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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Modular multiplication without trial division

Author: Peter L. Montgomery
Journal: Math. Comp. 44 (1985), 519-521
MSC: Primary 11Y16
MathSciNet review: 777282
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Abstract: Let $N > 1$. We present a method for multiplying two integers (called N-residues) modulo N while avoiding division by N. N-residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one N. The addition and subtraction algorithms are unchanged.

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Keywords: Modular arithmetic, multiplication
Article copyright: © Copyright 1985 American Mathematical Society