Abstract: Based on the polynomial theory on a Galois field, the author presents linear complexity and minimal polynomials of all binary Whiteman generalized cyclotomic sequences with the period pq. The results obtained show that the upper bound and the lower bound of their linear complexity are pq-1 and (p-1)(q-1)/2 respectively. From the viewpoint of stream cipher cryptosystems, almost all these sequences have good linear complexity. They can resist the attacks from the application of the Berlekamp-Massey algorithm.

Key words: stream cipher, cyclotomic class, cyclotomic sequence, linear complexity；minimal polynomial