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MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
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: 22)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 8)
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: 5)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
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: 6)
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: 8)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
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: 3)
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: 9)
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   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
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: 20)
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: 5)
BIBECHANA     Open Access   (Followers: 1)
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: 8)
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: 1)
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: 20)
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: 3)
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: 14)
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: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
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: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
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)

        1 2 3 4 | Last

Journal Cover Cryptography and Communications
  [SJR: 0.55]   [H-I: 8]   [14 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447
   Published by Springer-Verlag Homepage  [2352 journals]
  • Character values of the Sidelnikov-Lempel-Cohn-Eastman sequences
    • Authors: Şaban Alaca; Goldwyn Millar
      Pages: 665 - 682
      Abstract: Abstract Binary sequences with good autocorrelation properties and large linear complexity are useful in stream cipher cryptography. The Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences have nearly optimal autocorrelation. However, the problem of determining the linear complexity of the SLCE sequences is still open. It is well known that one can gain insight into the linear complexity of a sequence if one can say something about the divisors of the gcd of a certain pair of polynomials associated with the sequence. Helleseth and Yang (IEEE Trans. Inf. Theory 49(6), 1548–1552 2002), Kyureghyan and Pott (Des. Codes Crypt. 29, 149–164 2003) and Meidl and Winterhof (Des. Codes Crypt. 8, 159–178 2006) were able to obtain some results of this type for the SLCE sequences. Kyureghyan and Pott (Des. Codes Crypt. 29, 149–164 2003) mention that it would be nice to obtain more such results. We derive new divisibility results for the SLCE sequences in this paper. Our approach is to exploit the fact that character values associated with the SLCE sequences can be expressed in terms of a certain type of Jacobi sum. By making use of known evaluations of Gauss and Jacobi sums in the “pure” and “small index” cases, we are able to obtain new insight into the linear complexity of the SLCE sequences.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-016-0208-3
      Issue No: Vol. 9, No. 6 (2017)
  • Design sequences with high linear complexity over finite fields using
           generalized cyclotomy
    • Authors: Vladimir Edemskiy; Xiaoni Du
      Pages: 683 - 691
      Abstract: Abstract Based on the generalized cyclotomy theory, we design some classes of sequences with high linear complexity over the finite fields. First, we construct a new class of sequence from some generalized cyclotomic sequences of different orders with different prime powers period. Then we obtain the discrete Fourier transform, defining pairs and the linear complexity of the new sequences. Finally, we study the linear complexity of a special class of q−ary (q prime) sequences.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-016-0209-2
      Issue No: Vol. 9, No. 6 (2017)
  • Several classes of permutation trinomials from Niho exponents
    • Authors: Nian Li; Tor Helleseth
      Pages: 693 - 705
      Abstract: Abstract Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field \({\mathbb F}_{2^n}\) , where n is a positive even integer, we focus on the construction of permutation trinomials over \({\mathbb F}_{2^n}\) from Niho exponents. As a consequence, several new classes of permutation trinomials over \({\mathbb F}_{2^n}\) are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-016-0210-9
      Issue No: Vol. 9, No. 6 (2017)
  • Generalized methods to construct low-hit-zone frequency-hopping sequence
           sets and optimal constructions
    • Authors: Limengnan Zhou; Daiyuan Peng; Hongbin Liang; Changyuan Wang; Hongyu Han
      Pages: 707 - 728
