Title

Montgomery Multiplication Over Rings

Keywords

Arithmetic; Finite fields; Finite rings; Montgomery multiplication; Multiplier

Abstract

Montgomery multiplication of two elements a and b of a finite field Fq is defined as abr- 1 where r is a fixed field element in Fq×. 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. © 2008 The Franklin Institute.

Publication Date

2-1-2009

Publication Title

Journal of the Franklin Institute

Volume

346

Issue

1

Number of Pages

10-16

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfranklin.2008.06.002

Socpus ID

58149483419 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/58149483419

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