Smooth Operator – The Use of Smooth Integers in Fast Generation of RSA Keys
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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.
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