1. A New Attack on the Filter Generator.
- Author
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Rønjom, Sondre and Helleseth, Tor
- Subjects
MATHEMATICS ,NONLINEAR systems ,SYSTEMS theory ,EQUATIONS ,ALGEBRA ,MATHEMATICAL analysis ,ALGORITHMS ,NUMERICAL analysis - Abstract
The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2′ - 1 filtered through a Boolean function of degree d that combines bits from the shift register and creates an output bit z
t at any time t. The previous best attacks aimed at reconstructing the initial state from an observed keystream, have essentially reduced the problem to solving a nonlinear system of D = (Multiple line equation(s) cannot be represented in ASCII text) (i) equations in n unknowns using techniques based on linear algebra. This attack needs about D bits of keystream and the system can be solved in complexity O (Dω ), where ω can be taken to be Strassen's reduction exponent ω = log2 (7) ≈ 2.807. This paper describes a new algorithm that recovers the initial state of most filter generators after observing O(D) keystream bits with complexity O((D - n)/2) ≈ O(D), after a pre-computation with complexity O(D(log2 D)³). [ABSTRACT FROM AUTHOR]- Published
- 2007
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