The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation
The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation
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DOI：
10.1007/s12095-017-0233-x
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Yuhua Sun;Qiang Wang;Tongjiang Yan
中科院分区：
文献类型：
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作者：
Yuhua Sun;Qiang Wang;Tongjiang Yan
伪随机序列具有良好的统计特性，如低自相关、高线性复杂度和大2-adic复杂度，已被用于设计可靠的流密码。本文给出了一类具有三阶自相关的二元序列的精确自相关分布，并分析了这类序列的2-adic复杂度。我们的结果表明，这样一个周期为N的二元序列的2-adic复杂度至少是（N+ 1）− log 2（N+ 1）。我们进一步证明，对于无限多种情况，它是最大的。这表明这类序列的2-adic复杂度足够大，可以抵抗带有进位移位寄存器（FCSR）的反馈有理逼近算法（RAA）的攻击。
Pseudo-random sequences with good statistical properties, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of binary sequences with three-level autocorrelation and analyze the 2-adic complexity of this class of sequences. Our results show that the 2-adic complexity of such a binary sequence with periodNis at least (N+ 1) − log2(N+ 1). We further show that it is maximal for infinitely many cases. This indicates 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).