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Modular Inverse Algorithms Without Multiplications for Cryptographic Applications

EURASIP Journal on Embedded Systems volume 2006, Article number: 032192 (2006) Cite this article

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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  1. Seagate Research, 1251 Waterfront Place, Pittsburgh, PA, 15222, USA

    Laszlo Hars

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Correspondence to Laszlo Hars.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hars, L. Modular Inverse Algorithms Without Multiplications for Cryptographic Applications. J Embedded Systems 2006, 032192 (2006). https://doi.org/10.1155/ES/2006/32192

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