VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
Introduction to finite fields and their applications
Introduction to finite fields and their applications
Designs, Codes and Cryptography
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Low Complexity Bit-Parallel Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
A New Hardware Architecture for Operations in GF(2m)
IEEE Transactions on Computers
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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 mis 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 is 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.