Hardware Implementation of Efficient Elliptic Curve Scalar Multiplication using Vedic Multiplier

Abstract

This paper presents an area efficient and high-speed FPGA implementation of scalar multiplication using a Vedic multiplier. Scalar multiplication is the most important operation in Elliptic Curve Cryptography(ECC), which used for public key generation and the performance of ECC greatly depends on it. The scalar multiplication is multiplying integer k with scalar P to compute  Q=kP, where k is private key and P is a base point on the Elliptic curve. The Scalar multiplication underlying finite field arithmetic operation i.e. addition multiplication, squaring and inversion to compute Q. From these finite field operations, multiplication is the most time-consuming operation, occupy more device space and it dominates the speed of Scalar multiplication. This paper presents an efficient implementation of finite field multiplication using a Vedic multiplier.  The scalar multiplier is designed over Galois Binary field GF(2233) for field size=233-bit which is secured curve according to NIST.  The performances of the proposed design are evaluated by comparing it with  Karatsuba based scalar multiplier for area and delay. The results show that the proposed scalar multiplication using Vedic multiplier has consumed 22% less area on FPGA and also has 12% less delay, than Karatsuba, based scalar multiplier. The scalar multiplier is coded in Verilog HDL, synthesize and simulated in Xilinx 13.2 ISE on Virtex6 FPGA.