International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Threshold Cryptography Secure Against the Adaptive Adversary, Concurrently

Anna Lysyanskaya
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Abstract: A threshold cryptosystem or signature scheme is a system with $n$ participants where an honest majority can successfully decrypt a message or issue a signature, but where the security and functionality properties of the system are retained even as the adversary corrupts up to $t$ players. We present the novel technique of a committed proof, which is a new general tool that enables security of threshold cryptosystems in the presence of the adaptive adversary. We also put forward a new measure of security for threshold schemes secure in the adaptive adversary model: security under concurrent composition. Using committed proofs, we construct concurrently and adaptively secure threshold protocols for a variety of cryptographic applications. In particular, based on the recent scheme by Cramer-Shoup, we construct adaptively secure threshold cryptosystems secure against adaptive chosen ciphertext attack under the DDH intractability assumption.
  title={Threshold Cryptography Secure Against the Adaptive Adversary, Concurrently},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / threshold cryptography; adaptive adversary},
  note={Part of this paper will appear in Eurocrypt2000 11090 received 12 May 2000},
  author={Anna Lysyanskaya},