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On the use of expansion series for stream ciphers

Part of: Arithmetic problems. Diophantine geometry Computational number theory Theory of computing Communication, information

Published online by Cambridge University Press:  01 September 2012

Claus Diem
Claus Diem*
Affiliation:
Mathematical Institute, University of Leipzig, Johannisgasse 26, D-04103 Leipzig, Germany (email: diem@math.uni-leipzig.de)

Abstract

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From power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.

MSC classification

Secondary: 11Y16: Algorithms; complexity 14G50: Applications to coding theory and cryptography 68Q25: Analysis of algorithms and problem complexity 94A60: Cryptography
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 326 - 340
Copyright
Copyright © London Mathematical Society 2012

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