Bit serial multiplication in finite fields
SIAM Journal on Discrete Mathematics
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
New Low-Complexity Bit-Parallel Finite Field Multipliers Using Weakly Dual Bases
IEEE Transactions on Computers
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Combined circuit architecture for computing normal basis and Montgomery multiplications over GF(2m)
International Journal of Autonomous and Adaptive Communications Systems
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Montgomery multiplication in GF(2m) is defined by a(x)b(x) r-1(x) mod f(x), where the field is generated by irreducible polynomial f(x), a(x) and b(x) are two field elements in GF(2m), and r(x) is a fixed field element in GF(2m). In this paper, first we present a generalized Montgomery multiplication algorithm in GF(2m). Then by choosing r(x) according to f(x), we show that efficient architecture for bit-parallel Montgomery multiplier and squarer can be obtained for the fields generated with irreducible trinomials. Complexities in terms of gate counts and time propagation delay of the circuits are investigated and found to be comparable to or better than that of polynomial basis or weakly dual basis multiplier for the same class of fields.