Cryptographic Application of Elliptic Curve generated through the formation of Diophantine triples using Hex Numbers and Pronic Numbers

Abstract

A public-key encryption technique akin to RSA can be referred to as elliptic curve cryptography (ECC). While RSA's security relies on huge prime numbers, ECC leverages the mathematical idea of elliptic curves to offer the same level of security with much smaller keys. In this paper, we will discuss elliptic curves and examine their applications in cryptography. A Diophantine pair of Hex numbers and Pronic numbers is extended to a Diophantine triple with appropriate property, that generates the elliptic curve and perform the encryption-decryption process.