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.