Efficient multiplication in finite field for FPGA design of EC cryptosystem

Abstract

The Elliptic Curve Cryptography (ECC) was introduced in the 1980s. It has superior strength per bit compared to the existing public key cryptosystems such as RSA. This fact made ECC a popular one. It can provide a secured data communication among the portable devices using small key sizes. The scalar multiplication carried out in ECC is expensive in terms of time, power and area. Major time consuming operations are reduced with projective coordinate. The proposed Elliptic Curve Cryptosystem over GF(2160) is designed with various point multiplication schemes in the Galois Field. The operations in the elliptic curve are explored using the finite field arithmetic in generating the keys and digital signatures, based on Elliptic Curve Digital Signature Algorithm (ECDSA). The ECC protocol algorithm is parallelizable and well adapted to FPGA design of Elliptic Curve Cryptosystems.