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Mathematics of Computation

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New frameworks for Montgomery's modular multiplication method

Author: Philip B. McLaughlin Jr.
Journal: Math. Comp. 73 (2004), 899-906
MSC (2000): Primary 11-04, 11Y16; Secondary 11A07, 11T55
Published electronically: May 7, 2003
MathSciNet review: 2031414
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Abstract: We present frameworks for fast modular multiplication based on a modification of Montgomery's original method. For (fixed) large integers, our algorithms may be significantly faster than conventional methods. Our techniques may also be extended to modular polynomial arithmetic.

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Additional Information

Philip B. McLaughlin Jr.
Affiliation: 237 N. Harris Avenue, Tucson, Arizona 85716

Keywords: Modular arithmetic, multiplication, factorization, primality testing, polynomial arithmetic, public-key cryptography
Received by editor(s): May 5, 2000
Received by editor(s) in revised form: July 2, 2002
Published electronically: May 7, 2003
Article copyright: © Copyright 2003 American Mathematical Society