Abstract:

Pseudorandom sequences are widely used in secret communications, spread spectrum communications and code division multiple address communications. They are usually used as the key sequences, spread spectrum sequences and address sequences. In the design theory of stream ciphers, complexity is introduced to evaluate the unpredictability of the cipher stream, that is, its level of safety. Linear complexity of sequences is an important measure for security in these applications, and this paper investigates the linear complexity of a family of p-ary d-form sequences under certain conditions, and the upper bound is given. There exists a family of p-ary d-form sequences whose linear complexity can reach the upper bound , which suggests that our upper bound is tight.

Key words: parydform sequences;linear complexity;trace functions