groups \(GL_n(q)\) , special linear groups \(SL_n(q)\) , and symplectic groups \(Sp_n(q)\) with q a power of primes and for orthogonal groups \(O_n(q)\) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group \(O_n(q)\) and \(SO_n(q)\) with q a power of an odd prime. Furthermore, we give constructions of MLSs for a type of classical groups—the projective commutator subgroup \(P{\varOmega }_n(q)\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0302-y
      Issue No: Vol. 28, No. 2 (2017)
  • Mirror theory and cryptography
    • Authors: Jacques Patarin
      Abstract: “Mirror Theory” is the theory that evaluates the number of solutions of affine systems of equalities \(({=})\) and non equalities ( \(\ne \) ) in finite groups. It is deeply related to the security and attacks of many generic cryptographic secret key schemes, for example random Feistel schemes (balanced or unbalanced), Misty schemes, Xor of two pseudo-random bijections to generate a pseudo-random function etc. In this paper we will assume that the groups are abelian. Most of time in cryptography the group is \(((\mathbb {Z}/2\mathbb {Z})^n, \oplus )\) and we will concentrate this paper on these cases. We will present here general definitions, some theorems, and many examples and computer simulations.
      PubDate: 2017-05-20
      DOI: 10.1007/s00200-017-0326-y
  • New binary linear codes from quasi-cyclic codes and an augmentation
    • Authors: Nuh Aydin; Nicholas Connolly; John Murphree
      Abstract: Explicit construction of linear codes with best possible parameters is one of the major problems in coding theory. Among all alphabets of interest, the binary alphabet is the most important one. In this work we use a comprehensive search strategy to find new binary linear codes in the well-known and intensively studied class of quasi-cyclic (QC) codes. We also introduce a generalization of an augmentation algorithm to obtain further new codes from those QC codes. Also applying the standard methods of obtaining new codes from existing codes, such as puncturing, extending and shortening, we have found a total of 62 new binary linear codes.
      PubDate: 2017-05-17
      DOI: 10.1007/s00200-017-0327-x
  • A class of primitive BCH codes and their weight distribution
    • Authors: Haode Yan
      Abstract: BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. Recently, several classes of BCH codes with length \(n=q^m-1\) and designed distances \(\delta =(q-1)q^{m-1}-1-q^{\lfloor (m-1)/2\rfloor }\) and \(\delta =(q-1)q^{m-1}-1-q^{\lfloor (m+1)/2\rfloor }\) were widely studied, where \(m\ge 4\) is an integer. In this paper, we consider the case \(m=3\) . The weight distribution of a class of primitive BCH codes with designed distance \(q^3-q^2-q-2\) is determined, which solves an open problem put forward in Ding et al. (Finite Fields Appl 45:237–263, 2017).
      PubDate: 2017-05-16
      DOI: 10.1007/s00200-017-0320-4
  • Linear codes from quadratic forms
    • Authors: Xiaoni Du; Yunqi Wan
      Abstract: Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power q, we present a class of linear codes over finite fields \(F_q\) with quadratic forms via a general construction and then determine the explicit complete weight enumerators of these linear codes. Our construction covers some related ones via quadratic form functions and the linear codes may have applications in cryptography and secret sharing schemes.
      PubDate: 2017-05-15
      DOI: 10.1007/s00200-017-0319-x
  • Geometric approach to the MacWilliams Extension Theorem for codes over
           module alphabets
    • Authors: Serhii Dyshko
      Abstract: The minimal code length for which there exists an unextendable Hamming isometry of a linear code defined over a matrix module alphabet is found. An extension theorem for MDS codes over module alphabets is proved. An extension theorem for the case of MDS group codes is observed.
      PubDate: 2017-05-15
      DOI: 10.1007/s00200-017-0324-0
  • An improved method for determining the weight distribution of a family of
           q -ary cyclic codes
    • Authors: Gerardo Vega
      Abstract: The purpose of this work is to use an already known identity among the weight enumerator polynomials, in order to present an improved method for determining the weight distribution of a family of q-ary reducible cyclic codes, that generalize, in an easier way, the results in Yu and Liu (Des Codes Cryptogr 78:731–745, 2016).
      PubDate: 2017-04-18
      DOI: 10.1007/s00200-017-0318-y
  • Spaces of directed paths on pre-cubical sets
    • Authors: Krzysztof Ziemiański
      Abstract: The spaces of directed paths on the geometric realizations of pre-cubical sets, called also \(\square \) -sets, can be interpreted as the spaces of possible executions of Higher Dimensional Automata, which are models for concurrent computations. In this paper we construct, for a sufficiently good pre-cubical set K, a CW-complex \(W(K)_v^w\) that is homotopy equivalent to the space of directed paths between given vertices v, w of K. This construction is functorial with respect to K, and minimal among all functorial constructions. Furthermore, explicit formulas for incidence numbers of the cells of \(W(K)_v^w\) are provided.
      PubDate: 2017-03-02
      DOI: 10.1007/s00200-017-0316-0
  • Some cyclic codes from some monomials
    • Authors: Zohreh Rajabi; Kazem Khashyarmanesh
      Abstract: Cyclic codes are an important class of linear codes. The objectives of this paper are to earn and extend earlier results over cyclic codes from some monomials. In fact, we determine the dimension and the generator polynomial of the code \({\mathcal {C}}_s\) defined by the monomial \(f(x)=x^{\frac{p^h+1}{2}}\) over \({\mathrm {GF}}(p^m)\) , where p is an odd prime and h is an integer. Also, we provide some answers for Open Problems 5.26 and 5.30 in Ding (SIAM J Discrete Math 27:1977–1994, 2013). Moreover, we study the code \({\mathcal {C}}_s\) defined by the monomial \(f(x)=x^{\frac{q^h-1}{q-1}}\) over \(\mathrm {GF}(q^m)\) , where h is an integer, without any restriction on h (see Section 5.3 in the above mentioned paper).
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-017-0317-z
  • 1-Generator quasi-cyclic and generalized quasi-cyclic codes over the ring
           $$\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1}\right\rangle }}$$
           Z 4 [ u ] u 2 - 1
    • Authors: Yun Gao; Jian Gao; Tingting Wu; Fang-Wei Fu
      Abstract: In this paper, we study 1-generator quasi-cyclic and generalized quasi-cyclic codes over the ring \(R=\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1} \right\rangle }}\) . We determine the structure of the generators and the minimal generating sets of 1-generator QC and GQC codes. We also give a lower bound for the minimum distance of free 1-generator quasi-cyclic and generalized quasi-cyclic codes over this ring, respectively. Furthermore, some new \(\mathbb {Z}_4\) -linear codes via the Gray map which have better parameters than the best known \(\mathbb {Z}_4\) -linear codes are presented.
      PubDate: 2017-02-20
      DOI: 10.1007/s00200-017-0315-1
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