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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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  1. Laszlo Hars
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Correspondence to Laszlo Hars.

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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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  • DOI: https://doi.org/10.1155/ES/2006/32192

Keywords

  • Algorithmic Optimization
  • Optimization Technique
  • Control Structure
  • Elliptic Curve
  • Theoretical Argument