Cart (Loading....) | Create Account
Close category search window

Low-Weight Polynomial Form Integers for Efficient Modular Multiplication

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

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

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.