Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits

SPDZ (pronounced “Speedz”) is the nickname of the MPC protocol of Damgard et al. from Crypto 2012. In this paper we both resolve a number of open problems with SPDZ; and present several theoretical and practical improvements to the protocol. In detail, we start by designing and implementing a covertly secure key generation protocol for obtaining a BGV public key and a shared associated secret key. We then construct both a covertly and actively secure preprocessing phase, both of which compare favourably with previous work in terms of efficiency and provable security.

[1]  Vinod Vaikuntanathan,et al.  Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages , 2011, CRYPTO.

[2]  Donald Beaver,et al.  Efficient Multiparty Protocols Using Circuit Randomization , 1991, CRYPTO.

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

[4]  Ivan Damgård,et al.  Asynchronous Multiparty Computation: Theory and Implementation , 2008, IACR Cryptol. ePrint Arch..

[5]  Marcel Keller,et al.  Secure Multiparty AES , 2010, Financial Cryptography.

[6]  I. Damglurd.  Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation , 2006 .

[7]  Dan Bogdanov,et al.  Sharemind: A Framework for Fast Privacy-Preserving Computations , 2008, ESORICS.

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

[9]  Yihua Zhang,et al.  Secure Computation on Floating Point Numbers , 2013, NDSS.

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

[11]  Masahiro Yagisawa,et al.  Fully Homomorphic Encryption without bootstrapping , 2015, IACR Cryptol. ePrint Arch..

[12]  Octavian Catrina,et al.  Secure Computation with Fixed-Point Numbers , 2010, Financial Cryptography.

[13]  Yehuda Lindell,et al.  Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries , 2007, Journal of Cryptology.

[14]  Craig Gentry,et al.  Homomorphic Evaluation of the AES Circuit , 2012, IACR Cryptol. ePrint Arch..

[15]  GentryCraig,et al.  Leveled) Fully Homomorphic Encryption without Bootstrapping , 2014 .

[16]  Yehuda Lindell,et al.  Implementing Two-Party Computation Efficiently with Security Against Malicious Adversaries , 2008, SCN.

[17]  Claudio Orlandi,et al.  A New Approach to Practical Active-Secure Two-Party Computation , 2012, IACR Cryptol. ePrint Arch..

[18]  Craig Gentry,et al.  (Leveled) fully homomorphic encryption without bootstrapping , 2012, ITCS '12.

[19]  Abhi Shelat,et al.  Towards Billion-Gate Secure Computation with Malicious Adversaries , 2012, IACR Cryptol. ePrint Arch..

[20]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

[21]  P. L. Montgomery.  Modular multiplication without trial division , 1985 .

[22]  Benny Pinkas,et al.  Fairplay - Secure Two-Party Computation System , 2004, USENIX Security Symposium.

[23]  Benny Pinkas,et al.  Fairplay - Secure Two-Party Computation System (Awarded Best Student Paper!) , 2004 .

[24]  Craig Gentry,et al.  Fully Homomorphic Encryption with Polylog Overhead , 2012, EUROCRYPT.

[25]  Marcel Keller,et al.  Implementing AES via an Actively/Covertly Secure Dishonest-Majority MPC Protocol , 2012, SCN.

[26]  Ivan Damgård,et al.  Multiparty Computation from Somewhat Homomorphic Encryption , 2012, IACR Cryptol. ePrint Arch..