On the Randomness of Generalized Cyclotomic Sequences of Order Two and Length pq

The linear complexity and autocorrelation values are very important measures for evaluating the randomness of sequences. The engineering interpretation of linear complexity (LC) is as the length of the shortest linear feedback shift register (LFSR) that generates the sequence. By BerlekampMassey algorithm, if the linear complexity of a key stream is L, then 2L consecutive characters of the sequence could be used to construct the whole key stream. Thus, it is cryptographically necessary to require key stream sequences to have large linear complexity. In practice, if LC > 2 (N denotes the length of a sequence) then the sequence is deemed to be “good” sequence. Given a partition {ZN \ C,C} of the residue class ring ZN , define a sequence s = (s0, s1, · · ·):