Issue No. 05 - May (1986 vol. 35)
J.J. Thomas , Department of Research Engineering, Ven-Tel Inc.
The extended Euclidean algorithm is typically used to calculate multiplicative inverses over finite fields and rings of integers. The algorithm presented here has approximately the same number of average iterations and maximum number of iterations. It is shown, when P is a Mersenne prime, implementation of this algorithm on a processor, designed especially for mod P arithmetic operations, produces a more efficient algorithm with respect to the amount of program statements and number of operations. It is then shown heuristically, when the division and multiplications are performed simultaneously, the Euclidean algorithm has fewer subiterations.
rings of integers, Euclid's algorithm, Fermat prime, finite fields, Mersenne prime, modulo P, multiplicative inverse, prime number
J.J. Thomas, G.N. Larsen, J.M. Keller, "The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime", IEEE Transactions on Computers, vol. 35, no. , pp. 478-482, May 1986, doi:10.1109/TC.1986.1676791