Generator of primality criteria based on properties of the composition of generating functions

Authors: Shablya Yu. V., Kruchinin D. V., Shelupanov A. A.

Annotation: In this paper are considered the mathematical aspects of cryptographic systems, i.e. checking of natural numbers for primality. The current situation of the primality criteria and its problems were analysed, and the necessity and the relevance of the study was identified. During the study an algorithm for constructing the new primality criteria based on the properties of the composition of ordinary generating functions with integer coefficients was introduced. Also, a software that will be used to search for new effective primality tests named Primality Criterion Generator was developed.

Keywords: prime, generating function, primality criterion, primality criterion generator