Hardware implementations of GF (2^m) arithmetic using normal basis

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 + 3/2m(m - 1) XOR gates and a time complexity of T_A+ (1+[log₂ (m)])T_x. The study also show that the Itoh-Tsujii inversion algorithm was the best inverter and it requires almost log₂ (m-1) multiplications.