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中文摘要：
具有较强密码学性质的序列应该具有较大的2-adic复杂度，以抗击已知的带进位操作反馈移位寄存器综合算法，同时改变较少的几项也不应引起序列的2-adic复杂度的急剧减小，即k错2-adic复杂度也应尽可能地大．近来，向量化流密码的设计逐渐成为国内外密码学界关注的一个重要方向．对这种类型的流密码的安全性分析需要研究多重序列一有限多个序列的并行流的复杂度．目前对多重序列的复杂度研究多集中于线性复杂度．基于此，文中首先给出了多重二元序列的联合k错2-adic复杂度的定义．随后，借助数论中的中国剩余定理等相关理论给出了联合k错2-adic复杂度的下界，并讨论了具有最大联合2-adic复杂度以及较大联合k错2-adic复杂度的N周期序列的存在性及具有此种性质的序列的数目下界．以此种周期序列作为密钥流序列可以有效抵抗穷举攻击．
英文摘要：
Cryptographically strong sequences should have a large 2-adic complexity to thwart the known feedback with carry shift register synthesis algorithms. At the same time the change of a few terms should not cause a significant decrease of the 2-adic complexity, that is, the k-error 2-adic complexity should also be large. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multi-sequences. This paper introduces joint k-error 2-adic complexity measures for multi-sequences. Several results on the existence and lower bounds on the number of multi-sequences with maximal joint 2-adic complexity and large joint k-error 2-adic complexity are proved. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.
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