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MATHEMATICS (642 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: 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: 3)
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 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: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 6)
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)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Cryptography and Communications
  [SJR: 0.55]   [H-I: 8]   [12 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  [2340 journals]
  • 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)
  • Cyclic codes of odd length over ℤ 4 [ u ] / 〈 u k 〉
    • Authors: Yuan Cao; Qingguo Li
      Pages: 599 - 624
      Abstract: Abstract Let \(R=\mathbb{Z}_{4}[u]/ \langle u^k \rangle=\mathbb{Z}_{4}+u \mathbb{Z}_{4}+\ldots+u^{k-1}\mathbb{Z}_{4}\) ( \(u^{k}=0\) ), where k ≥ 2 is an positive integer. For any odd positive integer n, it is known that cyclic codes of length n over R are identified with ideals of the ring \(R[x]/\langle x^{n}-1\rangle\) . In this paper, an explicit representation for each cyclic code over R of length n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes of length n over R is obtained. Precisely, the dual code of each cyclic code and self-dual cyclic codes of length n over R are investigated. As an application, some good quasi-cyclic codes of length 7k and index k over ℤ4 are obtained from cyclic codes over R = ℤ4 [u] / 〈u k 〉 when k = 2, 3, 4.
      PubDate: 2017-09-01
      DOI: 10.1007/s12095-016-0204-7
      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)
  • Practical construction of ring LFSRs and ring FCSRs with low diffusion
           delay for hardware cryptographic applications
    • Authors: Zhiqiang Lin; Dongdai Lin; Dingyi Pei
      Pages: 431 - 443
      Abstract: Abstract Linear Feedback Shift Registers (LFSRs) and Feedback with Carry Shift Registers (FCSRs) are two pseudo-random generators which are widely used in many cryptographic applications. The Ring representation of them has been proposed using a matrix approach. In this paper, we show how to construct Ring LFSRs and Ring FCSRs with low diffusion delay (close to the expected value \(\sqrt {n}\) ) when considering other hardware cryptographic criteria.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0183-8
      Issue No: Vol. 9, No. 4 (2017)
  • Linear complexity and trace representation of quaternary sequences over
    • Authors: Zhixiong Chen
      Pages: 445 - 458
      Abstract: Abstract We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0185-6
      Issue No: Vol. 9, No. 4 (2017)
  • (1−2 u 3 )-constacyclic codes and quadratic residue codes over F p [ u ]
           / 〈 u 4 − u 〉 $\mathbb {F}_{p}[u]/\langle u^{4}-u\rangle $
    • Authors: Madhu Raka; Leetika Kathuria; Mokshi Goyal
      Pages: 459 - 473
      Abstract: Abstract Let \(\mathcal {R}=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^{2}\mathbb {F}_{p}+u^{3}\mathbb {F}_{p}\) with u 4 = u be a finite non-chain ring, where p is a prime congruent to 1 modulo 3. In this paper we study (1−2u 3)-constacyclic codes over the ring \(\mathcal {R}\) , their equivalence to cyclic codes and find their Gray images. To illustrate this, examples of (1−2u 3)-constacyclic codes of lengths 2 m for p = 7 and of lengths 3 m for p = 19 are given. We also discuss quadratic residue codes over the ring \(\mathcal {R}\) and their extensions. A Gray map from \(\mathcal {R}\) to \(\mathbb {F}_{p}^{4}\) is defined which preserves self duality and gives self-dual and formally self-dual codes over \(\mathbb {F}_{p}\) from extended quadratic residue codes.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0184-7
      Issue No: Vol. 9, No. 4 (2017)
  • Cyclic codes from the second class two-prime Whiteman’s generalized
           cyclotomic sequence with order 6
    • Authors: Pramod Kumar Kewat; Priti Kumari
      Pages: 475 - 499
      Abstract: Abstract Let \(n_{1}=df+1\) and \(n_{2}=df^{\prime }+1\) be two distinct odd primes with positive integers \(d,\ f,\ f^{\prime }\) and \(\gcd (f,f^{\prime })=1\) . In this paper, we compute the linear complexity and the minimal polynomial of the two-prime Whiteman’s generalized cyclotomic sequence of order \(d=6\) over \(\text {GF}(q)\) , where \(q=p^{m}\) and p is an odd prime and m is an integer. We employ this sequence of order 6 to construct several classes of cyclic codes over \(\text {GF}(q)\) with length \(n_{1}n_{2}\) . We also obtain lower bounds on the minimum distance of these cyclic codes.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0191-8
      Issue No: Vol. 9, No. 4 (2017)
  • Expansion complexity and linear complexity of sequences over finite fields
    • Authors: László Mérai; Harald Niederreiter; Arne Winterhof
      Pages: 501 - 509
      Abstract: Abstract The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo p. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0189-2
      Issue No: Vol. 9, No. 4 (2017)
  • New sets of optimal low-hit-zone frequency-hopping sequences based on m
