Novel performant primality test on a Pell's cubic

TL;DR

This paper introduces a new deterministic primality test based on Pell's cubic, which is efficient for integers less than 2^32, and proves its primality conditions using related integer sequences.

Contribution

It presents a novel primality testing algorithm leveraging Pell's cubic and establishes its primality conditions through associated integer sequences.

Findings

Number of operations grows linearly with input size

Deterministic for integers less than 2^32

Provides primality conditions based on Pell's cubic sequences

Abstract

Primality testing is an especially useful topic for public-key cryptography. In this paper, a novel primality test algorithm based on the Pell's cubic will be introduced, and its necessary primality conditions will be proved using three integer sequences connected to operations applied in the projectivization of the Pell's cubic. The number of operations involved in the test grows linearly with respect to the bit-length $\log_2(n)$ of the input integer $n$. The algorithm is deterministic for integers less than $2^{32}$.