Secure distributed key generation for discrete-log based cryptosystems

  • Authors:
  • Rosario Gennaro;Stanisław Jarecki;Hugo Krawczyk;Tal Rabin

  • Affiliations:
  • IBM T.J.Watson Research Center, Yorktown Heights, NY;MIT Laboratory for Computer Science, Cambridge, MA;Department of Electrical Engineering, Technion, Haifa, Israel and IBM T.J. Watson Research Center, New York;IBM T.J.Watson Research Center, Yorktown Heights, NY

  • Venue:
  • EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
  • Year:
  • 1999

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Abstract

Distributed key generation is a main component of threshold cryptosystems and distributed cryptographic computing in general. Solutions to the distributed generation of private keys for discrete-log based cryptosystems have been known for several years and used in a variety of protocols and in many research papers. However, these solutions fail to provide the full security required and claimed by these works. We show how an active attacker controlling a small number of parties can bias the values of the generated keys, thus violating basic correctness and secrecy requirements of a key generation protocol. In particular, our attacks point out to the places where the proofs of security fail. Based on these findings we designed a distributed key generation protocol which we present here together with a rigorous proof of security. Our solution, that achieves optimal resiliency, can be used as a drop-in replacement for key generation modules as well as other components of threshold or proactive discrete-log based cryptosystems.