【摘要】 在密码学的流密码理论当中,2-adic复杂度、k错2-adic复杂度类似于其它复杂度测度,同样要具有较大的数值.文中借助数论中的中国剩余定理等相关理论研究了二元序列的2-adic复杂度与线性复杂度的关系,证明了具有最大2-adic复杂度以及较大k错2-adic复杂度的N周期序列的存在性,给出了具有这种性质的周期序列的数目的下界.以此种周期序列作为密钥流序列可以有效地抵抗穷举攻击.更多还原

【Abstract】 According to the theory of stream ciphers in cryptology,the 2-adic complexity and the k-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 k-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.更多还原