Smooth Operator – The Use of Smooth Integers in Fast Generation of RSA Keys
share
Primality generation is the cornerstone of several essential cryptographic system, most notably, the RSA cryptosystem. The problem has been a subject of deep investigations by the computational number theorists, but there is still room for improvement. 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. It is particularly suitable for a decentralized RSA key generation. The computational simulations show reduction of the primality generation time for about 30 the case of 1024-bit RSA private keys. We are also proposing one new one-way function that can be used either as a hash function or as cryptographic puzzle for mining purposes.
READ FULL TEXT
