Cryptosystem design based on Hermitian curves for IoT security

Abstract

The ultimate goal of modern cryptography is to protect the information resource and make it absolutely unbreakable and beyond compromise. However, throughout the history of cryptography, thousands of cryptosystems emerged and believed to be invincible and yet attackers were able to break and compromise their security. The main objective of this paper is to design a robust cryptosystem that will be suitable to be implemented in Internet of Things. The proposed cryptosystem is based on algebraic geometric curves, more specifically on Hermitian curves. The new cryptosystem design is called Hermitian-based cryptosystem (HBC). During the development of the HBC design, Kerckhoffs’s desideratum was the main guidance principle, which has been satisfied by choosing the Hermitian curves as the core of the proposed design. The proposed HBC inherits all the advantageous characteristics of Hermitian curve which are large number of points that satisfy the curve and high genus curves. The aforementioned characteristics play a crucial role in generating a large size encryption key for HBC and determine the block size of plaintext. Due to the fact that HBC used algebraic geometric codes over Hermitian curve, it has the ability to perform error correction in addition to data encryption. The error correction is another advantage of HBC compared with many existing cryptosystems such as McEliece cryptosystem. The number of errors that can be corrected by HBC is larger (high data rate) than other algebraic geometric codes such as elliptic and hyperelliptic curves. It also uses non-binary representation which increases its attack resistance. In this paper, the proposed HBC has been mathematically compared with elliptic curve cryptosystem. The results show that HBC has many advantages over the elliptic curves in terms of number of points and genus of the curve.