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arxiv: 2604.23516 · v1 · submitted 2026-04-26 · 💻 cs.CR

Recognition: unknown

Time-Delayed Publicly Verifiable Quantum Computation for Classical Verifiers

Ameer Mohammed , Aydin Abadi , Jaffer Mahdi
Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:02 UTC · model grok-4.3

classification 💻 cs.CR
keywords quantum computationpublicly verifiabletime-lock puzzlesdelegated computationnon-interactive proofspost-quantum cryptographyquantum random oracle model
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The pith

A classical verifier outsources quantum computation and receives a publicly checkable result after a built-in time delay enforced by time-lock puzzles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that time-delayed public verification of quantum computations is achievable non-interactively for classical users by compiling existing 2-round private verification protocols with commitment schemes and time-lock puzzles. This approach outsources not only the quantum circuit evaluation but also the solving of the time-lock puzzle to the prover, ensuring that the verification key becomes public only after the computation is guaranteed complete. A sympathetic reader would care because it sidesteps the need for impractical cryptographic tools like indistinguishability obfuscation while relying on standard post-quantum assumptions and the quantum random oracle model. The result enables any party to verify the outcome without requiring quantum capabilities or real-time interaction.

Core claim

By wrapping a 2-round privately verifiable quantum computation scheme inside commitments and time-lock puzzles, the protocol produces timestamped proofs whose verification keys are released publicly only after a sufficient delay, allowing classical verifiers to confirm the correctness of outsourced quantum tasks under post-quantum assumptions in the quantum random oracle model with a common reference string.

What carries the argument

Time-lock puzzles that delay the public release of the verification key while committing to the proof, which converts the private 2-round interaction into a non-interactive public one with enforced timing.

If this is right

  • The protocol allows outsourcing of quantum computation along with the time-lock puzzle solution to a single quantum prover.
  • Security is established against quantum adversaries assuming standard post-quantum properties of the underlying primitives.
  • Timestamped proofs become possible for quantum computation results without additional trusted setup beyond a common reference string.
  • Verification can be performed by any classical party once the delay period has passed and the key is public.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such time-delayed verification might support applications where premature result checking must be prevented, such as in sequential decision processes.
  • The approach could be adapted to other resource-intensive computations where timing guarantees are valuable.
  • Future work might explore reducing the delay parameter or combining with blockchain timestamps for the proofs.

Load-bearing premise

That 2-round privately verifiable quantum computation schemes can be securely combined with time-lock puzzles without creating new quantum attacks or undermining the time-delay guarantee, and that these puzzles admit efficient realizations under post-quantum assumptions.

What would settle it

Demonstration of a quantum algorithm that solves the time-lock puzzle and extracts the verification key in less time than the intended delay, or construction of a valid-looking proof that passes verification without correctly executing the quantum circuit.

Figures

Figures reproduced from arXiv: 2604.23516 by Ameer Mohammed, Aydin Abadi, Jaffer Mahdi.

Figure 1
Figure 1. Figure 1: A simplified diagram illustrating the high-level view at source ↗
Figure 3
Figure 3. Figure 3: Outline of the post-quantum PV-CVQC protocol. view at source ↗
Figure 2
Figure 2. Figure 2: The Time-Delayed PV-CVQC Protocol in the QROM view at source ↗
Figure 4
Figure 4. Figure 4: (a) Circuit depth scaling with matrix size, showing a linear relationship between the two. (b) The average running time view at source ↗
read the original abstract

Publicly verifiable delegation is a well-known problem involving a user who wishes to outsource a resource-intensive computational task to a more powerful but potentially untrusted server such that any other party is able to efficiently check the veracity of the computation's result. This problem has been extensively studied in the classical domain where the user and server are both non-quantum machines. However, the problem becomes more challenging when the classical user wants to delegate a quantum circuit to a single prover with quantum-computing capabilities. Previous solutions have resorted to using impractical or non-standard cryptographic solutions (e.g. indistinguishability obfuscation) to achieve this requirement. In this work, we relax the requirement to have time-delayed publicly verifiable proofs, where the verification key is made known to the public only when the computation (and its proof) are guaranteed to have been completed. We propose a practical non-interactive scheme leveraging commitment schemes and time-lock puzzles, which can be efficiently realized through well-established and standard post-quantum assumptions. The main idea of our technique lies in using time-lock puzzles to compile a 2-round privately verifiable scheme into a non-interactive publicly verifiable scheme with timestamped proofs, outsourcing not only the quantum computation but the puzzle solving as well. Security is proven in the quantum random oracle model with a common reference string (CRS).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to solve the problem of publicly verifiable delegation of quantum circuits to a quantum prover by a classical user, by introducing a time-delayed non-interactive scheme. It leverages commitment schemes and time-lock puzzles to convert 2-round privately verifiable quantum computation protocols into publicly verifiable ones, where the verification key is released only after the computation is guaranteed to be completed via the time-lock. The scheme is practical under standard post-quantum assumptions, and security is proven in the quantum random oracle model with a common reference string (CRS).

