A New Asymmetric Encryption Algorithm Involving Both Group And Number Theory: Derivation Of The Lucente Stabile Atkins Cryptosystem Using Gauss’s Generalization Of Wilson’s Theorem

Abstract

Our research led to the discovery of an asymmetric encryption algorithm that follows Kerckhoff's principle and relies on a specific case of Gauss's Generalization of Wilson's Theorem. Unlike prime factorization based algorithms, the eavesdropping cryptanalyst has no indication that he has successfully decrypted the cyphertext. For this reason, we aim to show that this algorithm is not only more secure than existing asymmetric algorithms, but it has the potential to be significantly computationally faster.