A faster pseudo-primality test

TL;DR

This paper introduces a new pseudo-primality test leveraging cyclic extensions of modular integers, offering a faster alternative that maintains the security level of multiple Miller-Rabin tests with reduced computational effort.

Contribution

The paper presents a novel pseudo-primality test based on cyclic extensions, improving efficiency while preserving security comparable to multiple Miller-Rabin tests.

Findings

Achieves security of k Miller-Rabin tests with fewer tests

Reduces computational complexity to approximately k^{1/2+o(1)}

Provides a faster primality testing method for large integers

Abstract

We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.