Significance. If the central security claim holds, this work would offer a practical advancement in verifiable quantum computation by avoiding impractical primitives like indistinguishability obfuscation. By outsourcing puzzle solving as well and using time delays for timestamping, it enables public verification after a guaranteed period. The use of the quantum random oracle model and CRS with standard assumptions is a positive aspect, potentially making it more feasible for real-world applications in quantum cloud services.

major comments (2)
  1. The security reduction for compiling 2-round privately verifiable schemes via time-lock puzzles must explicitly address quantum superposition queries to the TLP and the interaction with the delegated quantum circuit (as required for the non-interactivity and time-delay guarantee). The abstract asserts a QROM+CRS proof, but without detailed lemmas showing that no new quantum attacks allow forgery before the puzzle deadline, the central claim cannot be verified.
  2. The weakest assumption—that existing 2-round private schemes compile securely without violating the time-delay against quantum adversaries—requires a concrete theorem and reduction in the construction section. The manuscript should state the specific post-quantum assumptions for efficient TLP realization and prove sequential hardness is preserved.
minor comments (1)
  1. The abstract refers to 'well-established and standard post-quantum assumptions' without naming them; this should be clarified with explicit references in the introduction or preliminaries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important aspects of the security argument that require clearer exposition. We address each major comment below and will incorporate the suggested clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: The security reduction for compiling 2-round privately verifiable schemes via time-lock puzzles must explicitly address quantum superposition queries to the TLP and the interaction with the delegated quantum circuit (as required for the non-interactivity and time-delay guarantee). The abstract asserts a QROM+CRS proof, but without detailed lemmas showing that no new quantum attacks allow forgery before the puzzle deadline, the central claim cannot be verified.

    Authors: We agree that the high-level security sketch in the current version does not contain the full sequence of lemmas needed to handle quantum superposition queries to the time-lock puzzle. In the revised manuscript we will add a new subsection to the security proof that presents an explicit quantum reduction. The reduction will simulate the private verifier while answering superposition TLP queries via the quantum random oracle, and will prove that any forgery before the deadline contradicts the sequential hardness of the underlying TLP. The interaction between the delegated quantum circuit and the TLP is modeled by treating circuit outputs as additional oracle inputs; this preserves the time-delay guarantee because the reduction aborts on early extraction attempts. We will also state the precise QROM+CRS assumptions under which the reduction holds. revision: yes

  2. Referee: The weakest assumption—that existing 2-round private schemes compile securely without violating the time-delay against quantum adversaries—requires a concrete theorem and reduction in the construction section. The manuscript should state the specific post-quantum assumptions for efficient TLP realization and prove sequential hardness is preserved.

    Authors: We accept that a standalone theorem is required. The revised construction section will contain a new theorem (Theorem 4.3) that states: under the post-quantum sequential hardness of the TLP (realized via standard lattice-based or hash-based assumptions in the QROM), the compilation of any 2-round privately verifiable protocol yields a time-delayed publicly verifiable scheme. The proof will show that sequential hardness is preserved because any quantum adversary that solves the puzzle in parallel time less than the delay can be used to break the underlying TLP hardness assumption via a black-box reduction that rewinds the quantum oracle queries. We will explicitly list the concrete post-quantum assumptions (e.g., the quantum hardness of the short-integer-solution problem or the quantum random-oracle hardness of iterated hashing) and include the corresponding reduction. revision: yes

Circularity Check

0 steps flagged

No circularity: construction uses external primitives and QROM proof

full rationale

The paper constructs a non-interactive time-delayed publicly verifiable quantum computation scheme by compiling 2-round privately verifiable protocols via commitment schemes and time-lock puzzles under standard post-quantum assumptions, with security proven in the quantum random oracle model plus CRS. No load-bearing step reduces by definition, fitted input, or self-citation chain to the target result itself; the derivation depends on independent cryptographic building blocks and an external security model rather than internal renaming or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The scheme rests on standard post-quantum cryptographic assumptions for commitments and time-lock puzzles plus the existence of a secure 2-round private verification protocol; no new free parameters or invented entities are introduced at the abstract level.

axioms (3)
  • domain assumption Secure commitment schemes exist under post-quantum assumptions
    Used to create binding proofs that can be opened after the time delay.
  • domain assumption Time-lock puzzles exist that are hard to solve before a set time but easy afterward under post-quantum assumptions
    Central to delaying public release of the verification key.
  • domain assumption A 2-round privately verifiable quantum computation scheme exists that can be securely compiled
    The base protocol being transformed into the public non-interactive version.

pith-pipeline@v0.9.0 · 5538 in / 1551 out tokens · 63386 ms · 2026-05-08T06:02:47.303465+00:00 · methodology

discussion (0)

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Reference graph

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