On the Linear Syndrome Method in Cryptanalysis

Abstract

The linear syndrome (LS) method is elaborated for the purpose of solving problems encountered in cryptanalysis, which can be reduced to the following mathematical setting. Suppose the cryptanalyst has at his hand a sufficiently long segment of the binary sequence B = A + X, where A is a linear sequence with known feedback polynomial f(x) and X is a sequence with unknown or very complicated algebraic structure, but is sparse in the sense that, if we denote its signals by x(i), i > o, then we shall have s = prob( x(i) = 1) = 1/2 − ε, o < ∈ < 1/2. we call s the error rate of the sequence A in the sequence 8, and the job of the cryptanalyst is to recover the former from the captured segment of the latter.