Prime numbers are fundamental within cryptography, with a variety of the modern day encryption algorithms keeping our information secure relying on primality testing for their utility. Primality ...

Optimized AKS Primality Test with Fast Fourier Transform (FFT) for enhanced performance in large number primality checking. This implementation improves the efficiency of the AKS algorithm using FFT ...

Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes ...

Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes ...

Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an ...

Abstract: With the increasing popularity and usage of cryptography and network security, prime generation and primality testing has become a significant issue. Various primality tests have been ...

It is also a generalization of the problem of testing if a polynomial is absolutely irreducible. Assuming GRH, we show that for certain classes of ideals, namely radical ideals and complete ...