Cyclotomy Primality Proofs and their Certificates

TL;DR

This paper reviews the theoretical foundations and implementation details of Cyclotomy Primality Proving (CPP), an efficient method for primality testing developed since 1980, highlighting its significance in computational number theory.

Contribution

It provides a comprehensive overview of the theoretical background and practical implementation of CPP as understood in 2007, consolidating knowledge on this primality proving technique.

Findings

Summarizes the development of CPP since 1980.

Details the implementation specifics of CPP as of 2007.

Highlights the importance of Jacobi sums in primality testing.

Abstract

The first efficient general primality proving method was proposed in the year 1980 by Adleman, Pomerance and Rumely and it used Jacobi sums. The method was further developed by H. W. Lenstra Jr. and more of his students and the resulting primality proving algorithms are often referred to under the generic name of Cyclotomy Primality Proving (CPP). In the present paper we give an overview of the theoretical background and implementation specifics of CPP, such as we understand them in the year 2007.