Introduction to finite fields and their applications
Introduction to finite fields and their applications
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF (2m)
IEEE Transactions on Computers
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
On Computing Multiplicative Inverses in GF(2/sup m/)
IEEE Transactions on Computers
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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Euclid's Greatest Common Divisor (GCD) algorithm is an efficient approach for calculating multiplicative inversions. It relies mainly on a fast modular arithmetic algorithm to run quickly. A traditional modular arithmetic algorithm based on nonrestoring division needs a magnitude comparison for each iteration of shift-and-subtract operation. This process is time consuming, since it requires magnitude comparisons for every computation iteration step. To eradicate this problem, this study develops a new fast Euclidean GCD algorithm without magnitude comparisons. The proposed modular algorithm has an execution time that is about 33% shorter than the conventional modular algorithm.