GCD-Free Algorithms for Computing Modular Inverses

  • Marc Joye
  • Pascal Paillier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2779)


This paper describes new algorithms for computing a modular inverse e − 1 given coprime integers e and f. Contrary to previously reported methods, we neither rely on the extended Euclidean algorithm, nor impose conditions on e or f. The main application of our gcd-free technique is the computation of an RSA private key in both standard and CRT modes based on simple modular arithmetic operations, thus boosting real-life implementations on crypto-accelerated devices.


Modular inverses RSA key generation prime numbers efficient implementations embedded software GCD algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marc Joye
    • 1
  • Pascal Paillier
    • 2
  1. 1.Gemplus, Card Security Group, La VigieLa CiotatFrance
  2. 2.Gemplus, Cryptography GroupIssy-les-MoulineauxFrance

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