Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
A New Aspect of Dual Basis for Efficient Field Arithmetic
PKC '99 Proceedings of the Second International Workshop on Practice and Theory in Public Key Cryptography
A Generalized Method for Constructing Subquadratic Complexity GF(2^k) Multipliers
IEEE Transactions on Computers
IEEE Transactions on Computers
Fast arithmetic architectures for public-key algorithms over Galois fields GF((2n)m)
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
VLSI architecture for bit parallel systolic multipliers for special class of GF(2m) using dual bases
VDAT'12 Proceedings of the 16th international conference on Progress in VLSI Design and Test
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In this transaction brief we consider the design of dual basis inversion circuits for GF(2/sup m/). Two architectures are presented-one bit-serial and one bit-parallel-both of which are based on Fermat's theorem. Finite field inverters based on Fermat's theorem have previously been presented which operate over the normal basis and the polynomial basis. However there are two advantages to be gained by forcing inversion circuits to operate over the dual basis. First, these inversion circuits can be utilized in circuits using hardware efficient dual basis multipliers without any extra basis converters. And second, the inversion circuits themselves can take advantage of dual basis multipliers, thus reducing their own hardware levels. As both these approaches require squaring in a finite field to take place, a theorem is presented which allows circuits to be easily designed to carry out squaring over the dual basis.