James Bartusek

We construct a publicly-verifiable non-interactive zero-knowledge argument system for QMA with the following properties of interest. - Transparent setup. Our protocol only requires a uniformly random string (URS) setup. The only prior publicly-verifiable NIZK for QMA (Bartusek and Malavolta, ITCS 2022) requires an *entire obfuscated program* as the common reference string. - Extractability. Valid QMA witnesses can be extracted directly from our accepting proofs. That is, we obtain a publicly-verifiable non-interactive argument of *quantum knowledge*, which was previously only known in a privately-verifiable setting (Coladangelo, Vidick, and Zhang, CRYPTO 2020). Our construction introduces a novel type of ZX QMA verifier with "strong completeness" and builds upon the coset state authentication scheme from (Bartusek, Brakerski, and Vaikuntanathan, STOC 2024) within the context of QMA verification. Along the way, we establish new properties of the authentication scheme. The security of our construction rests on the heuristic use of a post-quantum indistinguishability obfuscator. Rather than rely on the full-fledged classical oracle model (i.e. ideal obfuscation), we isolate a particular game-based property of the obfuscator that suffices for our proof, which we dub the *evasive composability* heuristic. As an additional contribution, we study a general method for replacing heuristic use of obfuscation with heuristic use of hash functions in the post-quantum setting. In particular, we establish security of the ideal obfuscation scheme of Jain, Lin, Luo, and Wichs (CRYPTO 2023) in the *quantum* pseudorandom oracle model (QPrO), which can be heuristically instantiated with a hash function. This gives us NIZK arguments of quantum knowledge for QMA in the QPrO, and additionally allows us to translate several quantum-cryptographic results that were only known in the classical oracle model to results in the QPrO.

A classical obfuscator for quantum circuits is a classical program that, given the classical description of a quantum circuit Q, outputs the classical description of a functionally equivalent quantum circuit Q' that hides as much as possible about Q. Previously, the only known feasibility result for classical obfuscation of quantum circuits (Bartusek and Malavolta, ITCS 2022) was limited to "nul" security, which is only meaningful for circuits that always reject. On the other hand, if the obfuscator is allowed to compile the quantum circuit Q into a quantum state |Q'>, there exist feasibility results for obfuscating much more expressive classes of circuits: All pseudo-deterministic quantum circuits (Bartusek, Kitagawa, Nishimaki and Yamakawa, STOC 2023, Bartusek, Brakerski and Vaikuntanathan, STOC 2024), and even all unitaries (Huang and Tang, FOCS 2025). We show that (relative to a classical oracle) there exists a classical obfuscator for all pseudo-deterministic quantum circuits. As our main technical step, we give the first construction of a compact quantum fully-homomorphic encryption (QFHE) scheme that supports public verification of (pseudo-deterministic) quantum evaluation, relative to a classical oracle. To construct our QFHE scheme, we improve on an approach introduced by Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023), which previously required ciphertexts that are both quantum and non-compact due to a heavy use of quantum coset states and their publicly-verifiable properties. As part of our core technical contribution, we introduce new techniques for analyzing coset states that can be generated "on the fly", by proving new cryptographic properties of the one-shot signature scheme of Shmueli and Zhandry (CRYPTO 2025). Our techniques allow us to produce QFHE ciphertexts that are purely classical, compact, and publicly-verifiable. This additionally yields the first classical verification of quantum computation protocol for BQP that simultaneously satisfies blindness and public-verifiability.

