Further Result of Compressing Maps on Primitive Sequences Modulo Odd Prime Powers

Let be the integer residue ring with odd prime and integer . For a sequence over , there is an unique -adic expansion , where each is a sequence over , and can be regarded as a sequence over the prime field GF naturally. Let be a strongly primitive polynomial over , and the set of all primitive sequences generated by over . Suppose that GF GF . It is shown that any function in is an injective map from to GF, and the derived sequences of different functions are also different. That is, if and only if and for and . These injective functions in can be considered as good candidates for the keys of a stream cipher.