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arXiv:2006.08444

Taxonomy and Practical Evaluation of Primality Testing Algorithms

Anas Ahmad Abudaqa, Nujud Alyami, Mostefa Kara, Farid Binbeshr, Muhammad Imam

Published Jun 15, 2020• 1 citation
arXivHTMLPDF

Abstract

Abstract Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime factors, a problem that remains challenging for classical computers but potentially solvable using quantum algorithms. On the other hand, generating large prime numbers is also challenging due to their irregular distribution among integers, necessitat- ing the use of primality testing algorithms to verify candidate primes. In this paper, we intensively review and classify various classical and quantum algorithms for factorization and primality testing, highlighting their advantages, limitations, speed/accuracy tradeoffs, time complexities, along with a brief summary. Furthermore, we apply and compare these algorithms to gain practical insights and conduct a comprehensive performance comparison. The insights from this paper show that while quantum factoring algorithms, particularly Shor’s algorithm and its refinements, have introduced significant advancements over their classical counterparts, quantum primality testing algorithms have not demonstrated comparable advantages.

DOI
10.48550/arxiv.2006.08444

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