## Cryptology ePrint Archive: Report 2010/622

A new result on the distinctness of primitive sequences over Z(pq) modulo 2

Qunxiong Zheng and Wenfeng Qi

Abstract: Let Z/(pq) be the integer residue ring modulo pq with odd prime numbers p and q. This paper studies the distinctness problem of modulo 2 reductions of two primitive sequences over Z/(pq), which has been studied by H.J. Chen and W.F. Qi in 2009. First, it is shown that almost every element in Z/(pq) occurs in a primitive sequence of order n > 2 over Z/(pq). Then based on this element distribution property of primitive sequences over Z/(pq), previous results are greatly improved and the set of primitive sequences over Z/(pq) that are known to be distinct modulo 2 is further enlarged.

Category / Keywords: foundations / integer residue rings, linear recurring sequences, primitive polynomials, primitive sequences, modular reduction