Montgomery multiplication over rings
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 of the Franklin Institute-Engineering and Applied Mathematics
"Montgomery multiplication over rings" (2009). Faculty Bibliography 2000s. 7051.