GF(2m) Arithmetic Modules for Elliptic Curve Cryptography

This paper reports work in progress in the design, implementation and evaluation of a reconfigurable finite field arithmetic architecture with a direct application in elliptic curve cryptography (ECC) for mobile devices. This module contributes to manage the current interoperability problems in ECC, that are due to the several choices in the implementation of ECC crypto systems. We report an evaluation of some finite field arithmetic modules in an architecture for computing scalar multiplication, which is the most time consuming in ECC cryptographic schemes. The arithmetic modules were evaluated for all the GF(2^m) NIST elliptic curves in a hardware architecture implemented in field programmable technology