Analysis Of Cryptographic Properties Of Two Classes Of Quaternary Generalized Cyclotomic Sequences

Pseudorandom sequences play important roles in information security system, and have widely applications in many domains, including ranging system, spread spectrum communication system, radar navigation system, stream cipher systems, etc. The linear complexity of sequences is one important indictor for measuring the randomness properties of cryptographic sequence. By the B-M algorithm, the linear complexity of a sequence must not be less than the half of its period. In this paper, we mainly study two classes of new generalized cyclotomic sequences. We examine their constructions and then determine their linear complexity, respectively. The main results are as follows:1. Based on the construction presented by Chang et al., a new class of quater-nary balanced generalized cyclotomic sequences with period 2pq over finite field F₄ is constructed. Using the theory of polynomial roots over finite field, we determine it's linear complexity.2. Based on the theory of Gray mapping and Ding-generalized cyclotomic, a new class of quaternary sequences over Z₄ with period pq is established. We will determine the corresponding Fourier spectral sequence of the new sequence on the finite field Fr?r?5, prime?. Then we will obtain the linear complexity of the new sequence from the weights of it's Fourier spectral sequence.Results show that all the sequences we designed have large linear complexity and can resist the attack by B-M algorithm. They are good sequences from the viewpoint of cryptography.