A Constructive Method of Algebraic Attack with Less Keystream Bits

Xiaoyan ZHANG  Qichun WANG  Bin WANG  Haibin KAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.10   pp.2059-2062
Publication Date: 2011/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.2059
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
algebraic attack,  primitive polynomial,  linearization,  multivariate equations,  

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In algebraic attack on stream ciphers based on LFSRs, the secret key is found by solving an overdefined system of multivariate equations. There are many known algorithms from different point of view to solve the problem, such as linearization, relinearization, XL and Grobner Basis. The simplest method, linearization, treats each monomial of different degrees as a new variable, and consists of variables (the degree of the system of equations is denoted by d). Thus it needs at least equations, i.e. keystream bits to recover the secret key by Gaussian reduction or other. In this paper we firstly propose a concept, called equivalence of LFSRs. On the basis of it, we present a constructive method that can solve an overdefined system of multivariate equations with less keystream bits by extending the primitive polynomial.