A Unified Characterization of Completeness and Triviality for Secure Function Evaluation

We present unified combinatorial characterizations of completeness for 2-party secure function evaluation (SFE) against passive and active corruptions in the information-theoretic setting, so that all known characterizations appear as special cases.

[1]  Joe Kilian.  More general completeness theorems for secure two-party computation , 2000, STOC '00.

[2]  Joe Kilian,et al.  Achieving Oblivious Transfer Using Weakened Security Assumptions (Extended Abstract) , 1988, FOCS 1988.

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

[4]  Manoj Prabhakaran,et al.  Exploring the Limits of Common Coins Using Frontier Analysis of Protocols , 2011, TCC.

[5]  H. S. WITSENHAUSEN,et al.  The zero-error side information problem and chromatic numbers (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[6]  Carl Pomerance,et al.  Advances in Cryptology — CRYPTO ’87 , 2000, Lecture Notes in Computer Science.

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

[8]  Joe Kilian,et al.  Achieving oblivious transfer using weakened security assumptions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[9]  A. Yao,et al.  Fair exchange with a semi-trusted third party (extended abstract) , 1997, CCS '97.

[10]  Yehuda Lindell,et al.  On the Limitations of Universally Composable Two-Party Computation Without Set-Up Assumptions , 2003, Journal of Cryptology.

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

[12]  Manoj Prabhakaran,et al.  Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations , 2008, CRYPTO.

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

[14]  Stefan Wolf,et al.  Oblivious Transfer Is Symmetric , 2006, EUROCRYPT.

[15]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

[16]  Yuval Ishai,et al.  Founding Cryptography on Oblivious Transfer - Efficiently , 2008, CRYPTO.

[17]  Joe Kilian,et al.  A general completeness theorem for two party games , 1991, STOC '91.

[18]  Kirill Morozov,et al.  Efficient Unconditional Oblivious Transfer from Almost Any Noisy Channel , 2004, SCN.

[19]  Serge Vaudenay,et al.  Advances in Cryptology - EUROCRYPT 2006 , 2006, Lecture Notes in Computer Science.

[20]  Kenneth Rose,et al.  On zero-error coding of correlated sources , 2003, IEEE Trans. Inf. Theory.

[21]  Jörn Müller-Quade,et al.  Completeness Theorems with Constructive Proofs for Finite Deterministic 2-Party Functions , 2010, TCC.

[22]  Oded Goldreich,et al.  How to Solve any Protocol Problem - An Efficiency Improvement , 1987, CRYPTO.

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

[24]  Yotaro Kubo.  A Proof of Lemma 1 , 2014 .

[25]  Yehuda Lindell,et al.  On the Limitations of Universally Composable Two-Party Computation without Set-up Assumptions , 2003, EUROCRYPT.

[26]  Jörn Müller-Quade,et al.  Secure Computability of Functions in the IT Setting with Dishonest Majority and Applications to Long-Term Security , 2009, TCC.

[27]  Martijn Stam.  Beyond Uniformity: Better Security/Efficiency Tradeoffs for Compression Functions , 2008, CRYPTO.

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