Guess-and-Determine Algebraic Attack on the Self-Shrinking Generator
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The self-shrinking Generator (SSG) was proposed by Meier and Staffelbach at Eurocrypt’94. Two similar guess-and-determine attacks were independently proposed by Hell-Johansson and Zhang-Feng in 2006, and give the best time/data tradeoff on this cipher so far. These attacks do not depend on the Hamming weight of the feedback polynomial (defining the LFSR in SSG).
In this paper we propose a new attack strategy against SSG, when the Hamming weight is at most 5. For this case we obtain a better tradeoff than all previously known attacks (including Hell-Johansson and Zhang-Feng). Our main idea consists in guessing some information about the internal bitstream of the SSG, and expressing this information by a system of polynomial equations in the still unknown key bits. From a practical point of view, we show that using a SAT solver, such as MiniSAT, is the best way of solving this polynomial system.
Since Meier and Staffelbach original paper, avoiding low Hamming weight feedback polynomials has been a widely believed principle. However this rule did not materialize in previous recent attacks. With the new attacks described in this paper, we show explicitly that this principle remains true.
Keywordsstream cipher guess-and-determine attacks multivariate quadratic equations SAT solver self-shrinking generator algebraic cryptanalysis
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