周期为2(2~n–1)的四进制序列族的构造

A New Construction of Quaternary Sequence Family with Period of 2(2~n–1)

伪随机序列在密码学、扩频通信系统等许多领域都具有广泛的应用.特别是在密码学中,序列密码的安全性依赖于密钥序列的随机性.因此,伪随机序列的构造和性能分析是近年来研究的热点.而由于二元序列的一些理论研究已经非常熟悉,随着扩频通信的发展,对于多元序列的研究逐渐成为研究的热点.因此,构造性质较好的四进制伪随机序列族具有重要的意义.本文通过对序列族A进行格雷映射和逆格雷映射得到了一类新的四进制序列族P.其中新的四进制序列族P包含2n+1条,周期为2(2n–1)的序列.当n为奇数时,序列间最大相关函数值为Rmax=2(n+1)/2+2,满足Welch和Sidelnikov界.与原来序列族A相比,序列族P的周期是序列族A的2倍;与已知序列族不同,序列族P构造方法简单.为扩频通信提供了一种新的四进制扩频码.与同样长度的二进制扩频码相比,四进制扩频码扩频增益更高,可用扩频码的数量更多.在密码学中,序列密码是密码技术的主要技术之一,序列密码的安全性主要依赖于密钥序列的随机性,序列族P可以作为新的密钥序列对序列密码进行加密解密.

Families of pseudorandom sequences have wide applications in cryptogrphy systems, Spread Spectrum Communication systems. Especially in cryptogrphy systems, the security of stream cipher depends on the randomness of the key sequence, Therefore, the construction and the Performance analysis of pseudorandom sequences analysis is the hotspot in recent years. And we are already familiar with the study of Binary sequences, because some theoretical study on Binary sequences are already familiar, With the development of Spread Spectrum Communication, research on the study of multi-sequence become hot spots. Therefore, the construction of new quaternary sequences with good properties are of important significance. In this paper, we use the Gray map and the inverse Gray map to present a new quaternary sequences family P on the optimal quaternary sequences family A, which have even period 2(2n–1), family size 2n+1, and the maximum nontrivial correlation value Rmax=2(n+1)/2+2, which is optimal with repect to the Welch and Sidelnikow bounds, where n is an odd integer. In contrast to the known optimal family, the new quaternary sequences family P is easy to construct, and provides a new quaternary sequences for Spread Spectrum Communication. In contrast to the binary sequences having the same period, the quaternary sequences have a higher Spread Spectrum, and more number of spreading codes available. In cryptography, the security of stream cipher depends on the randomness of the key sequence, and the new quaternary sequences family P can be used as a new key sequence on stream cipher for encryption and decryption.