A Full Characterization of Completeness for Two-Party Randomized Function Evaluation

We settle a long standing open problem which has pursued a full characterization of completeness of (potentially randomized) finite functions for 2-party computation that is secure against active adversaries. Since the first such complete function was discovered [Kilian, FOCS 1988], the question of which finite 2-party functions are complete has been studied extensively, leading to characterization in many special cases. In this work, we completely settle this problem.

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

[2]  Avi Wigderson,et al.  Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation (Extended Abstract) , 1988, STOC.

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

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

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

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

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

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

[9]  Rafail Ostrovsky,et al.  Reducibility and Completeness in Private Computations , 2000, SIAM J. Comput..

[10]  Rafail Ostrovsky,et al.  Reducibility and completeness in multi-party private computations , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[11]  Moni Naor,et al.  Completeness in Two-Party Secure Computation: A Computational View , 2004, STOC '04.

[12]  Daniel R. Simon,et al.  Finding Collisions on a One-Way Street: Can Secure Hash Functions Be Based on General Assumptions? , 1998, EUROCRYPT.

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

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

[15]  Rafail Ostrovsky,et al.  Constant-Rate Oblivious Transfer from Noisy Channels , 2011, CRYPTO.

[16]  Mike Rosulek.  Universal Composability from Essentially Any Trusted Setup , 2011, IACR Cryptol. ePrint Arch..

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

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

[19]  Matthias Fitzi,et al.  From partial consistency to global broadcast , 2000, STOC '00.

[20]  Ivan Damgård,et al.  Unfair Noisy Channels and Oblivious Transfer , 2003, TCC.

[21]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.

[22]  Rudolf Ahlswede,et al.  Founding Cryptography on Oblivious Transfer , 2016 .

[23]  Gilles Brassard,et al.  Oblivious transfers and intersecting codes , 1996, IEEE Trans. Inf. Theory.

[24]  Donald Beaver,et al.  Precomputing Oblivious Transfer , 1995, CRYPTO.

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

[26]  Rafail Ostrovsky,et al.  Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data , 2004, SIAM J. Comput..

[27]  C. Moler,et al.  Advances in Cryptology , 2000, Lecture Notes in Computer Science.

[28]  Tal Malkin,et al.  Simple, Black-Box Constructions of Adaptively Secure Protocols , 2009, TCC.

[29]  Sampath Kannan,et al.  The relationship between public key encryption and oblivious transfer , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[30]  Michael Luby,et al.  How to Construct Pseudo-Random Permutations from Pseudo-Random Functions (Abstract) , 1986, CRYPTO.

[31]  Tal Malkin,et al.  On the impossibility of basing trapdoor functions on trapdoor predicates , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[32]  Jean-Sébastien Coron,et al.  The Random Oracle Model and the Ideal Cipher Model Are Equivalent , 2008, CRYPTO.

[33]  Manoj Prabhakaran,et al.  Limits of random oracles in secure computation , 2012, Electron. Colloquium Comput. Complex..

[34]  Russell Impagliazzo,et al.  Limits on the provable consequences of one-way permutations , 1988, STOC '89.

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

[36]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[38]  Yehuda Lindell,et al.  Black-box constructions for secure computation , 2006, STOC '06.

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

[40]  Rafail Ostrovsky,et al.  Efficient Non-interactive Secure Computation , 2011, EUROCRYPT.

[41]  Gilles Brassard,et al.  All-or-Nothing Disclosure of Secrets , 1986, CRYPTO.

[42]  Rafail Ostrovsky,et al.  Minimal Complete Primitives for Secure Multi-Party Computation , 2001, Journal of Cryptology.

[43]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

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

[45]  Yuval Ishai,et al.  On the Cryptographic Complexity of the Worst Functions , 2014, TCC.

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

[47]  Arno Mittelbach,et al.  Reset Indifferentiability and its Consequences , 2013, IACR Cryptol. ePrint Arch..

[48]  Claude Crépeau,et al.  Equivalence Between Two Flavours of Oblivious Transfers , 1987, CRYPTO.

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

[50]  Salil P. Vadhan,et al.  Theory of Cryptography , 2016, Lecture Notes in Computer Science.

[51]  Stefano Tessaro,et al.  The equivalence of the random oracle model and the ideal cipher model, revisited , 2010, STOC '11.

[52]  C. Peirce.  An unpublished manuscript) , 2016 .

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

[54]  Ivan Damgård,et al.  On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions , 1998, EUROCRYPT.

[55]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[56]  Russell Impagliazzo,et al.  A personal view of average-case complexity , 1995, Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference.

[57]  Daniel Kraschewski.  Completeness Theorems for All Finite Stateless 2-Party Primitives , 2013, IACR Cryptol. ePrint Arch..

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

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

[60]  Manoj Prabhakaran,et al.  A Zero-One Law for Cryptographic Complexity with Respect to Computational UC Security , 2010, CRYPTO.

[61]  Iftach Haitner,et al.  Semi-honest to Malicious Oblivious Transfer - The Black-Box Way , 2008, TCC.

[62]  Silvio Micali,et al.  The All-or-Nothing Nature of Two-Party Secure Computation , 1999, CRYPTO.