On the distinctness of modular reductions of primitive sequences modulo square-free odd integers

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• 作者：Qunxiong Zheng ; Wenfeng Qi ; Tian Tian
• 关键词：Cryptography ; Integer residue rings ; Linear recurring sequences ; Primitive polynomials ; Primitive sequences ; Modular reductions
• 刊名：Information Processing Letters
• 出版年：2012
• 出版时间：30 November, 2012
• 年：2012
• 卷：112
• 期：22
• 页码：872-875
• 全文大小：146 K

文摘

Let M be a square-free odd integer with at least two different prime factors and the integer residue ring modulo M. In this paper, it is shown that for two primitive sequences and generated by a primitive polynomial of degree n over , if and only if for all , where is an integer divisible by a prime number coprime with M. This result is obtained basing on the assumption that every element in occurs in a primitive sequence of order n over , which is known to be valid for most M?s if .