تحسين سرعة بروتوكول تبادل المفاتيح Diffie-Hellman المستند إلى تناسق التماثل الفائق ما بعد الكم

Abstract

Super singular Isogeny-based Diffie-Hellman (SIDH) key exchange protocol has recently gained an increasing attraction and is considered as a good candidate of the post-quantum algorithms family. As of today, the best-known algorithms against the SIDH protocol have an exponential time complexity for both classical and quantum attackers. The core of SIDH built with the elliptic curve cryptography (ECC) which is a public key encryption method based on elliptic curve. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. In other words, it’s also called scalar multiplication which is quite computationally expensive. Therefore, it is more attractive to implement the ECC with their scalar multiplication operations in faster way. In this thesis, we propose a faster scalar multiplication of the implementation the elliptic curve point multiplication in binary Galois field GF(2^m). Experimental results demonstrate that the proposed approach which is called here the Reference Point Array (RPA), The implementation can speed up the elliptic curve scalar multiplication by 25.2% better than other’s implementations, that saved time and enhancement caused by the number of saved doubles, This because using the advantage of RPA. We have simulated the proposed approach of the elliptic curve point multiplication using Java programming language and Implemented it on High-end Intel Core i7-7500U @ 2.9Ghz. The platform used is NetBeans IDE version 8.2 as research programming environment for simulating our proposed approach.

Keywords: Elliptic Curve, Cryptography, Public Key Encryption, ECC, Symmetric Cryptography, Information Security, Scalar Multiplication, Point Multiplication, Cryptosystems, Key Exchange.