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Overdrive2k: Efficient Secure MPC over \(\mathbb {Z}_{2^k}\) from Somewhat Homomorphic Encryption

  • Emmanuela Orsini
  • Nigel P. SmartEmail author
  • Frederik Vercauteren
Conference paper
  • 151 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12006)

Abstract

Recently, Cramer et al. (CRYPTO 2018) presented a protocol, \(\mathsf {SPDZ2k}\), for actively secure multiparty computation for dishonest majority in the pre-processing model over the ring \(\mathbb {Z}_{2^k}\), instead of over a prime field \(\mathbb {F}_p\). Their technique used oblivious transfer for the pre-processing phase, more specifically the MASCOT protocol (Keller et al. CCS 2016). In this paper we describe a more efficient technique for secure multiparty computation over \(\mathbb {Z}_{2^k}\) based on somewhat homomorphic encryption. In particular we adapt the Overdrive approach (Keller et al. EUROCRYPT 2018) to obtain a protocol which is more like the original SPDZ protocol (Damgård et al. CRYPTO 2012). To accomplish this we introduce a special packing technique for the BGV encryption scheme operating on the plaintext space defined by the \(\mathsf {SPDZ2k}\) protocol, extending the ciphertext packing method used in SPDZ to the case of \(\mathbb {Z}_{2^k}\). We also present a more complete pre-processing phase for secure computation modulo \(2^k\) by adding a new technique to produce shared random bits.

Notes

Acknowledgments

We thank Cyprien Delpech de Saint Guilhem for many helpful discussions. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070, and by the FWO under an Odysseus project GOH9718N.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.imec-COSICKU LeuvenLeuvenBelgium
  2. 2.University of BristolBristolUK

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