    • Authors: Hongyu Han; Daiyuan Peng; Udaya Parampalli
      Pages: 511 - 522
      Abstract: Abstract In quasi-synchronous frequency-hopping multiple-access systems where relative delays are restricted within a certain correlation zone, low-hit-zone frequency-hopping sequences (LHZ-FHSs) are commonly employed to minimize multiple-access interferences. In this paper, we present two classes of optimal LHZ-FHS sets with respect to the Peng-Fan-Lee bound, which are obtained from an m-sequence and its decimated sequence, respectively. The parameters of these LHZ-FHS sets are new and flexible.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0192-7
      Issue No: Vol. 9, No. 4 (2017)
  • Probabilistic signature based generalized framework for differential fault
           analysis of stream ciphers
    • Authors: Santanu Sarkar; Prakash Dey; Avishek Adhikari; Subhamoy Maitra
      Pages: 523 - 543
      Abstract: Abstract Differential Fault Attack (DFA) considers injection of faults and the most general set-up should take care of faults at random location and random time. Then one should be able to identify the exact location as well as the exact timing of the fault (including the multi bit ones) with the help of fault signatures. In this paper we solve the problem of DFA under a general frame-work, introducing the idea of probabilistic signatures. The method considers the Maximum Likelihood approach related to probability distributions. Our techniques subsume all the existing DFAs against the Grain family, MICKEY 2.0 and Trivium. In the process we provide improved fault attacks for all the versions of Grain family and also for MICKEY 2.0. Our generalized method successfully takes care of the cases where certain parts of the keystream bits are missing (this situation may arise for authentication purpose). In particular, we show that the unsolved problem of identifying the faults in random time for Grain 128a can be solved in this manner. Moreover, for MICKEY 2.0, our method not only provides improvement in fault identification probability but also reduces the required faults by 60 %, compared to the best known result.
      PubDate: 2017-07-01
      DOI: 10.1007/s12095-016-0197-2
      Issue No: Vol. 9, No. 4 (2017)
  • A kind of three-weight linear codes
    • Authors: Qiuyan Wang; Kelan Ding; Dongdai Lin; Rui Xue
      Pages: 315 - 322
      Abstract: Abstract Recently, linear codes with few weights have been constructed through defining sets. Results show that some optimal codes can be obtained if the defining sets were well chosen. In this paper, we investigate the linear codes constructed from the absolute trace function. It is shown that the constructed codes are binary linear codes with three weights. The dual codes of the proposed linear codes are also studied and proved to be optimal or almost optimal.
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-015-0180-3
      Issue No: Vol. 9, No. 3 (2017)
  • Complete weight distributions of two classes of cyclic codes
    • Authors: Ziling Heng; Qin Yue
      Pages: 323 - 343
      Abstract: Abstract Complete weight distribution can be used to study authentication codes and the Walsh transform of monomial functions over finite fields. Also, the Hamming weight distribution of a code can be obtained from its complete weight distribution. In this paper, we investigate the complete weight distributions of two classes of cyclic codes. We explicitly present the complete weight enumerators of the cyclic codes. Particularly, we partly solve an open problem proposed in Luo and Feng (IEEE Trans. Inf. Theory 54(12), 5345–5353 (2008)).
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-015-0177-y
      Issue No: Vol. 9, No. 3 (2017)
  • On the nonlinearity of S-boxes and linear codes
    • Authors: Jian Liu; Sihem Mesnager; Lusheng Chen
      Pages: 345 - 361
      Abstract: Abstract For multi-output Boolean functions (also called S-boxes), various measures of nonlinearity have been widely discussed in the literature but many problems are left open in this topic. The purpose of this paper is to present a new approach to estimating the nonlinearity of S-boxes. A more fine-grained view on the notion of nonlinearity of S-boxes is presented and new connections to some linear codes are established. More precisely, we mainly study the nonlinearity indicator (denoted by \(\mathcal {N}_{\mathrm {v}}\) ) for S-boxes from a coding theory point of view. Such a cryptographic parameter \(\mathcal {N}_{\mathrm {v}}\) is more related to best affine approximation attacks on stream ciphers. We establish a direct link between \(\mathcal {N}_{\mathrm {v}}\) and the minimum distance of the corresponding linear code. We exploit that connection to derive the first general lower bounds on \(\mathcal {N}_{\mathrm {v}}\) of non-affine functions from \(\mathbb {F}_{2^{n}}\) to \(\mathbb {F}_{2^{m}}\) for m dividing n. Furthermore, we show that \(\mathcal {N}_{\mathrm {v}}\) can be determined directly by the weight distribution of the corresponding linear code.
