Fast Generation of RSA Keys using Smooth Integers

TL;DR

This paper introduces a technique to speed up RSA key generation by eliminating trial division, reducing time by 30%, and presents a new one-way function for cryptographic applications.

Contribution

It proposes a novel primality generation method that skips trial division and introduces a simpler one-way function for cryptography.

Findings

30% reduction in RSA key generation time for 1024-bit keys

Elimination of trial division phase in primality testing

Introduction of a new, computationally simpler one-way function

Abstract

Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites. In this paper, we will showcase a technique that will eliminate the first phase of the primality testing algorithms. The computational simulations show a reduction of the primality generation time by about 30% in the case of 1024-bit RSA key pairs. This can be particularly beneficial in the case of decentralized environments for shared RSA keys as the initial trial division part of the key generation algorithms can be avoided at no cost. This also significantly reduces the communication complexity. Another essential contribution of the paper is the introduction of a new one-way function that is computationally simpler than the existing ones used in public-key cryptography. This function can be used to create new random number generators, and it also could be potentially used for designing entirely new public-key encryption systems.