Comments on "A Computer Algorithm for Calculating the Product AB Modulo M"

Authors:
K. R. , Jr. Sloan
Affiliations:
Department of Computer Science, University of Washington
Venue:
IEEE Transactions on Computers
Year:
1985

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Abstract

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.