Quantum-accelerated algorithms for generating random primitive polynomials over finite fields

TL;DR

This paper introduces hybrid quantum-classical algorithms and quantum circuits to efficiently generate random primitive polynomials over finite fields, enhancing applications in cryptography and coding theory.

Contribution

It presents the first efficient quantum-accelerated algorithms and circuit designs for generating primitive polynomials over finite fields.

Findings

Quantum algorithms outperform classical methods in speed.

Designed quantum circuits enable real-time polynomial generation.

Potential applications in quantum communication and cryptography.

Abstract

Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient classical algorithm for generating random primitive polynomials over finite fields remains an ongoing challenge. In this paper, we show how to solve this problem efficiently through hybrid quantum-classical algorithms, and designs of the specific quantum circuits to implement them are also presented. Our research paves the way for the rapid and real-time generation of random primitive polynomials in diverse quantum communication and computation applications.