Stehle, Damien

Cryptologia

Macquarie University ResearchOnline

Breaking Littlewood's Cipher

Article dans revue scientifique avec comité de lecture. internationale.International audienceIn 1953, the celebrated mathematician John Edensor Littlewood proposed a stream cipher based on logarithm tables. Fifty years later, we propose the first analysis of his scheme. Littlewood suggests the idea of using real functions as tools to build cryptographic primitives. Even when considering modern security parameters, the original scheme can be broken by a simple attack based on differentiation. We generalise the scheme such that it resists this attack based on differentiation. We generalise the scheme such that it resists this attacks, but describe another attack which is derived from both polynomial approximation and Coppersmith's technique to find the small roots of modular multivariate polynomials. In contrast with these negative results we describe a candidate for a very efficient one-way function and present an open problem based on this work

Stehlé, Damien

INRIA a CCSD electronic archive server

In 1953, the celebrated mathematician John Edensor Littlewood proposed a stream cipher based on logarithm tables. Fifty years later, we propose the first analysis of his scheme. Littlewood suggests the idea of using real functions as tools to build cryptographic primitives. Even when considering modern security parameters, the original scheme can be broken by a simple attack based on differentiation. We generalise the scheme such that it resists this attack, but describe another attack which is derived from both polynomial approximation and Coppersmith's technique to find the small roots of modular multivariate polynomials. In contrast with these negative results we describe a candidate for a very efficient one-way function and present an open problem based on this work

Breaking Littlewood's Cipher

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Macquarie University ResearchOnline

INRIA a CCSD electronic archive server

INRIA a CCSD electronic archive server