International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2000: Advances in Cryptology — EUROCRYPT 2000 pp 190-206

Computing Inverses over a Shared Secret Modulus

  • Dario Catalano
  • Rosario Gennaro
  • Shai Halevi
Conference paper

DOI: 10.1007/3-540-45539-6_14

Volume 1807 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Catalano D., Gennaro R., Halevi S. (2000) Computing Inverses over a Shared Secret Modulus. In: Preneel B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg

Abstract

We discuss the following problem: Given an integer φ shared secretly among n players and a prime number e, how can the players efficiently compute a sharing of e−1 mod φ. The most interesting case is when φ is the Euler function of a known RSA modulus N, φ = φ(N). The problem has several applications, among which the construction of threshold variants for two recent signature schemes proposed by Gennaro-Halevi-Rabin and Cramer-Shoup.

We present new and efficient protocols to solve this problem, improving over previous solutions by Boneh-Franklin and Frankel et al. Our basic protocol (secure against honest but curious players) requires only two rounds of communication and a single GCD computation. The robust protocol (secure against malicious players) adds only a couple of rounds and a few modular exponentiations to the computation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Dario Catalano
    • 1
  • Rosario Gennaro
    • 2
  • Shai Halevi
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaCatania
  2. 2.IBM T.J.Watson Research CenterYorktown HeightsUSA