摘要： Welch-Gong(WG)序列是一类具有良好随机性的二元序列,该随机性包括长周期、0,1分布均匀、理想的二元分布、二值自相关、与m序列三值互相关、指数级增长的线性复杂度等。针对WG序列变换,对奇数项式进行研究,考虑多项式通过WG变换的复杂程度,将WG变换中特定的五项式推广为一般的三项式。分析结果证明,相应WG序列能够保持较好的随机特性和较高的线性复杂度。选取一个具体实例对基于三项式的WG密码体制的硬件实现进行分析,对算法设计的评估有一定的参考价值。
关键词:
Welch-Gong序列,
伪随机,
自相关,
互相关,
线性复杂度
Abstract: Welch-Gong(WG) sequences have good randomness,including long period,balance property,ideal 2-tuple distribution,two-level autocorrelation,three-level cross correlation with m-sequences,and linear complexity increasing exponentially.For the WG transformation,the odd term of polynomial function is studied.Considering the complexity of polynomial function by WG transformation,this paper extends the specific five-term function to general three-term function in WG transformation,and analyzes that the new sequences still have good randomness and low linear complexity.It selects a specific instance to analyze the hardware implementation of WG cipher based on the three-term function,and gives a certain reference value for the design of the algorithm.
Key words:
Welch-Gong(WG) sequences,
pseudorandom,
autocorrelation,
cross correlation,
linear complexity
中图分类号:
叶婷,陈克非,沈忠华,孟倩,张文政. 扩展的Welch-Gong序列构造与分析[J]. 计算机工程, doi: 10.3969/j.issn.1000-3428.2016.08.019.
YE Ting,CHEN Kefei,SHEN Zhonghua,MENG Qian,ZHANG Wenzheng. Construction and Analysis of Extended Welch-Gong Sequences[J]. Computer Engineering, doi: 10.3969/j.issn.1000-3428.2016.08.019.