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

Exponentiation using division chains

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

1 Author(s)
Walter, C.D. ; Dept. of Comput., Univ. of Manchester Inst. of Sci. & Technol., UK

Exponentiation may be performed faster than the traditional square and multiply method by iteratively reducing the exponent module numbers which, as exponents themselves, require few multiplications. This mainly includes those with few nonzero bits. For a suitable choice of such divisors, the resulting mixed basis representation of the exponent reduces the expected number of nonsquaring multiplications by over half at the cost of a single extra register. Preprocessing effort depends entirely on the exponent and can be kept down to the work saved in a single exponentiation. Moreover, no precomputed look-up tables are required, so the method is especially applicable where space is at a premium. In particular, it outperforms the instance of the m-ary method which uses the same space. However, for 512-bit exponents, it beats every instance of the m-ary method, achieving well under 635 multiplications on average. Both hardware and software implementations of the RSA crypto-system can benefit from this algorithm

Published in:

Computers, IEEE Transactions on  (Volume:47 ,  Issue: 7 )

Date of Publication:

Jul 1998

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.