Adaptive Security for Threshold Cryptosystems

We present adaptively-secure efficient solutions to several central problems in the area of threshold cryptography. We prove these solutions to withstand adaptive attackers that choose parties for corruption at any time during the run of the protocol. In contrast, all previously known efficient protocols for these problems were proven secure only against less realistic static adversaries that choose and fix the subset of corrupted parties before the start of the protocol run. Specifically, we provide adaptively-secure solutions for distributed key generation in discrete-log based cryptosystems, and for the problem of distributed generation of DSS signatures (threshold DSS). We also show how to transform existent static solutions for threshold RSA and proactive schemes to withstand the stronger adaptive attackers. In doing so, we introduce several techniques for the design and analysis of adaptively-secure protocols that may well find further applications.

[1]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[2]  Hugo Krawczyk,et al.  On the Composition of Zero-Knowledge Proof Systems , 1990, ICALP.

[3]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

[4]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[5]  Joe Kilian,et al.  Lower bounds for zero knowledge on the Internet , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[6]  Tal Rabin,et al.  A Simplified Approach to Threshold and Proactive RSA , 1998, CRYPTO.

[7]  Ivan Damgård,et al.  Efficient Multiparty Computations Secure Against an Adaptive Adversary , 1999, EUROCRYPT.

[8]  Ivan Damgård,et al.  Zero-Knowledge Proofs for Finite Field Arithmetic or: Can Zero-Knowledge be for Free? , 1997 .

[9]  Tal Rabin,et al.  Simplified VSS and fast-track multiparty computations with applications to threshold cryptography , 1998, PODC '98.

[10]  Ronald Cramer,et al.  Efficient Multiparty Computations with Dishonest Minority , 1998 .

[11]  Kouichi Sakurai,et al.  On the Complexity of Constant Round ZKIP of Possession of Knowledge , 1991, ASIACRYPT.

[12]  Ran Canetti,et al.  Maintaining Authenticated Communication in the Presence of Break-Ins , 1997, PODC '97.

[13]  Judit Bar-Ilan,et al.  Non-cryptographic fault-tolerant computing in constant number of rounds of interaction , 1989, PODC '89.

[14]  Ivan Damgård,et al.  Zero-Knowledge Proofs for Finite Field Arithmetic; or: Can Zero-Knowledge be for Free? , 1998, CRYPTO.

[15]  Markus Jakobsson,et al.  Proactive public key and signature systems , 1997, CCS '97.

[16]  Donald Beaver,et al.  Cryptographic Protocols Provably Secure Against Dynamic Adversaries , 1992, EUROCRYPT.

[17]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

[18]  Moni Naor,et al.  Concurrent zero-knowledge , 1998, STOC '98.

[19]  Paul C. van Oorschot,et al.  Authentication and authenticated key exchanges , 1992, Des. Codes Cryptogr..

[20]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[21]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[22]  Susan K. Langford.  Threshold DSS Signatures without a Trusted Party , 1995, CRYPTO.

[23]  Hugo Krawczyk,et al.  Robust Threshold DSS Signatures , 1996, Inf. Comput..

[24]  Hugo Krawczyk,et al.  Secure Distributed Key Generation for Discrete-Log Based Cryptosystems , 1999, EUROCRYPT.

[25]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[26]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.

[27]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

[28]  Torben P. Pedersen.  A Threshold Cryptosystem without a Trusted Party (Extended Abstract) , 1991, EUROCRYPT.

[29]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.