stream cipher, pseudorandom sequence, generalized cyclotomy, linear complexity
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p–1, q–1)=gcd(p–1, r–1)=gcd(q–1, r–1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.
Tsinghua University Press
Longfei Liu, Xiaoyuan Yang, Xiaoni Du et al. On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr. Tsinghua Science and Technology 2016, 21(3): 295-301.