An adaptive cryptosystem on a Finite Field

Abstract

Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme. This system is based on product, exponent, and modulo operation on a finite field. At the heart of this algorithm lies an innovative and robust trapdoor function that operates in the Galois Field and is responsible for the superior speed and security offered by it. Prime number theorem plays a fundamental role in this system, to keep unwelcome adversaries at bay. This is a self-adjusting cryptosystem that autonomously optimizes the system parameters thereby reducing effort on the user’s side while enhancing the level of security. This paper provides an extensive analysis of a few notable attributes of this cryptosystem such as its exponential rise in security with an increase in the length of plaintext while simultaneously ensuring that the operations are carried out in feasible runtime. Additionally, an experimental analysis is also performed to study the trends and relations between the cryptosystem parameters, including a few edge cases.