Secure Applications of Pedersen’s Distributed Key Generation Protocol

  • Rosario Gennaro
  • Stanislaw Jarecki
  • Hugo Krawczyk
  • Tal Rabin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2612)

Abstract

A Distributed Key Generation (DKG)p rotocol is an essential component of any threshold cryptosystem. It is used to initialize the cryptosystem and generate its private and public keys, and it is used as a subprotocol, for example to generate a one-time key pair which is a part of any threshold El-Gamal-like signature scheme. Gennaro et al. showed [GJKR99] that a widely-known non-interactive DKG protocol suggested by Pedersen does not guarantee a uniformly random distribution of generated secret keys even in the static adversary model. Furthermore, Gennaro et al. proposed to replace this protocol with one that guarantees a uniform distribution of the generated key but requires an extra round of reliable broadcast communication.

We investigate the question whether some discrete-log based threshold cryptosystems remain secure when implemented using the more efficient DKG protocol of Pedersen, in spite of the fact that the adversary can skew the distribution of the secret key generated by this protocol. We answer this question in the positive. We show that threshold versions of some schemes whose security reduces to the hardness of the discrete logarithm problem, remain secure when implemented with Pedersen DKG. We exemplify this claim with a threshold Schnorr signature scheme.

However, the resulting scheme has less efficient security reduction (in the random oracle model)from the hardness of the discrete logarithm problem than the same scheme implemented with the computationally more expensive DKG protocol of Gennaro et al. Thus our results imply a trade-o. in the design of threshold versions of certain discrete-log based schemes between the round complexity of a protocol and the size of the modulus.

Keywords

Threshold cryptography distributed key generation discrete logarithm exact security random oracle model 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Rosario Gennaro
    • 1
  • Stanislaw Jarecki
    • 2
  • Hugo Krawczyk
    • 1
  • Tal Rabin
    • 1
  1. 1.IBM T.J.Watson ResearchUSA
  2. 2.Stanford UniversityUSA

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