Novel performant primality test on a Pell's cubic

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 $2^{32}$.