Efficient implementation of scalar multiplication for ECC in GF (2m) on FPGA

Abstract

In the era where major portion of transactions take place online, security of the data becomes prime concern. Elliptic Curve Cryptography (ECC) is an approach to public-key cryptography based on Elliptic curves over finite fields. Elliptic curve cryptography is used for secure transmission of data with smaller key length. The underlying operation of ECC is scalar point multiplication. For the ECC to be efficient, the multiplication should be done at high speed. In this work high speed crypto-processor architecture for computing point multiplication for the elliptic curves defined over the binary field is designed. The projective coordinate system is used to increase the efficiency. The proposed architecture for computing 163-bit scalar multiplication for ECC can reach maximum frequency of 45.60 MHz and occupies 101 slices. It completes one 163-bit scalar multiplication in 9.9µs.