Open Access

Modular Inverse Algorithms Without Multiplications for Cryptographic Applications

EURASIP Journal on Embedded Systems20062006:032192

DOI: 10.1155/ES/2006/32192

Received: 19 July 2005

Accepted: 17 January 2006

Published: 22 March 2006

Abstract

Hardware and algorithmic optimization techniques are presented to the left-shift, right-shift, and the traditional Euclidean-modular inverse algorithms. Theoretical arguments and extensive simulations determined the resulting expected running time. On many computational platforms these turn out to be the fastest known algorithms for moderate operand lengths. They are based on variants of Euclidean-type extended GCD algorithms. On the considered computational platforms for operand lengths used in cryptography, the fastest presented modular inverse algorithms need about twice the time of modular multiplications, or even less. Consequently, in elliptic curve cryptography delaying modular divisions is slower (affine coordinates are the best) and the RSA and ElGamal cryptosystems can be accelerated.

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Authors’ Affiliations

(1)
Seagate Research

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Copyright

© Laszlo Hars. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.