Open Access Published by De Gruyter

Volume 8 Issue 4

Issue of Journal of Mathematical Cryptology

Contents
Journal Overview

Publicly Available December 1, 2014

Frontmatter

Page range: i-iv

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Open Access July 11, 2014

Efficient computation of pairings on Jacobi quartic elliptic curves

Sylvain Duquesne, Nadia El Mrabet, Emmanuel Fouotsa

Page range: 331-362

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Abstract

This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y2=dX4+Z4$Y^{2}=dX^{4}+Z^{4}$. We improve the doubling and addition steps in Miller's algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best result to date among curves with quartic twists. For the doubling and addition steps in Miller's algorithm for the computation of the Tate pairing, we obtain a theoretical gain up to 27%$27\%$ and 39%$39\%$, depending on the embedding degree and the extension field arithmetic, with respect to Weierstrass curves and previous results on Jacobi quartic curves. Furthermore and for the first time, we compute and implement Ate, twisted Ate and optimal pairings on the Jacobi quartic curves. Our results are up to 27%$27\%$ more efficient compared to the case of Weierstrass curves with quartic twists.

Open Access July 23, 2014

A subexponential construction of graph coloring for multiparty computation

Hassan Jameel Asghar, Yvo Desmedt, Josef Pieprzyk, Ron Steinfeld

Page range: 363-403

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Abstract

We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non-Abelian groups which is both optimal (secure against an adversary who possesses any t<n2$t < \frac{n}{2}$ inputs) and has subexponential complexity of construction based on coloring of planar graphs. More specifically, following the result of Desmedt et al. (2012) that the problem of MPC over non-Abelian groups can be reduced to finding a t -reliable n -coloring of planar graphs, we show the construction of such a graph which allows a path from the input nodes to the output nodes when any t -party subset is in the possession of the adversary. Unlike the deterministic constructions from Desmedt et al. (2012) our construction has subexponential complexity and is optimal at the same time, i.e., it is secure for any t<n2$t < \frac{n}{2}$.

Open Access July 8, 2014

Quantum computation of discrete logarithms in semigroups

Andrew M. Childs, Gábor Ivanyos

Page range: 405-416

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Abstract

We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete logarithm problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete logarithm problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to k ≥ 2 generators in a black-box abelian semigroup of order N requires Θ˜(N12-12k)$\tilde{\Theta }(N^{\frac{1}{2}-\frac{1}{2k}})$ quantum queries.

Open Access April 17, 2014

On the non-idealness of cyclotomic families of pairing-friendly elliptic curves

Min Sha

Page range: 417-440

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Abstract

Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$. Our bounds imply that none of the families are ideal.

About this journal

Objective
The Journal of Mathematical Cryptology (JMC) is a forum for original research articles in the area of mathematical cryptology. JMC is a fully peer-reviewed, open access, electronic-only journal publishing works of wide significance, originality and relevance. Works in the theory of cryptology and articles linking mathematics with cryptology (including quantum cryptology) are welcome. Submissions from all areas of mathematics significant for cryptology are invited, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes

The scope includes mathematical results of algorithmic or computational nature that are of interest to cryptology. While JMC does not cover information security as a whole, the submission of manuscripts on information security with a strong mathematical emphasis is explicitly encouraged.

Topics

Boolean functions
Elliptic curve cryptography
Mathematical cryptology
Information security
Quantum cryptology
Algebra
Algebraic geometry
Coding theory
Combinatorics and graph theory
Number theory
Probability and stochastic processes
Work linking math to cryptology
Work in the mathematical foundations of crypto
Theoretical aspects of cryptology
Mathematical foundations of cryptology

Article formats
Original research articles

Information on Submission Process