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Low-Weight Polynomial Form Integers for Efficient Modular Multiplication

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2 Author(s)
Jaewook Chung ; Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont. ; Hasan, M.A.

In 1999, Solinas introduced families of moduli called the generalized Mersenne numbers (GMNs), which are expressed in low-weight polynomial form, p=f(t), where t is limited to a power of 2. GMNs are very useful in elliptic curve cryptosystems over prime fields since modular reduction by a GMN requires only integer additions and subtractions. However, since there are not many GMNs and each GMN requires a dedicated implementation, GMNs are hardly useful for other cryptosystems. Here, we modify GMN by removing restriction on the choice of t and restricting the coefficients of f(t) to 0 and plusmn1. We call such families of moduli low-weight polynomial form integers (LWPFIs). We show an efficient modular multiplication method using LWPFI moduli. LWPFIs allow general implementation and there exist many LWPFI moduli. One may consider LWPFIs as a trade-off between general integers and GMNs

Published in:

Computers, IEEE Transactions on  (Volume:56 ,  Issue: 1 )

Date of Publication:

Jan. 2007

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