From Passive to Covert Security at Low Cost

Aumann and Lindell defined security against covert attacks, where the adversary is malicious, but is only caught cheating with a certain probability. The idea is that in many real-world cases, a large probability of being caught is sufficient to prevent the adversary from trying to cheat. In this paper, we show how to compile a passively secure protocol for honest majority into one that is secure against covert attacks, again for honest majority and catches cheating with probability 1/4. The cost of the modified protocol is essentially twice that of the original plus an overhead that only depends on the number of inputs.

[1]  Ivan Damgård,et al.  Secure Multiparty Computation Goes Live , 2009, Financial Cryptography.

[2]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[3]  Xiaotie Deng,et al.  Optimal Amortized Distributed Consensus , 1995, Inf. Comput..

[4]  Ivan Damgård,et al.  Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor , 2001, CRYPTO.

[5]  Yehuda Lindell,et al.  Sequential composition of protocols without simultaneous termination , 2002, PODC '02.

[6]  Yehuda Lindell,et al.  Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries , 2007, TCC.

[7]  Martin Hirt,et al.  Perfectly-Secure MPC with Linear Communication Complexity , 2008, TCC.

[8]  Adam D. Smith,et al.  Efficient Two Party and Multi Party Computation Against Covert Adversaries , 2008, EUROCRYPT.

[9]  Ran Canetti,et al.  Universally composable protocols with relaxed set-up assumptions , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

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

[11]  Yuval Ishai,et al.  Scalable Multiparty Computation with Nearly Optimal Work and Resilience , 2008, CRYPTO.

[12]  Piotr Berman,et al.  Optimal Early Stopping in Distributed Consensus (Extended Abstract) , 1992, WDAG.

[13]  Jan Camenisch,et al.  Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products , 2002, CRYPTO.

[14]  Ivan Damgård,et al.  Scalable and Unconditionally Secure Multiparty Computation , 2007, CRYPTO.

[15]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.