P. Montgomery. Mathematics of Computation, 44 (170):
519--521(1985)
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.
%0 Journal Article
%1 Montgomery85
%A Montgomery, Peter L.
%D 1985
%J Mathematics of Computation
%K modular montgomery multiplication rsa
%N 170
%P 519--521
%T Modular Multiplication without Trial Division
%V 44
%X 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.
@article{Montgomery85,
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.},
added-at = {2012-09-02T14:01:30.000+0200},
author = {Montgomery, Peter L.},
bdsk-url-1 = {http://www.ams.org/journals/mcom/1985-44-170/S0025-5718-1985-0777282-X/S0025-5718-1985-0777282-X.pdf},
biburl = {https://www.bibsonomy.org/bibtex/2385a79d0393cb53efc9418758c6ef0b5/cgommel},
citeulike-article-id = {6592219},
date-added = {2012-08-26 14:17:01 +0000},
date-modified = {2012-08-26 14:21:39 +0000},
interhash = {8c05967188adaa127ab0f9953856f872},
intrahash = {385a79d0393cb53efc9418758c6ef0b5},
journal = {Mathematics of Computation},
keywords = {modular montgomery multiplication rsa},
number = 170,
pages = {519--521},
posted-at = {2010-01-27 00:32:40},
priority = {2},
timestamp = {2012-09-02T14:01:30.000+0200},
title = {Modular Multiplication without Trial Division},
volume = 44,
year = 1985
}