Title

Montgomery multiplication over rings

Authors

Authors

J. P. Brennan;R. Katti

Comments

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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

WOS:000262611600002

ISSN

0016-0032

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