计算有限域GF(q)上2pn-周期序列的k-错线性复杂度及其错误序列的算法

牛志华; 孔得宇

doi:10.11999/JEIT170972

计算有限域GF(q)上2pⁿ-周期序列的k-错线性复杂度及其错误序列的算法

doi: 10.11999/JEIT170972

^①(上海大学计算机工程与科学学院上海 200444) ^②(上海大学先进研究院上海 200444)

基金项目:

上海市自然科学基金 (16ZR1411200, 17ZR1409800)，国家自然科学基金(61772022, 61572309, 61462077)

详细信息

作者简介:
牛志华：女，1976年生，副教授，研究方向为序列密码. 孔得宇：男，1991年生，硕士生，研究方向为序列密码.

中图分类号: TN918.1
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出版历程
- 收稿日期: 2017-10-20
- 修回日期: 2018-01-15
- 刊出日期: 2018-07-19

Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pⁿ-periodic Sequences over GF(q)

NIU Zhihua^①② KONG Deyu^①

Funds:

Shanghai Natural Science Foundation (16ZR1411200, 17ZR1409800), The National Nature Science Foundation of China (61772022, 61572309, 61462077)

摘要

摘要: 序列的k-错线性复杂度是序列线性复杂度稳定性的重要评价指标。在求得一个序列k-错线性复杂度的同时，也需要求出是哪些位置的改变导致了序列线性复杂度的下降。该文提出一个在GF(q)上计算2pⁿ-周期序列s的k-错线性复杂度以及对应的错误序列e的算法，这里p和q是素数，且q是一个模p²的本原根。该文设计了一个追踪代价向量的trace函数，算法通过trace函数追踪最小的代价向量来求出对应的错误序列e，算法得到的序列e使得(s+e)的线性复杂度达到k-错线性复杂度的值。
- 密码学 /
- 周期序列 /
- 线性复杂度 /
- k-错线性复杂度 /
- 错误序列
Abstract: The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that make the linear complexity reduced also need to be computed. For 2pⁿ-periodic sequence over GF(q) , where p and q are odd primes and q is a primitive root modulo p², an algorithm is presented, which not only computes the k-error linear complexity of a sequence s but also gets the corresponding error sequence e. A function is designed to trace the vector cost called “trace function”, so the error sequence e can be computed by calling the “trace function”, and the linear complexity of (s+e) reaches the k-error linear complexity of the sequence s.
- Cryptography、Periodic sequence、Linear complexity、k-error linear complexity、Error sequence /

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参考文献(21)

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