EURASIP Journal on Embedded Systems
Volume 2006 (2006), Article ID 32192, 13 pages
doi:10.1155/ES/2006/32192
Modular Inverse Algorithms Without Multiplications for Cryptographic Applications
Seagate Research, 1251 Waterfront Place, Pittsburgh 15222, PA, USA
Received 19 July 2005; Revised 1 December 2005; Accepted 17 January 2006
Academic Editor: Sandro Bartolini
Copyright © 2006 Laszlo Hars. 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.
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.