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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.
Index Terms:
multiple precision arithmetic, Algorithms, integer arithmetic, long division, modular arithmetic, modular multiplication
Citation:
K.R., Jr. Sloan, "Comments on "A Computer Algorithm for Calculating the Product AB Modulo M"," IEEE Transactions on Computers, vol. 34, no. 3, pp. 290-292, March 1985, doi:10.1109/TC.1985.1676574
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