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A New Framework for Quantum Oblivious Transfer

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Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14004))

Abstract

We present a new template for building oblivious transfer from quantum information that we call the “fixed basis” framework. Our framework departs from prior work (e.g., Crepeau and Kilian, FOCS’88) by fixing the correct choice of measurement basis used by each player, except for some hidden trap qubits that are intentionally measured in a conjugate basis. We instantiate this template in the quantum random oracle model (QROM) to obtain simple protocols that implement, with security against malicious adversaries:

  • Non-interactive random-input bit OT in a model where parties share EPR pairs a priori.

  • Two-round random-input bit OT without setup, obtained by showing that the protocol above remains secure even if the (potentially malicious) OT receiver sets up the EPR pairs.

  • Three-round chosen-input string OT from BB84 states without entanglement or setup. This improves upon natural variations of the CK88 template that require at least five rounds.

Along the way, we develop technical tools that may be of independent interest. We prove that natural functions like XOR enable seedless randomness extraction from certain quantum sources of entropy. We also use idealized (i.e. extractable and equivocal) bit commitments, which we obtain by proving security of simple and efficient constructions in the QROM.

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Notes

  1. 1.

    We use the terms"one-shot", "one-message", and "non-interactive" interchangably in this work, all referring to a protocol between two parties Alice and Bob that consists only of a single message from Alice to Bob.

  2. 2.

    While this framing of the problem is different from the previous page, the two turn out to be equivalent thanks to OT reversal and reorientation methods [36].

  3. 3.

    Here non-trivial quantum OT means OT based on assumptions (such as symmetric-key cryptography) or ideal models that are not known to imply classical OT.

  4. 4.

    Another line of work studies (unconditional) oblivious transfer with imperfect security [17, 18, 45], which we view as largely orthogonal to our work.

  5. 5.

    Our actual protocol involves an additional step that allows Alice to program any input \(m_b\) of her choice, but we suppress this detail in this overview.

  6. 6.

    One idea would be to sample the seed s as part of the output of the random oracle. However, this does not ensure that s is uniformly random. For example Alice could bias certain bits of s by choosing her commitments in a certain way.

  7. 7.

    For example, consider an adversary that, via a single superposition query to the random oracle, sets register \(\mathcal{B}\) to be a superposition over all x such that the first bit of \(\textsf{RO}(x)\) is 0. Then, measuring \(\mathcal{B}\) in the computational basis will result in an x with high min-entropy, but where \(\textsf{RO}(x)\) is distinguishable from a uniformly random r.

  8. 8.

    Technically, one party prepares and the other measures BB84 states.

  9. 9.

    That is, consider sampling H, running a purified \(A_1^H\), measuring at the end to obtain \((T,\{x_i\}_{i \in T})\), and then defining \(|\gamma \rangle \) to be the left-over state on \(\mathcal{A}\)’s remaining registers.

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Acknowledgments

A. Agarwal, D. Khurana and N. Kumar were supported in part by by NSF CNS-2238718, DARPA SIEVE and a gift from Visa Research. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024.

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  1. University of Illinois Urbana-Champaign, Champaign, USA

    Amit Agarwal, Dakshita Khurana & Nishant Kumar

  2. University of California Berkeley, Berkeley, USA

    James Bartusek

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Agarwal, A., Bartusek, J., Khurana, D., Kumar, N. (2023). A New Framework for Quantum Oblivious Transfer. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14004. Springer, Cham. https://doi.org/10.1007/978-3-031-30545-0_13

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