Advances in Mathematics of Communications: latest papers Latest articles for selected journal Parity check systems of nonlinear codes over finite commutative Frobenius rings Thomas Westerbäck Tue, 1 Aug 2017 08:00:00 GMT Complete characterization of the first descent point distribution for the $k$-error linear complexity of $2^n$-periodic binary sequences Jianqin Zhou, Wanquan Liu and Xifeng Wang Tue, 1 Aug 2017 08:00:00 GMT Integer-valued Alexis sequences with large zero correlation zone Wei-Wen Hu Tue, 1 Aug 2017 08:00:00 GMT Computing elliptic curve discrete logarithms with improved baby-step giant-step algorithm     Another contribution of our paper is to give an analysis of the average-case running time of Bernstein and Lange's "grumpy giants and a baby" algorithm, and also to consider this algorithm in the case of groups with efficient inversion.
    Our conclusion is that, in the fully-optimised context, both the interleaved BSGS and grumpy-giants algorithms have superior average-case running time compared with Pollard rho. Furthermore, for the discrete logarithm problem in an interval, the interleaved BSGS algorithm is considerably faster than the Pollard kangaroo or Gaudry-Schost methods. ]]>
Steven D. Galbraith, Ping Wang and Fangguo Zhang Tue, 1 Aug 2017 08:00:00 GMT The weight distributions of constacyclic codes (r-1)m$, where $s,t, r$ are positive integers and $\xi\in \mathbb{F}_q$ is a primitive n-th root of unity. Moreover, we give the weight distributions of $\lambda$-constacyclic codes of length $nm$ explicitly in several cases: (1) $r=1$, $n>1$; (2) $r=2$, $m=2$ and $n>2$; (3) $r=2$, $m=3$ and $n>3$; (4) $r=3$, $m=2$ and $n>4$. ]]> Fengwei Li, Qin Yue and Fengmei Liu Tue, 1 Aug 2017 08:00:00 GMT Private set intersection: New generic constructions and feasibility results     In the unconditional setting we evidence that PSI is impossible to realize and that unconditionally secure size-hiding PSI is possible assuming a set-up authority is present in an set up phase. In the computational setting we give a generic construction using smooth projective hash functions for languages derived from perfectly-binding commitments. Further, we give two size-hiding constructions: the first one is theoretical and evidences the equivalence between PSI, oblivious transfer and the secure computation of the AND function. The second one is a twist on the oblivious polynomial evaluation construction of Freedman et al. from EUROCRYPT 2004. We further sketch a generalization of the latter using algebraic-geometric techniques. Finally, assuming again there is a set-up authority (yet not necessarily trusted) we present very simple and efficient constructions that only hide the size of the client's set. ]]> Paolo D'Arco, María Isabel González Vasco, Angel L. Pérez del Pozo, Claudio Soriente and Rainer Steinwandt Tue, 1 Aug 2017 08:00:00 GMT Relative generalized Hamming weights of $q$-ary Reed-Muller codes Olav Geil and Stefano Martin Tue, 1 Aug 2017 08:00:00 GMT New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions Anna-Lena Horlemann-Trautmann and Kyle Marshall Tue, 1 Aug 2017 08:00:00 GMT Generalized bent functions - sufficient conditions and related constructions Samir Hodžić and Enes Pasalic Tue, 1 Aug 2017 08:00:00 GMT Network encoding complexity: Exact values, bounds, and inequalities Easton Li Xu, Weiping Shang and Guangyue Han Tue, 1 Aug 2017 08:00:00 GMT Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields     As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of $x^n-\lambda$ and the Chinese Remainder Theorem, quasi-twisted codes can be viewed as a product of linear codes of shorter length over some extension fields of $\mathbb{F}_{q^2}$. Necessary and sufficient conditions for quasi-twisted codes to be Hermitian self-dual are given. The enumeration of such self-dual codes is determined as well. ]]> Ekkasit Sangwisut, Somphong Jitman and Patanee Udomkavanich Tue, 1 Aug 2017 08:00:00 GMT Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma,\delta)$-codes     When $S$ is a Galois ring and $f$ base irreducible, these algebras yield families of finite unital nonassociative rings $A$, whose set of (left or right) zero divisors has the form $pA$ for some prime $p$.
    For reducible $f$, the $S_f$ can be employed both to design linear $(f,\sigma,\delta)$-codes over unital rings and to study their behaviour. ]]>
Susanne Pumplün Tue, 1 Aug 2017 08:00:00 GMT Self-dual codes with an automorphism of order 13 Nikolay Yankov, Damyan Anev and Müberra Gürel Tue, 1 Aug 2017 08:00:00 GMT