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

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

A Simple Attack on Some Clock-Controlled Generators

We present a new approach to edit distance attacks on certain clock-controlled generators, which applies basic concepts of Graph Theory to simplify the search trees of the original attacks in such a way that only the most promising branches are analyzed. In particular, the proposed improvement is based on cut sets defined on some graphs so that certain shortest paths provide the edit distances. The strongest aspects of the proposal are that the obtained results from the attack are absolutely deterministic, and that many inconsistent initial states of the target registers are recognized beforehand and avoided during search

Investigations in the design and analysis of key-stream generators

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Cryptanalysis of LFSR-based Pseudorandom Generators - a Survey

Pseudorandom generators based on linear feedback shift registers (LFSR) are a traditional building block for cryptographic stream ciphers. In this report, we review the general idea for such generators, as well as the most important techniques of cryptanalysis

Graph-Based Approach to the Edit Distance Cryptanalysis of Irregularly Clocked Linear Feedback Shift Registers

This paper proposes a speed-up of a known-plaintext attack on some stream ciphers based on Linear Feedback Shift Registers (LFSRs). The algorithm consists of two basic steps: first, to guess the initial seed value of one of the LFSRs, and then to use the resulting binary sequence in order to deduce useful information about the cipher parameters. In particular, the proposed divide-and-conquer attack is based on a combination of graph-based techniques with edit distance concepts. While the original edit distance attack requires the exhaustive search over the set of all possible initial states of the involved LFSR, this work presents a new heuristic optimization that avoids the evaluation of an important number of initial states through the identification of the most promising branches of the search graph. The strongest aspects of the proposal are the facts that the obtained results from the attack are absolutely deterministic, and that many inconsistent initial states of the target LFSRs are recognized and avoided during search.This work was supported by the Spanish Ministry of Science and Innovation and European FEDER Fund under Project TIN2008-02236/TSI as well as by CDTI (Spain)and the companies INDRA, Unin Fenosa, Tecnobit, Visual Tool, Brainstorm, SAC and Technosafe under Project Cenit-HESPERIA.Peer reviewe