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Periodic sequences, used as keys in cryptosystems, plays an important role in cryptography. Such periodic sequences should possess high linear complexity to resist B-M algorithm. Sequences constructed by cyclotomic cosets have been widely studied in the past few years. In this paper, the linear complexity of n-periodic cyclotomic sequences of order 2 and 4 over Fp has been calculated, where n and p are two distinct odd primes. The conclusions reveal that the presented sequences have high linear complexity in many cases, which indicates that the sequences can resist the linear attack. key words: Legendre sequences, cyclotomic sequences, linear complexity, Gauss periods

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

Linear Complexity of <i>n</i>-Periodic Cyclotomic Sequences over 𝔽<sub><i>p</i></sub>