The El-Gamal AA_{\beta} Public Key Cryptosystem - A new approach utilizing the subset sum problem in designing an asymmetric cryptosystem

TL;DR

This paper introduces the El-Gamal AA_{eta} cryptosystem, a novel asymmetric encryption method based on the subset sum problem, inspired by various cryptographic operations, offering a new approach to public key cryptography.

Contribution

It presents a new cryptosystem leveraging the subset sum problem and the AA_{eta}-function, combining ideas from El-Gamal, RSA, and elliptic curves.

Findings

The cryptosystem is based on an NP-complete problem, enhancing security.

It mimics existing cryptosystems like El-Gamal and elliptic curves.

The scheme uses a two-parameter ciphertext structure.

Abstract

The El-Gamal AA_{\beta} Public Key Cryptosystem is a new asymmetric cryptosystem based on the piecewise AA_{\beta}-function. The AA_{\beta}-function which is essentially a one way Boolean function was motivated by the squaring and multiplying process while computing g^a (mod p) in the Diffie Hellman key exchange procedure and also computing C \equiv M^e (mod N) and M \equiv C^d (mod N) in the RSA cryptosystem. It was also motivated by the add and double point operation E=kG in the elliptic curve cryptosystem. The hard mathematical problem surrounding this newly designed asymmetric cryptosystem is the NP-complete problem known as the subset sum problem. The El-Gamal AA_{\beta} Public Key Cryptosystem mimics the El-Gamal Cryptosystem and the Elliptic Curve Cryptosystem by sending a two parameter ciphertext to the recipient.