A New Parallel Multiplier for Type II Optimal Normal Basis

In hardware implementation for the finite field, the use of normal basis has several advantages, especially the optimal normal basis is the most efficient to hardware implementation in GF(2m). The finite field GF(2m) with type I optimal normal basis has the disadvantage not applicable to cryptography since m is even. The finite fields GF(2m) with type II optimal normal basis, however, such as GF(2233) are applicable to ECDSA recommended by NIST, and many researchers devote their attentions to efficient arithmetic over them. In this paper, we propose a new type II optimal normal basis parallel multiplier over GF(2m) whose structure and algorithm are clear at a glance, which performs multiplication over GF(2m) in the extension field GF(22m). The time and area complexity of the proposed multiplier is the same as the best known type II optimal normal basis parallel multiplier.