关键词: 信息安全, 密码学, 2-adic 复杂度, &kappa, 错2-adic 复杂度, 周期序列

Abstract:

According to the theory of stream ciphers in cryptology , the 2-adic complexity and. the κ-error 2-adic complexity similar to other complexity measures must have large values. In this paper , the relationship between the linear complexity and the 2-adic complexity is investigated based on the Chinese Remainder Theorem and some other related theories in the number theory , and the existence of N-periodic sequences that simultaneously achieve the maximum 2-adic complexity and a great κ-error 2-adic complexity is proved. Then , a lower bound of the number of the N-periodic sequences with such properties is given. The existence of many such sequences can effectively thwart the attacks against the keystreams by exhaustive search.

Key words: information security, cryptography, 2-adic complexity, κ-error 2-adic complexity, periodic sequence