Montgomery multiplication over rings |
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| Authors: | Joseph P Brennan Rajendra Katti |
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| Institution: | a Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, USA
b Department of Electrical and Computer Engineering, North Dakota State University, Fargo, ND 58105-5285, USA |
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| 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  . 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. |
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| Keywords: | 68M07 94A60 |
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