      Abstract: Abstract In a quasi-synchronous frequency-hopping multiple-access system, relative time delay between different users within a zone around the origin can be allowed. Therefore, frequency-hopping sequence (FHS) sets with low-hit-zone (LHZ) have attracted great interest of many related scholars. Moreover, on account of the limited synchronous time or hardware complexity, the periodic partial Hamming correlation (PPHC) plays a major role in determining the synchronization performance. In this paper, we first present three new generalized methods to construct LHZ-FHS sets via Cartesian product. Meanwhile, we pay our attention to the maximum periodic Hamming correlation (PHC) of the constructed LHZ-FHS sets in the first generalized method, and to the maximum PPHC of the constructed LHZ-FHS sets in the rest generalized methods. In addition, we also introduce five new classes of optimal LHZ-FHS sets based on these three generalized methods.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-017-0211-3
      Issue No: Vol. 9, No. 6 (2017)
  • Sequences of bent functions and near-bent functions
    • Authors: J. Wolfmann
      Pages: 729 - 736
      Abstract: Abstract We introduce infinite sequences of Boolean functions whose terms all are bent functions or all are near-bent functions.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-017-0212-2
      Issue No: Vol. 9, No. 6 (2017)
  • A new family of arrays with low autocorrelation
    • Authors: Heiko Dietrich; Nathan Jolly
      Pages: 737 - 748
      Abstract: Abstract Arrays with low autocorrelation are widely sought in applications; important examples are arrays whose periodic autocorrelation is zero for all nontrivial cyclic shifts, so-called perfect arrays. In 2001, Arasu and de Launey defined almost perfect arrays: these have size 2u×v and autocorrelation arrays with only two nonzero entries, namely 2u v and −2u v in positions (0,0) and (u,0), respectively. In this paper we present a new class of arrays with low autocorrelation: for an integer n≥1, we call an array n-perfect if it has size n u×v and if its autocorrelation array has only n nonzero entries, namely n u v λ i in position (i u,0) for i=0,1,…,n−1, where λ is a primitive n-th root of unity. Thus, an array is 1-perfect (2-perfect) if and only if it is (almost) perfect. We give examples and describe a recursive construction of families of n-perfect arrays of increasing size.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-017-0214-0
      Issue No: Vol. 9, No. 6 (2017)
  • On the irreducibility of the hyperplane sections of Fermat varieties in
           ℙ 3 $\mathbb {P}^{3}$ in characteristic 2. II
    • Authors: Eric Férard
      Pages: 749 - 767
      Abstract: Abstract Let t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial \(\phi _{t}(x, y) = \frac {x^{t} + y^{t} + 1 + (x + y + 1)^{t}}{(x + y)(x + 1)(y + 1)}\) (over \(\mathbb {F}_{2}\) ) plays an important role in the study of APN functions. We prove that this polynomial is absolutely irreducible under the assumptions that the largest odd integer which divides t − 1 is large enough and can not be written in a specific form.
      PubDate: 2017-11-01
      DOI: 10.1007/s12095-017-0213-1
      Issue No: Vol. 9, No. 6 (2017)
  • Complete weight enumerators of two classes of linear codes
    • Authors: Xianfang Wang; Jian Gao; Fang-Wei Fu
      Pages: 545 - 562
      Abstract: Abstract In this paper, we give the complete weight enumerators of two classes of linear codes over the finite field \(\mathbb {F}_{p}\) , where p is a prime. These linear codes are the torsion codes of MacDonald codes over the finite non-chain ring \(\mathbb {F}_{p}+v\mathbb {F}_{p}\) , where v 2 = v. We also employ these linear codes to construct systematic authentication codes with new parameters.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0198-1
      Issue No: Vol. 9, No. 5 (2017)
  • On the best linear approximation of addition modulo 2 n
    • Authors: Shuai Xue; Wen-Feng Qi; Xiao-Yuan Yang
      Pages: 563 - 580
      Abstract: Abstract In this paper, the best linear approximations of addition modulo 2 n are studied. Let x = (x n−1, x n−2,…,x 0) and y = (y n−1, y n−2,…,y 0) be any two n-bit integers, and let z = x + y (mod 2 n ). Firstly, all the correlations of a single bit z i approximated by x j ’s and y j ’s (0 ≤ i, j ≤ n − 1) are characterized, and similar results are obtained for the linear approximation of the xoring of the neighboring bits of z i ’s. Then the maximum correlations and the best linear approximations are presented when these z j ’s (0 ≤ j ≤ n − 1) are xored in any given means.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0203-8
      Issue No: Vol. 9, No. 5 (2017)
  • Localised multisecret sharing
    • Authors: Thalia M. Laing; Keith M. Martin; Maura B. Paterson; Douglas R. Stinson
      Pages: 581 - 597
