Physical Time-Lock Puzzles

Abstract

Traditional time-lock puzzles enforce delayed access to encrypted secrets by relying on inherently sequential computational steps. However, since software-based constructions impose no fundamental bound on the physical execution speed of individual steps, they remain vulnerable to hardware acceleration and improved implementations. In practice, this renders existing schemes ``step-lock'' rather than true ``time-lock'' puzzles, making long-term delay guarantees highly speculative against decades of unpredictable hardware advancement. To address this fundamental limitation, we introduce the Physical Time-Lock Puzzle (P-TLP), a new paradigm that anchors solving delay directly to the intrinsic, hardware-bounded evaluation latency of silicon hardware. By leveraging noisy Physical Unclonable Functions (PUFs) as non-parallelizable delay oracles, P-TLPs establish resistance against both parallel computation and algorithmic acceleration under the random oracle model. To tolerate PUF evaluation noise while maintaining a tightly concentrated and predictable solving-delay window, we propose a composite puzzle architecture that combines multiple independent basic puzzles. We formally prove the optimality of a sequential greedy solving strategy and derive tightly concentrated solving-delay windows using Hoeffding and Berry-Esseen bounds. We additionally prove early-solve hardness, establishing that adversaries with substantial classical computation budgets cannot bypass the physically-enforced PUF evaluation bottleneck. We validate our theoretical analysis with an FPGA prototype built around a configurable Ring Oscillator PUF, confirming that our analytical delay predictions tightly match empirical measurements. Our results demonstrate that P-TLPs can deliver highly predictable, long-term delay guarantees, enabling practical deployment in high-value applications such as digital legacy management.