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Breaking Littlewood's cipher

Damien Stehlé 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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.
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Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 6:05:27 PM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:27:17 PM


  • HAL Id : inria-00071590, version 1



Damien Stehlé. Breaking Littlewood's cipher. [Research Report] RR-4988, INRIA. 2003. ⟨inria-00071590⟩



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