Attacking the Filter Generator over GF (2 m )

We consider the filter generator over GF(2m ) consisting of a linear feedback shift register of length k that generates a maximal length linear sequence of period 2mk − 1 over GF(2m ) and a Boolean function of degree d that combines bits from one element in the shift register (considered as an element in GF(2)m ) and creates a binary output bit zt at 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 L keystream bits with complexity O(L), after a pre-computation with complexity O(L(log2L)3 ), where L is the linear complexity upper bounded by D = Pd i=1 `n i ´ with n = mk, which is also the number of monomials of degree ≤ d in GF(2). In addition we explain why a function of only one element in the shift register reduces the linear complexity of the keystream, compared to using the function freely on bits from several words in the ...

• Type: Conference
• Year: 2007
• Where: WAIFI
• Authors: Sondre Rønjom, Tor Helleseth
• Keywords: Linear Feedback Shift Register, Mathematics, Shift Register, WAIFI 2007, filter Generator