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Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)
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| Conference: | CRYPTO 2023 |
| Abstract: | Can a sender non-interactively transmit one of two strings to a receiver without knowing which was received? Does there exist minimally-interactive secure computation without the use of public-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource. - First, we construct one-shot string oblivious transfer (OT) in the shared EPR pair model, assuming the sub-exponential hardness of LWE. Building on this, we show that {\em secure teleportation} is possible: Given the description of any quantum operation $Q$, a sender with input $\rho$ can send a single classical message that securely transmits $Q(\rho)$ to a receiver. That is, we realize an ideal channel that takes input $\rho$ from the sender and provably delivers $Q(\rho)$ to the receiver without revealing any other information, achieving one-shot secure computation of unidirectional quantum functionalities in the shared EPR pair model. This immediately gives a number of applications in the shared EPR pair model: (1) We obtain one-shot secure computation of unidirectional \emph{classical} functionalities, (2) We obtain the first construction of NIZK for QMA from (sub-exponential) standard assumptions, and (3) We define a notion of \emph{zero-knowledge} state synthesis, and show that it can be achieved with one message. - Next, we investigate general-purpose secure \emph{multiparty} computation in the shared EPR pair model. Here, we obtain a (round-optimal) two-round protocol for secure computation of classical functionalities that is \emph{unconditionally-secure} in the (quantum-accessible) random oracle model. We also obtain a two-round protocol without random oracles assuming (non-interactive) extractable commitments and correlation-intractability for efficient functions. At the heart of our approach are novel techniques for making use of entangling operations to generate multibit OT correlations, and for instantiating the Fiat-Shamir transform using correlation-intractability in the quantum setting. |
BibTeX
@inproceedings{crypto-2023-33103,
title={Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)},
publisher={Springer-Verlag},
doi={10.1007/978-3-031-38554-4_8},
author={James Bartusek and Dakshita Khurana and Akshayaram Srinivasan},
year=2023
}