Use the Multiplicative Cyclic Group to Generate Pseudo Random Digital Sequences


The Multiplicative Cyclic Group [3] is one of the algebraic systems which can be used to generate a various long period digital sequences with elements ranged 0..m-1, where mZ+, m  2 that’s done by using one (or more than one) primitive element(s) of the group. The generated sequences can be used in Stream Cipher Systems. In this paper, we introduce the mathematical process to generate a sequence from one generator of The Multiplicative Cyclic Group (MCG). The generated sequence may have no good statistical properties, so we suggest a two generators sequence. The two generators with some initial variables (keys) make a unit called MCG unit. A number of MCG units are combined with each other by a combining logical function to get MCG system. This paper includes some algorithms to describe the mentioned process and some tables describe the tests results of the generated sequences.