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Secure distributed key generation for discrete-log based cryptosystems. (English) Zbl 0931.94021
Stern, Jacques (ed.), Advances in cryptology - EUROCRYPT ’99. 17th annual Eurocrypt conference, international conference on The theory and application of cryptographic techniques, Prague, Czech Republic, May 2–6, 1999. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1592, 295-310 (1999).
Summary: 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 the authors designed a distributed key generation protocol which they present here together with a rigorous proof of security. Their 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.
For the entire collection see [Zbl 0912.00038].

94A60 Cryptography
68P25 Data encryption (aspects in computer science)