      Abstract: Abstract A localised multisecret sharing scheme is a multisecret sharing scheme for an ordered set of players in which players in the smallest sets who are authorised to access secrets are close together in the underlying ordering. We define threshold versions of localised multisecret sharing schemes, we provide lower bounds on the share size of perfect localised multisecret sharing schemes in an information theoretic setting, and we give explicit constructions of schemes to show that these bounds are tight. We then analyse a range of approaches to relaxing the model that provide trade-offs between the share size and the level of security guarantees provided by the scheme, in order to permit the construction of schemes with smaller shares. We show how these techniques can be used in the context of an application to key distribution for RFID-based supply-chain management motivated by the proposal of Juels, Pappu and Parno from USENIX 2008.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0202-9
      Issue No: Vol. 9, No. 5 (2017)
  • Secret sharing schemes for compartmented access structures
    • Authors: Xianfang Wang; Can Xiang; Fang-Wei Fu
      Pages: 625 - 635
      Abstract: Abstract In this paper, we devise ideal and probabilistic secret sharing schemes for two kinds of compartmented access structures. The first one is a compartmented access structures with hierarchical compartments. The second one is the compartmented access structures with strictly lower bounds. We propose ideal and probabilistic schemes for these two compartmented access structures by using the idea of bivariate interpolation.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0205-6
      Issue No: Vol. 9, No. 5 (2017)
  • Two and three weight codes over F p + u F p $\mathbb {F}_{p}+u\mathbb
    • Authors: Minjia Shi; Rongsheng Wu; Yan Liu; Patrick Solé
      Pages: 637 - 646
      Abstract: Abstract We construct an infinite family of three-Lee-weight codes of dimension 2m, where m is singly-even, over the ring \(\mathbb {F}_{p}+u\mathbb {F}_{p}\) with u 2=0. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain an infinite family of abelian p-ary three-weight codes. When m is odd, and p≡3 (mod 4), we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. An application to secret sharing schemes is given.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0206-5
      Issue No: Vol. 9, No. 5 (2017)
  • A class of hyper-bent functions and Kloosterman sums
    • Authors: Chunming Tang; Yanfeng Qi
      Pages: 647 - 664
      Abstract: Abstract This paper is devoted to the characterization of hyper-bent functions. Several classes of hyper-bent functions have been studied, such as Charpin and Gong’s family \(\sum \limits _{r\in R}\text {Tr}_{1}^{n} (a_{r}x^{r(2^{m}-1)})\) and Mesnager’s family \(\sum \limits _{r\in R}\text {Tr}_{1}^{n}(a_{r}x^{r(2^{m}-1)}) +\text {Tr}_{1}^{2}(bx^{\frac {2^{n}-1}{3}})\) . In this paper, we generalize these results by considering the following class of Boolean functions over \(\mathbb {F}_{2^{n}}\) : $$\sum\limits_{r\in R}\sum\limits_{i=0}^{2}T{r^{n}_{1}}(a_{r,i} x^{r(2^{m}-1)+\frac{2^{n}-1}{3}i}) +T{r^{2}_{1}}(bx^{\frac{2^{n}-1}{3}}), $$ where \(n=2m\) , m is odd, \(b\in \mathbb {F}_{4}\) , and \(a_{r,i}\in \mathbb {F}_{2^{n}}\) . With the restriction of \(a_{r,i}\in \mathbb {F}_{2^{m}}\) , we present a characterization of hyper-bentness of these functions in terms of crucial exponential sums. For some special cases, we provide explicit characterizations for some hyper-bent functions in terms of Kloosterman sums and cubic sums. Finally, we explain how our results on binomial, trinomial and quadrinomial hyper-bent functions can be generalized to the general case where the coefficients \(a_{r,i}\) belong to the whole field \(\mathbb {F}_{2^{n}}\) .
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0207-4
      Issue No: Vol. 9, No. 5 (2017)
  • A new class of permutation trinomials constructed from Niho exponents
    • Authors: Tao Bai; Yongbo Xia
      Abstract: Abstract Permutation polynomials over finite fields are an interesting subject due to their important applications in the areas of mathematics and engineering. In this paper, we investigate the trinomial f(x) = x (p−1)q+1 + x p q − x q+(p−1) over the finite field \(\mathbb {F}_{q^{2}}\) , where p is an odd prime and q = p k with k being a positive integer. It is shown that when p = 3 or 5, f(x) is a permutation trinomial of \(\mathbb {F}_{q^{2}}\) if and only if k is even. This property is also true for a more general class of polynomials g(x) = x (q+1)l+(p−1)q+1 + x (q+1)l + p q − x (q+1)l + q+(p−1), where l is a nonnegative integer and \(\gcd (2l+p,q-1)=1\) . Moreover, we also show that for p = 5 the permutation trinomials f(x) proposed here are new in the sense that they are not multiplicative equivalent to previously known ones of similar form.
