基于代数曲线上具有高广义联合线性复杂度的多重序列

Multisequences with large generalized joint linear complexity from algebraic curves

多重序列的联合线性复杂度是衡量基于字的流密码体系安全的一个重要指标.由元素取自Fq上的m重序列和元素取自Fqm上的单个序列之间的一一对应,Meidl和zbudak定义多重序列的广义联合线性复杂度为对应的单个序列的线性复杂度.在本文中,我们利用代数曲线的常数域扩张,研究两类多重序列的广义联合线性复杂度.更进一步,我们指出这两类多重序列同时具有高联合线性复杂度和高广义联合线性复杂度.

The joint linear complexity of multisequence is one of the important security measures for wordbased stream cipher system.Since each multisequence over F q is identity to a single sequence over an appropriate extension field F q m,the linear complexity of this single sequence is called the generalized joint linear complexity of the corresponding multisequence.In the present paper,we study the generalized joint linear complexity for two classes of multi-sequences obtained from function fields.Moreover,we will show that these kinds of multisequences have large joint linear complexity as well as large generalized joint linear complexity.