Open Access Published by De Gruyter

Volume 10 Issue 2

Issue of Journal of Mathematical Cryptology

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Contents
Journal Overview

Publicly Available June 1, 2016

Frontmatter

Page range: i-iv

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Open Access May 18, 2016

Another look at normal approximations in cryptanalysis

Subhabrata Samajder, Palash Sarkar

Page range: 69-99

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Abstract

Statistical analysis of attacks on symmetric ciphers often requires assuming the normal behaviour of a test statistic. Typically such an assumption is made in an asymptotic sense. In this work, we consider concrete versions of some important normal approximations that have been made in the literature. To do this, we use the Berry–Esséen theorem to derive explicit bounds on the approximation errors. A basic mathematical requirement is that such approximation errors should be within reasonable bounds, a point which appears to have been overlooked in many of the earlier works on statistical aspects of cryptanalysis. Interpreting the error bounds in the cryptanalytic context yields several surprising results. One important implication is that this puts in doubt the applicability of the order statistics based approach for analysing key recovery attacks on block ciphers. This approach has been earlier used to obtain several results on the data complexities of (multiple) linear and differential cryptanalysis. The non-applicability of the order statistics based approach puts a question mark on the data complexities obtained using this approach. Fortunately, we are able to recover all of these results by utilising the hypothesis testing framework. This, however, necessitates using normal approximations for the χ2${\chi ^2}$ and the LLR test statistics considered in earlier works. These approximations themselves have issues which seem to be difficult to resolve satisfactorily. More generally, the message of our work is that all cryptanalytic attacks should properly derive and interpret the error bounds for any (normal) approximation that is made.

Open Access April 21, 2016

Indifferentiability security of the fast wide pipe hash: Breaking the birthday barrier

Dustin Moody, Souradyuti Paul, Daniel Smith-Tone

Page range: 101-133

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Abstract

A hash function secure in the indifferentiability framework (TCC 2004) is able to resist all meaningful generic attacks. Such hash functions also play a crucial role in establishing the security of protocols that use them as random functions. To eliminate multi-collision type attacks on the Merkle–Damgård mode (Crypto 1989), Lucks proposed widening the size of the internal state of hash functions (Asiacrypt 2005). The fast wide pipe (FWP) hash mode was introduced by Nandi and Paul at Indocrypt 2010, as a faster variant of Lucks' wide pipe mode. Despite the higher speed, the proven indifferentiability bound of the FWP mode has so far been only up to the birthday barrier of n/2${n/2}$ bits. The main result of this paper is the improvement of the FWP bound to 2n/3${2n/3}$ bits (up to an additive constant). We also provide evidence that the bound may be extended beyond 2n/3${2n/3}$ bits.

Open Access May 10, 2016

New lattice attacks on DSA schemes

Dimitrios Poulakis

Page range: 135-144

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Abstract

We prove that a system of linear congruences of a particular form has at most a unique solution below a certain bound which can be computed efficiently. Using this result, we develop attacks against the DSA schemes which, under some assumptions, can provide the secret key in the case where one or several signed messages are available.

About this journal

Journal of Mathematical Cryptology is a fully peer-reviewed, open access, electronic journal that provides readers with free, instant, and permanent access to all content worldwide.

Aims and Scope

Journal of Mathematical Cryptology is a forum for articles in the area of mathematical cryptology.

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

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.

Journal of Mathematical Cryptology accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published, or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before submission.