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Paper: Promise Zero Knowledge and Its Applications to Round Optimal MPC

Authors:
Saikrishna Badrinarayanan
Vipul Goyal
Abhishek Jain
Yael Tauman Kalai
Dakshita Khurana
Amit Sahai
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DOI: 10.1007/978-3-319-96881-0_16
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Conference: CRYPTO 2018
Abstract: We devise a new partitioned simulation technique for MPC where the simulator uses different strategies for simulating the view of aborting adversaries and non-aborting adversaries. The protagonist of this technique is a new notion of promise zero knowledge (ZK) where the ZK property only holds against non-aborting verifiers. We show how to realize promise ZK in three rounds in the simultaneous-message model assuming polynomially hard DDH (or QR or N$$^{th}$$-Residuosity).We demonstrate the following applications of our new technique:We construct the first round-optimal (i.e., four round) MPC protocol for general functions based on polynomially hard DDH (or QR or N$$^{th}$$-Residuosity).We further show how to overcome the four-round barrier for MPC by constructing a three-round protocol for “list coin-tossing” – a slight relaxation of coin-tossing that suffices for most conceivable applications – based on polynomially hard DDH (or QR or N$$^{th}$$-Residuosity). This result generalizes to randomized input-less functionalities. Previously, four round MPC protocols required sub-exponential-time hardness assumptions and no multi-party three-round protocols were known for any relaxed security notions with polynomial-time simulation against malicious adversaries.In order to base security on polynomial-time standard assumptions, we also rely upon a leveled rewinding security technique that can be viewed as a polynomial-time alternative to leveled complexity leveraging for achieving “non-malleability” across different primitives.
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BibTeX
@inproceedings{crypto-2018-28821,
  title={Promise Zero Knowledge and Its Applications to Round Optimal MPC},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10992},
  pages={459-487},
  doi={10.1007/978-3-319-96881-0_16},
  author={Saikrishna Badrinarayanan and Vipul Goyal and Abhishek Jain and Yael Tauman Kalai and Dakshita Khurana and Amit Sahai},
  year=2018
}