Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Open problems related to algebraic attacks on stream ciphers
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
A New Attack on the Filter Generator
IEEE Transactions on Information Theory
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We consider the filter generator over GF(2m) consisting of a linear feedback shift register of length kthat generates a maximal length linear sequence of period 2mk茂戮驴 1 over GF(2m) and a Boolean function of degree dthat combines bits from one element in the shift register (considered as an element in GF(2m)) and creates a binary output bit ztat any time t. We show how to extend a recent attack by the authors on the binary filter generator to the filter generator over GF(2m). The attack recovers the initial state of the filter generator from Lkeystream bits with complexity O(L), after a pre-computation with complexity $O(L (log_2 L)^3)$, where Lis the linear complexity upper bounded by $D=\sum_{i=1}^d {n \choose i}$ with n= mk, which is also the number of monomials of degree ≤ dover GF(2). In addition we explain why a function of only one element of the shift register reduces the linear complexity of the keystream significantly, compared to using the function freely on bits from several words in the initial state. We also discuss implications for the WG stream cipher [4].