Security Features of an Asymmetric Cryptosystem based on the Diophantine Equation Hard Problem

TL;DR

This paper introduces an asymmetric cryptosystem based on the Diophantine Equation Hard Problem (DEHP), combining it with prime factorization, aiming for low-complexity secure communication suitable for devices with limited computing power.

Contribution

It proposes the AA$_{\beta}$-cryptosystem, a novel scheme utilizing DEHP and prime factorization, with simple multiplication-based encryption and decryption for efficient security.

Findings

Uses DEHP to enhance cryptographic security.

Employs only multiplication for encryption and decryption.

Designed for low-power, resource-constrained devices.

Abstract

The Diophantine Equation Hard Problem (DEHP) is a potential cryptographic problem on the Diophantine equation $U=\sum \limits_{i=1}^n {V_i x_{i}}$. A proper implementation of DEHP would render an attacker to search for private parameters amongst the exponentially many solutions. However, an improper implementation would provide an attacker exponentially many choices to solve the DEHP. The AA\,$_{\beta}$-cryptosystem is an asymmetric cryptographic scheme that utilizes this concept together with the factorization problem of two large primes and is implemented only by using the multiplication operation for both encryption and decryption. With this simple mathematical structure, it would have low computational requirements and would enable communication devices with low computing power to deploy secure communication procedures efficiently.