FPGA Design of Elliptic Curve Cryptosystem (ECC) for Isomorphic Transformation and EC ElGamal Encryption

Abstract

Attacking or tampering with sensitive data continues to increase risks to economic processes or human activities. These risks are significant key factors to improve the development and implementation of security systems. Therefore, improving cryptography is essentially needed to enhance the security of critical data. For example, elliptic curve cryptography (ECC) over the Galois field GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">163</sup> ) is one of the public-key (asymmetric) cryptographic techniques, in which demands mapping a message (163-bit) to a point in the prime subgroup of the elliptic curve. To the best of our knowledge, mapping methods are not yet available on Field-Programmable Gate Arrays (FPGAs). Also, asymmetric encryption schemes often do not consider encrypting/decrypting data packets because of their computation complexity and performance limitations. In this letter, we propose and develop a concurrent reconfigurable cryptosystem to encrypt and decrypt stream of data using ECC on FPGA. First, we present hardware design and implementation to map a plain message on the elliptic curve based on isomorphic transformation, then second, we architect the elliptic curve ElGamal public-key encryption method by using point addition and multiplication on Koblitz elliptic curve on FPGA. Our proposed cryptosystem is synthesized and implemented on Intel Cyclone 10 GX and Xilinx Kintex-7 FPGAs to evaluate throughput, and it achieves 25.73-57.1 Mbps.