for Journals by Title or ISSN for Articles by Keywords help
 Subjects -> ENGINEERING (Total: 2270 journals)     - CHEMICAL ENGINEERING (191 journals)    - CIVIL ENGINEERING (183 journals)    - ELECTRICAL ENGINEERING (99 journals)    - ENGINEERING (1199 journals)    - ENGINEERING MECHANICS AND MATERIALS (390 journals)    - HYDRAULIC ENGINEERING (55 journals)    - INDUSTRIAL ENGINEERING (64 journals)    - MECHANICAL ENGINEERING (89 journals) ENGINEERING (1199 journals)                  1 2 3 4 5 6 | Last
 Applicable Algebra in Engineering, Communication and Computing   [SJR: 0.354]   [H-I: 27]   [2 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1432-0622 - ISSN (Online) 0938-1279    Published by Springer-Verlag  [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. http://eprint.iacr.org/2014/974.pdf). 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
algorithm
• 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

JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327

Home (Search)
Subjects A-Z
Publishers A-Z
Customise
APIs