Actively Secure Setup for SPDZ

We present an actively secure, practical protocol to generate the distributed secret keys needed in the SPDZ offline protocol. The resulting distribution of the public and secret keys is such that the associated SHE ‘noise’ analysis is the same as if the distributed keys were generated by a trusted setup. We implemented the presented protocol for distributed BGV key generation within the SCALE-MAMBA framework. Our method makes use of a new method for creating doubly (or even more) authenticated bits in different MPC engines, which has applications in other areas of MPC-based secure computation. We were able to generate keys for two parties and a plaintext size of 64 bits in around five minutes, and a little more than eighteen minutes for a 128 bit prime.

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

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

[3]  Daniel E. Escudero,et al.  SPDℤ 2 k : Efficient MPC mod 2 k for Dishonest Majority. , 2018 .

[4]  Yuval Ishai,et al.  Efficient Pseudorandom Correlation Generators: Silent OT Extension and More , 2019, IACR Cryptol. ePrint Arch..

[5]  Dragos Rotaru,et al.  MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security , 2019, IACR Cryptol. ePrint Arch..

[6]  Rachel Player,et al.  On the Feasibility and Impact of Standardising Sparse-secret LWE Parameter Sets for Homomorphic Encryption , 2019, IACR Cryptol. ePrint Arch..

[7]  Emmanuela Orsini,et al.  High-Performance Multi-party Computation for Binary Circuits Based on Oblivious Transfer , 2021, IACR Cryptol. ePrint Arch..

[8]  Frederik Vercauteren,et al.  Overdrive2k: Efficient Secure MPC over Z2k from Somewhat Homomorphic Encryption , 2020, IACR Cryptol. ePrint Arch..

[9]  Marcel Keller,et al.  Faster Secure Multi-party Computation of AES and DES Using Lookup Tables , 2017, ACNS.

[10]  Vinod Vaikuntanathan,et al.  Multiparty Computation with Low Communication, Computation and Interaction via Threshold FHE , 2012, EUROCRYPT.

[11]  Emmanuela Orsini,et al.  Zaphod: Efficiently Combining LSSS and Garbled Circuits in SCALE , 2019, IACR Cryptol. ePrint Arch..

[12]  Marcel Keller,et al.  Overdrive: Making SPDZ Great Again , 2018, IACR Cryptol. ePrint Arch..

[13]  Erdem Alkim,et al.  Post-quantum Key Exchange - A New Hope , 2016, USENIX Security Symposium.

[14]  Marcel Keller,et al.  Actively Secure OT Extension with Optimal Overhead , 2015, CRYPTO.

[15]  Jean-Pierre Hubaux,et al.  Computing across Trust Boundaries using Distributed Homomorphic Cryptography , 2019, IACR Cryptol. ePrint Arch..

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

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

[18]  Marcel Keller,et al.  Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits , 2013, ESORICS.

[19]  Ivan Damgård,et al.  Semi-Homomorphic Encryption and Multiparty Computation , 2011, IACR Cryptol. ePrint Arch..

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

[21]  Ellis Horowitz,et al.  Computing Partitions with Applications to the Knapsack Problem , 1974, JACM.

[22]  Marcel Keller,et al.  A Unified Approach to MPC with Preprocessing using OT , 2015, IACR Cryptol. ePrint Arch..

[23]  Craig Gentry,et al.  A fully homomorphic encryption scheme , 2009 .

[24]  Yan Huang,et al.  Practical MPC+FHE with Applications in Secure Multi-PartyNeural Network Evaluation , 2020, IACR Cryptol. ePrint Arch..

[25]  Marcel Keller,et al.  MASCOT: Faster Malicious Arithmetic Secure Computation with Oblivious Transfer , 2016, IACR Cryptol. ePrint Arch..

[26]  David Pisinger,et al.  Linear Time Algorithms for Knapsack Problems with Bounded Weights , 1999, J. Algorithms.

[27]  Jonathan Katz,et al.  Global-Scale Secure Multiparty Computation , 2017, CCS.

[28]  Feng Zhang,et al.  A Note on the Density of the Multiple Subset Sum Problems , 2011, IACR Cryptol. ePrint Arch..