一类平衡广义分圆序列2-adic复杂度的进一步结果
Further results on the 2-adic complexity of a class of balanced generalized cyclotomic sequences
摘要：
本文研究了周期为$pq$的平衡Whiteman广义割圆序列的2-adic复杂度。通过计算其中一个序列所构造的循环矩阵的行列式，得到了相应序列的2-adic复杂度的一个下界，进一步扩展了我们以前的工作（Zhao C，Sun Y and Yan T.一类平衡广义分圆序列的2-adic复杂度研究。Journal of Cryptologic Research，6（4）：455-462，2019）。结果表明，这类序列的2-adic复杂度足以抵抗带有进位移位寄存器（FCSR）的反馈有理近似算法（RAA）的攻击，即，它实际上是由$pq-p-q-1$下界的，$pq-p-q-1$远大于序列周期的一半。特别地，如果选择合适的参数，2-adic复杂度是最大的。
英文摘要：
In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period $pq$ is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive a lower bound on the 2-adic complexity of the corresponding sequence, which further expands our previous work (Zhao C, Sun Y and Yan T. Study on 2-adic complexity of a class of balanced generalized cyclotomic sequences. Journal of Cryptologic Research,6(4):455-462, 2019). The result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm(RAA) for feedback with carry shift registers(FCSRs), i.e., it is in fact lower bounded by $pq-p-q-1$, which is far larger than one half of the period of the sequences. Particularly, the 2-adic complexity is maximal if suitable parameters are chosen.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
