Common randomness for secure computing

We revisit A.C. Yao's classic problem of secure function computation by interactive communication, in an information theoretic setting. Our approach, based on examining the underlying common randomness, provides a new proof of the characterization of a securely computable function by deterministic protocols. This approach also yields a characterization of the minimum communication needed for secure computability.

[1]  Eyal Kushilevitz,et al.  Privacy and communication complexity , 1989, 30th Annual Symposium on Foundations of Computer Science.

[2]  Rudolf Ahlswede,et al.  Common randomness in information theory and cryptography - I: Secret sharing , 1993, IEEE Trans. Inf. Theory.

[3]  Michael O. Rabin,et al.  How To Exchange Secrets with Oblivious Transfer , 2005, IACR Cryptol. ePrint Arch..

[4]  Himanshu Tyagi,et al.  When Is a Function Securely Computable? , 2010, IEEE Transactions on Information Theory.

[5]  Manoj Prabhakaran,et al.  A Unified Characterization of Completeness and Triviality for Secure Function Evaluation , 2012, INDOCRYPT.

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

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

[8]  Mokshay M. Madiman,et al.  Information Inequalities for Joint Distributions, With Interpretations and Applications , 2008, IEEE Transactions on Information Theory.

[9]  Andrew Chi-Chih Yao,et al.  Protocols for secure computations , 1982, FOCS 1982.

[10]  Tal Rabin,et al.  Verifiable secret sharing and multiparty protocols with honest majority , 1989, STOC '89.

[11]  Donald Beaver.  Perfect Privacy For Two-Party Protocols , 1989, Distributed Computing And Cryptography.

[12]  Manoj Prabhakaran,et al.  Complexity of Multiparty Computation Problems: The Case of 2-Party Symmetric Secure Function Evaluation , 2009, IACR Cryptol. ePrint Arch..

[13]  U. Maurer,et al.  Secret key agreement by public discussion from common information , 1993, IEEE Trans. Inf. Theory.

[14]  Stefan Wolf,et al.  New Monotones and Lower Bounds in Unconditional Two-Party Computation , 2008, IEEE Transactions on Information Theory.

[15]  Vinod M. Prabhakaran,et al.  On the Communication Complexity of Secure Computation , 2013, IACR Cryptol. ePrint Arch..

[16]  Ye Wang,et al.  Information-theoretically secure three-party computation with One corrupted party , 2012, 2013 IEEE International Symposium on Information Theory.

[17]  Vinod M. Prabhakaran,et al.  Assisted Common Information With an Application to Secure Two-Party Sampling , 2014, IEEE Transactions on Information Theory.

[18]  Imre Csiszár,et al.  Secrecy Capacities for Multiterminal Channel Models , 2005, IEEE Transactions on Information Theory.

[19]  Manuel Blum,et al.  Coin flipping by telephone a protocol for solving impossible problems , 1983, SIGA.

[20]  Donald Beaver,et al.  Multiparty Protocols Tolerating Half Faulty Processors , 1989, CRYPTO.

[21]  Silvio Micali,et al.  Lower Bounds for Oblivious Transfer Reductions , 1999, EUROCRYPT.

[22]  Vinod M. Prabhakaran,et al.  On secure multiparty sampling for more than two parties , 2012, 2012 IEEE Information Theory Workshop.