Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States

Léo Colisson; Garazi Muguruza; Florian Speelman

Paper 2023/311

Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States

Léo Colisson

, Centrum Wiskunde & Informatica

Garazi Muguruza, University of Amsterdam

Florian Speelman

, University of Amsterdam

Abstract

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT. At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way, without public-key primitives, and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.

Note: Full version of the article published in ASIACRYPT 2023. We added notably more motivations regarding ZKoQS, and we corrected a minor mistake.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: A minor revision of an IACR publication in ASIACRYPT 2023
Keywords: Quantum Cryptography Oblivious Transfer Zero-Knowledge on Quantum States Multi-Party Computing Zero-Knowledge
Contact author(s): leo colisson @ cwi nl
g muguruza @ uva nl
f speelman @ uva nl
History: 2023-10-12: revised; 2023-03-02: received; See all versions
Short URL: https://ia.cr/2023/311
License: CC BY

BibTeX

@misc{cryptoeprint:2023/311,
      author = {Léo Colisson and Garazi Muguruza and Florian Speelman},
      title = {Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/311},
      year = {2023},
      url = {https://eprint.iacr.org/2023/311}
}