Introduction to finite fields and their applications
Introduction to finite fields and their applications
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
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
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
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Efficient Multiplication Beyond Optimal Normal Bases
IEEE Transactions on Computers
Low Complexity Sequential Normal Basis Multipliers over GF(2m)
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
Efficient digit-serial normal basis multipliers over binary extension fields
ACM Transactions on Embedded Computing Systems (TECS)
Low Complexity Word-Level Sequential Normal Basis Multipliers
IEEE Transactions on Computers
Modified sequential normal basis multipliers for type II optimal normal bases
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
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The curves recommended by NIST are defined over finite fields GF(2m) with m = 163, 233, 283, 409, 571. Among them GF(2163) and GF(2409) have type-IV Gaussian normal bases. Using the Reyhani-Masoleh and Hasan’s serial multiplier for type-I optimal normal basis, in this paper, we propose a new serial multiplier for GF(2m) with type-IV Gaussian normal basis, which reduces the critical XOR path delay of the best known Reyhani-Masoleh and Hasan’s serial multiplier by 25 % and the number of XOR gates of Kwon et al.’s multiplier by 2. Therefore our proposed multiplier can be applicable to implementing the protocols related to the area including ECC under in ubiquitous computing.