Introduction to finite fields and their applications
Introduction to finite fields and their applications
IEEE Transactions on Computers
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Mastrovito Multiplier for General Irreducible Polynomials
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Efficient semisystolic architectures for finite-field arithmetic
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
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Finite field multiplication in GF(2m) is an ineluctable operation in elliptic curve cryptography. The objective of this paper is to survey fast and efficient hardware implementations of systolic and semisystolic finite field multipliers in GF(2m) with two algorithmic schemes – LSB-first and MSB-first. These algorithms have been mapped to seven variants of recently proposed array-type finite-field multiplier implementations with different input-output configurations. The relative VLSI performance merits of these ASIC prototypes with respect to their field orders are evaluated and compared under uniform constraints and in properly defined simulation runs on a Synopsys environment using the TSMC 0.18μm CMOS standard cell library. The results of the simulation provide an insight into the behavior of various configurations of array-type finite-field multiplier so that system architect can use them to determine the most appropriate finite field multiplier topology for required design features.