LFSR cryptanalysis

Given a sequence obtained from a length n LFSR (see page 975)

Nest[Mod[Append[#, Take[#, -n].vec], 2] &, list, t]

the vector of taps vec can be deduced from

LinearSolve[Table[Take[seq, {i, i + n-1}], {i, n}], Take[seq, {n + 1, 2n}], Modulus->2]

(An iterative algorithm in n taking about n^^{2} rather than n^^{3} steps was given by Elwyn Berlekamp and James Massey in 1968.) The same basic approach can be used to deduce the rule for an additive cellular automaton from vertical sequences.