Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
IEEE Transactions on Computers
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
Storage-Efficient Finite Field Basis Conversion
SAC '98 Proceedings of the Selected Areas in Cryptography
A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
A Scalable Architecture for Modular Multiplication Based on Montgomery's Algorithm
IEEE Transactions on Computers
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Low-complexity multiplier for GF(2m) based on all-one polynomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Applying the matrix-vector product idea of the Mastrovito multiplier to the GF(2^{m}) Montgomery multiplication algorithm, we present a new parallel multiplier for irreducible trinomials. This multiplier and the corresponding shifted polynomial basis (SPB) multiplier have the same circuit structure for the same set of parameters. Furthermore, by establishing isomorphisms between the Montgomery and the SPB constructions of GF(2^{m}), we show that the Montgomery algorithm can be used to perform the SPB multiplication without any changes and vice versa.