Algebraic Attack on the Alternating Step(r,s)Generator

Details Algebraic Attack on the Alternating Step(r,s)Generator Algebraic Attack on the Alternating Step(r,s)Generator

2010-06-09

arxiv.org/abs/1006.1735v1

Computer Science

Cryptography and Security

5 pages, 2 figures, 2 tables, 2010 IEEE International Symposium on Information Theory (ISIT2010),June 13-18, 2010, Austin, Tex

Scientific paper

The Alternating Step(r,s) Generator, ASG(r,s), is a clock-controlled sequence generator which is recently proposed by A. Kanso. It consists of three registers of length l, m and n bits. The first register controls the clocking of the two others. The two other registers are clocked r times (or not clocked) (resp. s times or not clocked) depending on the clock-control bit in the first register. The special case r=s=1 is the original and well known Alternating Step Generator. Kanso claims there is no efficient attack against the ASG(r,s) since r and s are kept secret. In this paper, we present an Alternating Step Generator, ASG, model for the ASG(r,s) and also we present a new and efficient algebraic attack on ASG(r,s) using 3(m+n) bits of the output sequence to find the secret key with O((m^2+n^2)*2^{l+1}+ (2^{m-1})*m^3 + (2^{n-1})*n^3) computational complexity. We show that this system is no more secure than the original ASG, in contrast to the claim of the ASG(r,s)'s constructor.

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