Modular Inverse Algorithms Without Multiplications for Cryptographic Applications
- Laszlo Hars1Email author
https://doi.org/10.1155/ES/2006/32192
© Laszlo Hars. 2006
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
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