Quantum Time-Lock Puzzles in the Quantum Random Oracle Model

2026-09-29

AI Summary

This study addresses the long-standing open problem posed by Mahmoody et al. regarding the impossibility of time-lock puzzles in the classical random oracle model. To overcome this barrier, this work proposes quantum state-based time-lock puzzles and constructs a secure mechanism within the quantum random oracle model. By leveraging quantum computing techniques and sequential depth analysis, it achieves the first breakthrough beyond classical theoretical limitations. The resulting construction enables efficient single-round generation and at-most-T-round solving while provably defending against polynomial-width quantum adversaries. This work resolves the aforementioned open problem and establishes the first viable theoretical foundation and security paradigm for time-delay mechanisms in post-quantum cryptography.

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).

Problem

• Quantum Time-Lock Puzzles
• Quantum Random Oracle Model
• Sequential Computation
• Timed-Release Cryptography

Innovation

• Quantum Time-Lock Puzzles
• Quantum Random Oracle Model
• Sequential Computation
• Quantum Adversaries
• Time-Delay Cryptography