Issue No. 03 - March (1985 vol. 34)
K.R., Jr. Sloan , Department of Computer Science, University of Washington
The modular multiplication algorithm (MMA) was presented as a method of calculating " the smallest nonnegative integer R congruent modulo M to the product AB of two nonegative integers without dividing by M."1 The claim that division is avoided is technically correct, but misleading. A minor modification calculates both R and Q such that AB = MQ + R. A simplified version of the new algorithm is given and an alternate derivation is shown to illustrate the key ideas behind the method.
multiple precision arithmetic, Algorithms, integer arithmetic, long division, modular arithmetic, modular multiplication
K. J. Sloan, "Comments on "A Computer Algorithm for Calculating the Product AB Modulo M"," in IEEE Transactions on Computers, vol. 34, no. , pp. 290-292, 1985.