Title
Montgomery multiplication over rings
Abstract
Montogomery multiplication of two elements a and b of a finite field F(q) is defined as abr(-1) where r is a fixed field element in F(q)(x). In this paper we define Montgomery multiplication of elements a(x) and b(x) in a polynomial ring modulo the ideal generated by a reducible polynomial f(x). We then show that Montgomery multiplication over a field represented by a polynomial ring modulo an irreducible pentanomial can be performed more efficiently in terms of time delay by embedding the field in a quotient of a polynomial ring modulo a reducible trinomial. The trinomial has a degree that is slightly higher than that of the pentanomial, thereby increasing the number of gates in the multiplier by a small amount. (C) 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Journal Title
Journal of the Franklin Institute-Engineering and Applied Mathematics
Volume
346
Issue/Number
1
Publication Date
1-1-2009
Document Type
Article
First Page
10
Last Page
16
WOS Identifier
ISSN
0016-0032
Recommended Citation
"Montgomery multiplication over rings" (2009). Faculty Bibliography 2000s. 7051.
https://stars.library.ucf.edu/facultybib2000/7051
Comments
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