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arXiv:2609.38894

Quantum Time-Lock Puzzles in the Quantum Random Oracle Model

Prabhanjan Ananth, Yao-Ting Lin

quant-phcs.CRSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations
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Abstract

A time-lock puzzle allows a sender to hide a message in a puzzle such that recovering the message requires substantially more sequential computation than the time required to generate the puzzle, even when parallel computation is allowed. Applications of time-lock puzzles include timed-release encryption, sealed-bid auctions, electronic voting, fair contract signing, coin flipping, and Byzantine consensus. However, time-lock puzzles are known to be impossible in the classical random oracle model. To overcome the classical barrier, in this work we consider quantum time-lock puzzles, in which the puzzle itself is a quantum state. Our construction in the quantum random oracle model achieves generation in one oracle round, solving in at most $T$ oracle rounds, and security against polynomial-width quantum adversaries of depth $o(T)$ for every polynomially bounded delay $T=T(λ)$, resolving an open problem posed by Mahmoody, Moran, and Vadhan (2011).

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A time-lock puzzle allows a sender to hide a message in a puzzle such that recovering the message requires substantially more sequential computation than the time required to generate the puzzle, even when parallel computation is allowed. Applications of time-lock puzzles include timed-release encryption, sealed-bid auctions, electronic voting, fair contract signing, coin flipping, and Byzantine consensus. However, time-lock puzzles are known to be impossible in the classical random oracle model.
To overcome the classical barrier, in this work we consider quantum time-lock puzzles, in which the puzzle itself is a quantum state. Our construction in the quantum random oracle model achieves generation in one oracle round, solving in at most TTT oracle rounds, and security against polynomial-width quantum adversaries of depth o(T)o(T)o(T) for every polynomially bounded delay T=T(λ)T=T(λ)T=T(λ), resolving an open problem posed by Mahmoody, Moran, and Vadhan (2011).
We construct simulation-secure one-time memories (OTM) in the random oracle model, and present a plausible argument for their security against quantum adversaries with bounded and adaptive depth. Our contributions include: (1) A simple scheme where we use only single-qubit Wiesner states and conjunction obfuscation (constructible from LPN): no complex entanglement or quantum cryptography is required. (2) A new POVM bound where e prove that any measurement achieving (1−ε)(1 - ε)(1−ε) success on one basis has conjugate-basis guessing probability at most 12m+O(ε14)\frac{1}{2m} + O(ε^\frac{1}{4})2m1​+O(ε41​). (3) Simultation-secure OTMs in the quantum random oracle model where an adversary can only query the random oracle classically. (4) Adaptive depth security where, via an informal application of a lifting theorem from Arora et al., we conjecture security against adversaries with polynomial quantum circuit depth between random oracle queries. Security against adaptive, depth-bounded, quantum adversaries captures many realistic attacks on OTMs built from single-qubit states; our work thus paves the way for practical and truly secure one-time programs. Moreover, depth bounded adaptive adversarial models may allow for encoding one-time memories into error corrected memory states, opening the door to implementations of one-time programs which persist for long periods of time.
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Timed-release encryption is a kind of encryption scheme in which a recipient can decrypt only after a specified amount of time T (assuming that we have a moderately precise estimate of his computing power). A revocable timed-release encryption is one where, before the time T is over, the sender can “give back” the timed-release encryption, provably loosing all access to the data. We show that revocable timed-release encryption without trusted parties is possible using quantum cryptography (while trivially impossible classically). Along the way, we develop two proof techniques in the quantum random oracle model that we believe may have applications also for other protocols. Finally, we also develop another new primitive, unknown recipient encryption , which allows us to send a message to an unknown/unspecified recipient over an insecure network in such a way that at most one recipient will get the message.
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Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows: 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs). 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys. 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model. Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.
Quantum information is well-known to achieve cryptographic feats that are unattainable using classical information alone. Here, we add to this repertoire by introducing a new cryptographic functionality called uncloneable encryption. This functionality allows the encryption of a classical message such that two collaborating but isolated adversaries are prevented from simultaneously recovering the message, even when the encryption key is revealed. Clearly, such functionality is unattainable using classical information alone. We formally define uncloneable encryption, and show how to achieve it using Wiesner's conjugate coding, combined with a quantum-secure pseudorandom function (qPRF). Modelling the qPRF as a quantum random oracle, we show security by adapting techniques from the quantum one-way-to-hiding lemma, as well as using bounds from quantum monogamy-of-entanglement games.