Secret sharing allows a user to split a secret into many shares so that the secret can be recovered if, and only if, an authorized set of shares is collected. Although secret sharing typically does not require any computational hardness assumptions, its security does require that an adversary cannot collect an authorized set of shares. Over long periods of time where an adversary can benefit from multiple data breaches, this may become an unrealistic assumption. We initiate the systematic study of secret sharing with certified deletion in order to achieve security even against an adversary that eventually collects an authorized set of shares. In secret sharing with certified deletion, a (classical) secret s is split into quantum shares that can be destroyed in a manner verifiable by the dealer. We put forth two natural definitions of security. No-signaling security roughly requires that if multiple non-communicating adversaries delete sufficiently many shares, then their combined view contains negligible information about s, even if the total set of corrupted parties forms an authorized set. Adaptive security requires privacy of s against an adversary that can continuously and adaptively corrupt new shares and delete previously-corrupted shares, as long as the total set of corrupted shares minus deleted shares remains unauthorized. Next, we show that these security definitions are achievable: we show how to construct (i) a secret sharing scheme with no-signaling certified deletion for any monotone access structure, and (ii) a threshold secret sharing scheme with adaptive certified deletion. Our first construction uses Bartusek and Khurana's (CRYPTO 2023) 2-out-of-2 secret sharing scheme with certified deletion as a building block, while our second construction is built from scratch and requires several new technical ideas. For example, we significantly generalize the ``XOR extractor'' of Agarwal, Bartusek, Khurana, and Kumar (EUROCRYPT 2023) in order to obtain better seedless extraction from certain quantum sources of entropy, and show how polynomial interpolation can double as a high-rate randomness extractor in our context of threshold sharing with certified deletion.

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 {\em 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 \emph{classical} randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a non-interactive \emph{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 \emph{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.

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 \emph{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 \emph{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 \emph{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.

We build quantum cryptosystems that support publicly-verifiable deletion from standard cryptographic assumptions. We introduce target-collapsing as a weakening of collapsing for hash functions, analogous to how second preimage resistance weakens collision resistance; that is, target-collapsing requires indistinguishability between superpositions and mixtures of preimages of an honestly sampled image. We show that target-collapsing hashes enable publicly-verifiable deletion ($\PVD$), proving conjectures from [Poremba, ITCS'23] and demonstrating that the Dual-Regev encryption (and corresponding fully homomorphic encryption) schemes support $\PVD$ under the LWE assumption. We further build on this framework to obtain a variety of primitives supporting publicly-verifiable deletion from weak cryptographic assumptions, including: - Commitments with $\PVD$ assuming the existence of injective one-way functions, or more generally, {\em almost-regular} one-way functions. Along the way, we demonstrate that (variants of) target-collapsing hashes can be built from almost-regular one-way functions. - Public-key encryption with $\PVD$ assuming trapdoored variants of injective (or almost-regular) one-way functions. We also demonstrate that the encryption scheme of [Hhan, Morimae, and Yamakawa, Eurocrypt'23] based on pseudorandom group actions has $\PVD$. - $X$ with $\PVD$ for $X \in \{$attribute-based encryption, quantum fully-homomorphic encryption, witness encryption, time-revocable encryption$\}$, assuming $X$ and trapdoored variants of injective (or almost-regular) one-way functions.

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-NIZKs for QMA that only require one copy of the 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.

Abstract MiniQCrypt is a world where quantum-secure one-way functions exist, and quantum communication is possible. We construct an oblivious transfer (OT) protocol in MiniQCrypt that achieves simulation-security against malicious quantum polynomial-time adversaries, building on the foundational work of Bennett, Brassard, Crépeau and Skubiszewska (CRYPTO 1991). Combining the OT protocol with prior works, we obtain secure two-party and multi-party computation protocols also in MiniQCrypt. This is in contrast to the classical world, where it is widely believed that one-way functions alone do not give us OT.

Abstract We investigate the round complexity of maliciously-secure two-party quantum computation (2PQC) with setup, and obtain the following results: - A three-message protocol (two-message if only one party receives output) in the common random string (CRS) model assuming classical two-message oblivious transfer (OT) with post-quantum malicious security. This round complexity is optimal for the sequential communication setting. Under the additional assumption of reusable malicious designated-verifier non-interactive zero-knowledge (MDV-NIZK) arguments for NP, our techniques give an MDV-NIZK for QMA. Each of the assumptions mentioned above is known from the quantum hardness of learning with errors (QLWE). - A protocol with two simultaneous rounds of communication, in a quantum preprocessing model, assuming sub-exponential QLWE. In fact, we construct a three-round protocol in the CRS model with only two rounds of online communication, which implies the above result. Along the way, we develop a new delayed simulation technique that we call simulation via teleportation, which may be useful in other settings. In addition, we perform a preliminary investigation into barriers and possible approaches for two round 2PQC in the CRS model, including an impossibility result for a natural class of simulators, and a proof-of-concept construction from a strong form of quantum virtual black-box (VBB) obfuscation. Prior to our work, maliciously-secure 2PQC required round complexity linear in the size of the quantum circuit.