      PubDate: 2017-10-17
      DOI: 10.1007/s12095-017-0263-4
  • On the normality of p -ary bent functions
    • Authors: Wilfried Meidl; Ísabel Pirsic
      Abstract: Abstract Depending on the parity of n and the regularity of a bent function f from \({{\mathbb F}_{p}^{n}}\) to \({\mathbb F}_{p}\) , f can be affine on a subspace of dimension at most n/2, (n − 1)/2 or n/2 − 1. We point out that many p-ary bent functions take on this bound, and it seems not easy to find examples for which one can show a different behaviour. This resembles the situation for Boolean bent functions of which many are (weakly) n/2-normal, i.e. affine on a n/2-dimensional subspace. However applying an algorithm by Canteaut, some Boolean bent functions were shown to be not n/2-normal. We develop an algorithm for testing normality for functions from \({{\mathbb F}_{p}^{n}}\) to \({\mathbb F}_{p}\) . Applying the algorithm, for some bent functions in small dimension we show that they do not take on the bound on normality. Applying direct sum of functions this yields bent functions with this property in infinitely many dimensions.
      PubDate: 2017-10-17
      DOI: 10.1007/s12095-017-0259-0
  • On the pseudorandomness of automatic sequences
    • Authors: László Mérai; Arne Winterhof
      Abstract: Abstract We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating functions or from their generating finite automatons, respectively.
      PubDate: 2017-10-13
      DOI: 10.1007/s12095-017-0260-7
  • Success probability of multiple/multidimensional linear cryptanalysis
           under general key randomisation hypotheses
    • Authors: Subhabrata Samajder; Palash Sarkar
      Abstract: Abstract This work considers statistical analysis of attacks on block cyphers using several linear approximations. A general and unified approach is adopted. To this end, the general key randomisation hypotheses for multidimensional and multiple linear cryptanalysis are introduced. Expressions for the success probability in terms of the data complexity and the advantage are obtained using the general key randomisation hypotheses for both multidimensional and multiple linear cryptanalysis and under the settings where the plaintexts are sampled with or without replacement. Particularising to standard/adjusted key randomisation hypotheses gives rise to success probabilities in 16 different cases out of which in only five cases expressions for success probabilities have been previously reported. Even in these five cases, the expressions for success probabilities that we obtain are more general than what was previously obtained. A crucial step in the analysis is the derivation of the distributions of the underlying test statistics. Whilst we carry out the analysis formally to the extent possible, there are certain inherently heuristic assumptions that need to be made. In contrast to previous works which have implicitly made such assumptions, we carefully highlight these and discuss why they are unavoidable. Finally, we provide a complete characterisation of the dependence of the success probability on the data complexity.
      PubDate: 2017-09-27
      DOI: 10.1007/s12095-017-0257-2
  • Some bounds on binary LCD codes
    • Authors: Lucky Galvez; Jon-Lark Kim; Nari Lee; Young Gun Roe; Byung-Sun Won
      Abstract: Abstract A linear code with a complementary dual (or An LCD code) is defined to be a linear code C whose dual code C ⊥ satisfies C ∩ C ⊥= \(\left \{ \mathbf {0}\right \} \) . Let L D (n, k) denote the maximum of possible values of d among [n, k, d] binary LCD codes. We give the exact values of L D (n, k) for k = 2 for all n and some bounds on L D (n, k) for other cases. From our results and some direct search we obtain a complete table for the exact values of L D (n, k) for 1 ≤ k ≤ n ≤ 12. As a consequence, we also derive bounds on the dimensions of LCD codes with fixed lengths and minimum distances.
      PubDate: 2017-09-26
      DOI: 10.1007/s12095-017-0258-1
  • Characteristic digit-sum sequences
    • Authors: Aleksandr Tuxanidy; Qiang Wang
      Abstract: Abstract We introduce a new type of sequences using the sum of coefficients of characteristic polynomials for elements (in particular, primitive elements) in a finite field. These sequences are nonlinear filtering sequences of the well-known m-sequences. We show that they have large linear complexity and large period. We also provide some examples of such binary sequences with good autocorrelation values.
      PubDate: 2017-09-23
      DOI: 10.1007/s12095-017-0256-3
  • Backtracking-assisted multiplication
    • Authors: Houda Ferradi; Rémi Géraud; Diana Maimuţ; David Naccache; Hang Zhou
      Abstract: Abstract This paper describes a new multiplication algorithm, particularly suited to lightweight microprocessors when one of the operands is known in advance. The method uses backtracking to find a multiplication-friendly encoding of the operand known in advance. A 68hc05 microprocessor implementation shows that the new algorithm indeed yields a twofold speed improvement over classical multiplication for 128-byte numbers.
      PubDate: 2017-09-05
      DOI: 10.1007/s12095-017-0254-5
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