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Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14085))

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Abstract

Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-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 a one-shot (i.e., single message) string oblivious transfer (OT) protocol with random receiver bit in the shared EPR pairs model, assuming the (sub-exponential) hardness of LWE.

    Building on this, we show that secure teleportation through quantum channels is possible. Specifically, given the description of any quantum operation Q, a sender with (quantum) input \(\rho \) can send a single classical message that securely transmits \(Q(\rho )\) to a receiver. That is, we realize an ideal quantum channel that takes input \(\rho \) from the sender and provably delivers \(Q(\rho )\) to the receiver without revealing any other information.

    This immediately gives a number of applications in the shared EPR pairs model: (1) non-interactive secure computation of unidirectional classical randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a non-interactive zero-knowledge state synthesis protocol.

  • Next, we construct a two-round (round-optimal) secure multiparty computation protocol for classical functionalities in the shared EPR pairs model that is unconditionally-secure in the (quantum-accessible) random oracle model.

Classically, both of these results cannot be obtained without some form of correlated randomness shared between the parties, and the only known approach is to have a trusted dealer set up random (string) OT correlations. In the quantum world, we show that shared EPR pairs (which are simple and can be deterministically generated) are sufficient. At the heart of our work are novel techniques for making use of entangling operations to generate string OT correlations, and for instantiating the Fiat-Shamir transform using correlation-intractability in the quantum setting.

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Notes

  1. 1.

    We will also allow for preserving entanglement that \(\rho \) may have with its environment, so technically we consider Q to map a state on Alice’s input register \(\mathcal{A}\) to a state on Bob’s output register \(\mathcal{B}\).

  2. 2.

    We use one-shot, one-message, and non-interactive interchangeably to refer to a protocol that consists of a single message from a sender to a receiver.

  3. 3.

    Note that it is impossible to obtain a one-shot protocol for fixed receiver bit OT, since Bob does not send any message.

  4. 4.

    In chosen-input OT, the receiver specifies their input bit b, and they receive the message \(m_b\). We contrast this with the notion of OT discussed above, where the receiver’s bit b is chosen uniformly at random.

  5. 5.

    In particular, any (even semi-honest) dealer that sets up OT correlations can learn the parties’ private inputs by observing the resulting transcript of communication, while this is not necessarily true of an EPR pair setup, by monogamy of entanglement. We also remark that obtaining OT correlations from any deterministically generated shared quantum state is non-trivial. In particular, if the parties shared a (deterministically generated) superposition over classical OT correlations, the receiver could simply decide not to measure the register holding their choice bit, and obtain a superposition over the sender’s strings, which violates the security of OT.

  6. 6.

    A followup work of [5] showed that, assuming ideal obfuscation, there exists a protocol over a bit OT channel with \(1/\textrm{poly}(\lambda )\) security.

  7. 7.

    Note that despite the existence of quantum key distribution [14], public-key infrastructure would still likely be required for the quantum internet, since QKD requires authenticated classical channels.

  8. 8.

    We do stress that our model assumes the EPR pairs are generated honestly, for example by an honest network administrator. Otherwise, such secure one-message protocols would be impossible to achieve.

  9. 9.

    We also remark that [12] achieve NIZK for QMA in the (incomparable) common reference string model, but they argue security using classical oracles, or alternatively assuming indistinguishability obfuscation and the non-black-box use of a hash function modeled as a random oracle.

  10. 10.

    In this setting, publicly-verifiable revocation [10] seems crucial to ensure that no one need know the classical description of the secret key.

  11. 11.

    Technically, the random coins used to compute the commitments must also be included in the witness.

  12. 12.

    Note that this step is not efficient to implement, but this will not be important for our arguments.

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Acknowledgments

D. Khurana was supported in part by NSF CAREER CNS-2238718 and NSF CNS-2247727, DARPA SIEVE. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. A. Srinivasan is supported in part by a SERB startup grant and Google India Research Award.

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Authors and Affiliations

  1. UC Berkeley, Berkeley, USA

    James Bartusek

  2. UIUC, Champaign, USA

    Dakshita Khurana

  3. Tata Institute of Fundamental Research, Mumbai, India

    Akshayaram Srinivasan

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    Helena Handschuh

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    Anna Lysyanskaya

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Bartusek, J., Khurana, D., Srinivasan, A. (2023). Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge). In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14085. Springer, Cham. https://doi.org/10.1007/978-3-031-38554-4_8

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