Hidden Cosets and Applications to Unclonable Cryptography 📺
In 2012, Aaronson and Christiano introduced the idea of hidden subspace states to build public-key quantum money [STOC '12]. Since then, this idea has been applied to realize several other cryptographic primitives which enjoy some form of unclonability. In this work, we propose a generalization of hidden subspace states to hidden coset states. We study different unclonable properties of coset states and several applications: * We show that, assuming indistinguishability obfuscation (iO), hidden coset states possess a certain direct product hardness property, which immediately implies a tokenized signature scheme in the plain model. Previously, a tokenized signature scheme was known only relative to an oracle, from a work of Ben-David and Sattath [QCrypt '17]. * Combining a tokenized signature scheme with extractable witness encryption, we give a construction of an unclonable decryption scheme in the plain model. The latter primitive was recently proposed by Georgiou and Zhandry [ePrint '20], who gave a construction relative to a classical oracle. * We conjecture that coset states satisfy a certain natural monogamy-of-entanglement property. Assuming this conjecture is true, we remove the requirement for extractable witness encryption in our unclonable decryption construction. As potential evidence in support of the conjecture, we prove a weaker version of this monogamy property, which we believe will still be of independent interest. * Finally, we give the first construction of a copy-protection scheme for pseudorandom functions (PRFs) in the plain model. Our scheme is secure either assuming iO and extractable witness encryption, or iO, LWE and the conjectured monogamy property mentioned above. This is the first example of a copy-protection scheme with provable security in the plain model for a class of functions that is not evasive.
One-Way Functions Imply Secure Computation in a Quantum World 📺
We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Crépeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure quantum oblivious transfer.
On the Round Complexity of Secure Quantum Computation 📺
We construct the first constant-round protocols for secure quantum computation in the two-party (2PQC) and multi-party (MPQC) settings with security against malicious adversaries. Our protocols are in the common random string (CRS) model. - Assuming two-message oblivious transfer (OT), we obtain (i) three-message 2PQC, and (ii) five-round MPQC with only three rounds of online (input-dependent) communication; such OT is known from quantum-hard Learning with Errors (QLWE). - Assuming sub-exponential hardness of QLWE, we obtain (i) three-round 2PQC with two online rounds and (ii) four-round MPQC with two online rounds. - When only one (out of two) parties receives output, we achieve minimal interaction (two messages) from two-message OT; classically, such protocols are known as non-interactive secure computation (NISC), and our result constitutes the first maliciously-secure quantum NISC. Additionally assuming reusable malicious designated-verifier NIZK arguments for NP (MDV-NIZKs), we give the first MDV-NIZK for QMA that only requires one copy of the quantum witness. Finally, we perform a preliminary investigation into two-round secure quantum computation where each party must obtain output. On the negative side, we identify a broad class of simulation strategies that suffice for classical two-round secure computation that are unlikely to work in the quantum setting. Next, as a proof-of-concept, we show that two-round secure quantum computation exists with respect to a quantum oracle.
Non-Interactive Zero-Knowledge Arguments for QMA, with preprocessing 📺
We initiate the study of non-interactive zero-knowledge (NIZK) arguments for languages in QMA. Our first main result is the following: if Learning With Errors (LWE) is hard for quantum computers, then any language in QMA has an NIZK argument with preprocessing. The preprocessing in our argument system consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from verifier to prover. The instance-dependent phase of our argument system involves only a single classical message from prover to verifier. Importantly, verification in our protocol is entirely classical, and the verifier needs not have quantum memory; its only quantum actions are in the preprocessing phase. Our second contribution is to extend the notion of a classical proof of knowledge to the quantum setting. We introduce the notions of arguments and proofs of quantum knowledge (AoQK/PoQK), and we show that our non-interactive argument system satisfies the definition of an AoQK. In particular, we explicitly construct an extractor which can recover a quantum witness from any prover which is successful in our protocol. Finally, we show that any language in QMA has an (interactive) proof of quantum knowledge.
Verifier-on-a-Leash: New Schemes for Verifiable Delegated Quantum Computation, with Quasilinear Resources 📺
The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as $$O(g\log g)$$ for delegating a circuit of size g. This is in contrast to previous protocols, whose overhead in terms of resources employed, while polynomial, is far beyond what is feasible in practice. Our first protocol requires a number of rounds that is linear in the depth of the circuit being delegated, and is blind, meaning neither prover can learn the circuit or its input. The second protocol is not blind, but requires only a constant number of rounds of interaction.Our main technical innovation is an efficient rigidity theorem which allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of single-qubit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m. Our two-prover classical-verifier delegation protocols are obtained by combining this rigidity theorem with a single-prover quantum-verifier protocol for the verifiable delegation of a quantum computation, introduced by Broadbent.