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-015-0176-z
      Issue No: Vol. 9, No. 3 (2017)
  • New differentially 4-uniform permutations by modifying the inverse
           function on subfields
    • Authors: Jie Peng; Chik How Tan
      Pages: 363 - 378
      Abstract: Abstract Permutations over \(\mathbb {F}_{2^{2k}}\) with low differential uniformity, high algebraic degree and high nonlinearity are of great cryptographic importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers with SPN (Substitution Permutation Network) structure. A well known example is that the S-box of the famous Advanced Encryption Standard (AES) is derived from the inverse function on \(\mathbb {F}_{2^{8}}\) , which has been proved to be a differentially 4-uniform permutation with the optimal algebraic degree and known best nonlinearity. Recently, Zha et al. proposed two constructions of differentially 4-uniform permutations over \(\mathbb {F}_{2^{2k}}\) , say G t and G s, t with T r(s −1) = 1, by applying affine transformations to the inverse function on some subfields of \(\mathbb {F}_{2^{2k}}\) (Zha et al. Finite Fields Appl. 25, 64–78, 2014). In this paper, we generalize their method by applying other types of EA (extended affine) equivalent transformations to the inverse function on some subfields of \(\mathbb {F}_{2^{2k}}\) and present two new constructions of differentially 4-uniform permutations, say F α and F β, α with T r(β −1) = 1. Furthermore, we prove that all the functions G t with different t are CCZ (Carlet-Charpin-Zinoviev) equivalent to our subclass F 0, while all the functions G s, t with different t are CCZ-equivalent to our subclass F s,0. In addition, both our two constructions give many new CCZ-inequivalent classes of such functions, as checked by computer in small numbers of variables. Moreover, all these newly constructed permutations are proved to have the optimal algebraic degree and high nonlinearity.
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-016-0181-x
      Issue No: Vol. 9, No. 3 (2017)
  • Asymptotically optimal 2 ¯ $\overline {2}$ -separable codes with length 4
    • Authors: Minquan Cheng; Jing Jiang; Xiaohu Tang
      Pages: 397 - 405
      Abstract: Abstract Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we first show an equivalent condition of a \(\overline {2}\) -SC (4,M,q), and then construct two infinite families of \(\overline {2}\) -SCs of length 4, one of which is asymptotically optimal.
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-016-0182-9
      Issue No: Vol. 9, No. 3 (2017)
  • Some new classes of 2-fold optimal or perfect splitting authentication
    • Authors: Miao Liang; Lijun Ji; Jingcai Zhang
      Pages: 407 - 430
      Abstract: Abstract Optimal restricted strong partially balanced t-design can be used to construct splitting authentication codes which achieve combinatorial lower bounds or information-theoretic lower bounds. In this paper, we investigate the existence of optimal restricted strong partially balanced 2-designs ORSPBD (v, k×c,1), and show that there exists an ORSPBD (v,2×c,1) for any positive integer v≡ v 0 (mod 2c 2) and \(v_{0}\in \{1\leq x\leq 2c^{2}:\ \gcd (x,c)=1\ \text {or} \ \gcd (x,c)=c \} \setminus \) \(\{c^{2}+1\leq x\leq (c+1)^{2} :\gcd (x,c)=1\ \text {and}\ \gcd (x,2)=2\}\) . Furthermore, we determine the existence of an ORSPBD (v,k×c,1) for any integer v≥k c with (k,c)=(2,4), (2,5), (3,2) or for any even integer v≥k c with (k,c)=(4,2). As their applications, we obtain six new infinite classes of 2-fold optimal or perfect c-splitting authentication codes.
      PubDate: 2017-05-01
      DOI: 10.1007/s12095-015-0179-9
      Issue No: Vol. 9, No. 3 (2017)
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