Journal of Applied Sciences

Year: 2006 | Volume: 6 | Issue: 6 | Page No.: 1362-1372
DOI: 10.3923/jas.2006.1362.1372

Hardware Implementations of GF (2^m) Arithmetic Using Normal Basis

Turki F. Al-Somani and Alaaeldin Amin

Abstract: This study presents a survey of algorithms used in field arithmetic over GF (2^m) using normal basis and their hardware implementations. These include the following arithmetic field operations: addition, squaring, multiplication and inversion. This study shows that the type II Sunar-Koc multiplier is the best multiplier with a hardware complexity of m² AND gates + XOR gates and a time complexity of T_A+ (1+ l log₂ (m) l )T_x. The study also show that the Itoh-Tsujii inversion algorithm was the best inverter and it requires almost log₂ (m-1) multiplications.