### Obfuscation of Pseudo-Deterministic Quantum Circuits

##### Abstract

We show how to obfuscate pseudo-deterministic quantum circuits, assuming the quantum hardness of learning with errors (QLWE) and post-quantum virtual black-box (VBB) obfuscation for classical circuits. Given the classical description of a quantum circuit $Q$, our obfuscator outputs a quantum state $\ket{\widetilde{Q}}$ that can be used to evaluate $Q$ repeatedly on arbitrary inputs. Instantiating the VBB obfuscator for classical circuits with any candidate post-quantum indistinguishability obfuscator gives us the first candidate construction of indistinguishability obfuscation for all polynomial-size pseudo-deterministic quantum circuits. In particular, our scheme is the first candidate obfuscator for a class of circuits that is powerful enough to implement Shor's algorithm (SICOMP 1997). Our approach follows Bartusek and Malavolta (ITCS 2022), who obfuscate null quantum circuits by obfuscating the verifier of an appropriate classical verification of quantum computation (CVQC) scheme. We go beyond null circuits by constructing a publicly-verifiable CVQC scheme for quantum partitioning circuits, which can be used to verify the evaluation procedure of Mahadev's quantum fully-homomorphic encryption scheme (FOCS 2018). We achieve this by upgrading the one-time secure scheme of Bartusek (TCC 2021) to a fully reusable scheme, via a publicly-decodable Pauli functional commitment, which we formally define and construct in this work. This commitment scheme, which satisfies a notion of binding against committers that can access the receiver's standard and Hadamard basis decoding functionalities, is constructed by building on techniques of Amos, Georgiou, Kiayias, and Zhandry (STOC 2020) introduced in the context of equivocal but collision-resistant hash functions.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. STOC 2023
Keywords
ObfuscationCVQC
Contact author(s)
bartusek james @ gmail com
fuyuki kitagawa yh @ hco ntt co jp
ryo nishimaki zk @ hco ntt co jp
takashi yamakawa ga @ hco ntt co jp
History
2023-02-22: approved
See all versions
Short URL
https://ia.cr/2023/252

CC0

BibTeX

@misc{cryptoeprint:2023/252,
author = {James Bartusek and Fuyuki Kitagawa and Ryo Nishimaki and Takashi Yamakawa},
title = {Obfuscation of Pseudo-Deterministic Quantum Circuits},
howpublished = {Cryptology ePrint Archive, Paper 2023/252},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/252}},
url = {https://eprint.iacr.org/2023/252}
}
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