TinyLEGO: An Interactive Garbling Scheme for Maliciously Secure Two-party Computation

This paper reports on a number of conceptual and technical contributions to the currently very lively field of two-party computation (2PC) based on garbled circuits. Our main contributions are as follows: 1. We propose the notion of an interactive garbling scheme, where the garbled circuit is generated through an interactive protocol between the garbler and the evaluator. The garbled circuit is correct and privacy preserving even if one of the two parties was acting maliciously during garbling. The security notion is game based. 2. We show that an interactive garbling scheme combined with a Universally Composable (UC) secure oblivious transfer protocol can be used in a black-box manner to implement two-party computation (2PC) UC securely against any probabilistic polynomial time static and malicious adversary. The protocol abstracts many recent protocols for implementing 2PC from garbled circuits and will allow future designers of interactive garbling schemes to prove security with the simple game based definitions, as opposed to directly proving UC security for each new scheme. 3. We propose an instantiation of interactive garbling by designing a new protocol in the LEGO family of protocols for efficient garbling against a malicious adversary. The new protocol is based on several new technical contributions and optimizations, for example making it possible to get distinct output to both parties with minimal overhead. The scheme makes black-box usage of a XOR-homomorphic commitment scheme, an authentic, private and oblivious garbling scheme and a 2-correlation-robust and collision-resistant hash function. When comparing our resulting 2PC protocol to previous works in the same setting we see a noticeable reduction in the communication that directly depends on the size of the circuit (e.g. 33% for circuits larger than 501,271 AND gates).

[1]  Yuval Ishai,et al.  Extending Oblivious Transfers Efficiently , 2003, CRYPTO.

[2]  Ignacio Cascudo,et al.  Additively Homomorphic UC Commitments with Optimal Amortized Overhead , 2015, Public Key Cryptography.

[3]  Jonathan Katz,et al.  Faster Secure Two-Party Computation Using Garbled Circuits , 2011, USENIX Security Symposium.

[4]  Benny Pinkas,et al.  Non-Interactive Secure Computation Based on Cut-and-Choose , 2014, IACR Cryptol. ePrint Arch..

[5]  Claudio Orlandi,et al.  MiniLEGO: Efficient Secure Two-Party Computation from General Assumptions , 2013, EUROCRYPT.

[6]  Andrew Chi-Chih Yao,et al.  How to Generate and Exchange Secrets (Extended Abstract) , 1986, FOCS.

[7]  Silvio Micali,et al.  The round complexity of secure protocols , 1990, STOC '90.

[8]  Mihir Bellare,et al.  Foundations of garbled circuits , 2012, CCS.

[9]  Ben Riva,et al.  Richer Efficiency/Security Trade-offs in 2PC , 2015, TCC.

[10]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[11]  Alex J. Malozemoff,et al.  Amortizing Garbled Circuits , 2015, IACR Cryptol. ePrint Arch..

[12]  Wolfgang Ch. Schmid,et al.  MinT: A Database for Optimal Net Parameters , 2006 .

[13]  Yehuda Lindell,et al.  A Proof of Security of Yao’s Protocol for Two-Party Computation , 2009, Journal of Cryptology.

[14]  Berry Schoenmakers,et al.  A protocol issue for the malicious case of Yao's garbled circuit construction , 2006 .

[15]  Samuel Ranellucci,et al.  Constant-round secure two-party computation from a linear number of oblivious transfer , 2013 .

[16]  Wolfgang Ch. Schmid,et al.  MinT - Architecture and applications of the (t, m, s)-net and OOA database , 2010, Math. Comput. Simul..

[17]  Abhi Shelat,et al.  Billion-Gate Secure Computation with Malicious Adversaries , 2012, USENIX Security Symposium.

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

[19]  Vladimir Kolesnikov,et al.  Improved Garbled Circuit: Free XOR Gates and Applications , 2008, ICALP.

