CREATING AN ELLIPTIC CURVE ARITHMETIC UNIT FOR USE IN ELLIPTIC CURVE CRYPTOGRAPHY

Elliptic Curve Cryptography (ECC) is a very promising cryptographic method, offering the same security level as traditional Public Key Cryptosystems (RSA, El Gamal) but with considerably smaller key lengths. To increase the performance of an EC Cryptosystem, dedicated hardware is employed for all EC point operations. However, the computational complexity and hardware resources of an Elliptic Curve processing unit are very high and depend on the efficient design of the Elliptic Curve's underlined GF(2(k)) Field. In this paper, we propose an EC arithmetic unit that is structured over a high peformance, low gate number GF(2(k).) arithmetic unit. This proposed GF(2(k)) arithmetic unit is based on one dimensional systolic architecture that can perform GF(2(k)) multiplication and inversion with only the performance cost of inversion. This is achieved by utilizing a multiplication/inversion algorithm based on the modified extended Euclidean algorithm.