[20]  Arash Afshar,et al.  How to Efficiently Evaluate RAM Programs with Malicious Security , 2014, EUROCRYPT.

[21]  Yehuda Lindell,et al.  The IPS Compiler: Optimizations, Variants and Concrete Efficiency , 2011, CRYPTO.

[22]  Matthew K. Franklin,et al.  Efficiency Tradeoffs for Malicious Two-Party Computation , 2006, Public Key Cryptography.

[23]  Rafail Ostrovsky,et al.  Zero-knowledge from secure multiparty computation , 2007, STOC '07.

[24]  Hao Chen,et al.  Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields , 2006, CRYPTO.

[25]  Jonathan Katz,et al.  On the Security of the Free-XOR Technique , 2012, IACR Cryptol. ePrint Arch..

[26]  Jesper Buus Nielsen,et al.  On the Complexity of Additively Homomorphic UC Commitments , 2016, TCC.

[27]  Steven Myers,et al.  GPU and CPU parallelization of honest-but-curious secure two-party computation , 2013, ACSAC.

[28]  Mihir Bellare,et al.  Efficient Garbling from a Fixed-Key Blockcipher , 2013, 2013 IEEE Symposium on Security and Privacy.

[29]  Jonathan Katz,et al.  Efficient Secure Two-Party Computation Using Symmetric Cut-and-Choose , 2013, CRYPTO.

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

[31]  J. Nielsen,et al.  Fast and Maliciously Secure Two-Party Computation Using the GPU , 2013, ACNS.

[32]  Jonathan Katz,et al.  Quid-Pro-Quo-tocols: Strengthening Semi-honest Protocols with Dual Execution , 2012, 2012 IEEE Symposium on Security and Privacy.

[33]  Ben Riva,et al.  Garbled Circuits Checking Garbled Circuits: More Efficient and Secure Two-Party Computation , 2013, IACR Cryptol. ePrint Arch..

[34]  Claudio Orlandi,et al.  LEGO for Two-Party Secure Computation , 2009, TCC.

[35]  Moni Naor,et al.  Privacy preserving auctions and mechanism design , 1999, EC '99.

[36]  Luís T. A. N. Brandão,et al.  Secure Two-Party Computation with Reusable Bit-Commitments, via a Cut-and-Choose with Forge-and-Lose Technique , 2013, IACR Cryptol. ePrint Arch..

[37]  Yehuda Lindell,et al.  Cut-and-Choose Yao-Based Secure Computation in the Online/Offline and Batch Settings , 2014, CRYPTO.

[38]  Alain Tapp,et al.  Secure Two-Party Computation via Leaky Generalized Oblivious Transfer , 2013, IACR Cryptol. ePrint Arch..

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

[40]  Benny Pinkas,et al.  Secure Two-Party Computation is Practical , 2009, IACR Cryptol. ePrint Arch..

[41]  Yehuda Lindell.  Fast Cut-and-Choose-Based Protocols for Malicious and Covert Adversaries , 2015, Journal of Cryptology.

[42]  David Evans,et al.  Two Halves Make a Whole - Reducing Data Transfer in Garbled Circuits Using Half Gates , 2015, EUROCRYPT.

[43]  Abhi Shelat,et al.  Two-Output Secure Computation with Malicious Adversaries , 2011, EUROCRYPT.

[44]  R. Morelos-Zaragoza.  The art of error correcting coding , 2002 .

[45]  Jesper Buus Nielsen,et al.  Faster Maliciously Secure Two-Party Computation Using the GPU , 2014, SCN.

[46]  Yehuda Lindell,et al.  An Efficient Protocol for Secure Two-Party Computation in the Presence of Malicious Adversaries , 2007, Journal of Cryptology.

[47]  Abhi Shelat,et al.  Fast two-party secure computation with minimal assumptions , 2013, CCS.

[48]  Yehuda Lindell,et al.  Secure Two-Party Computation via Cut-and-Choose Oblivious Transfer , 2010, IACR Cryptol. ePrint Arch..