Practical Verifiable Time-Lock Puzzle: Pre- and Post-Solution Verification

A time-lock puzzle encapsulates a secret message such that the receiver needs to perform a sequential computation, which takes a specified amount of time, to recover the message. Time-lock puzzles can be used in various scenarios, such as sealed-bid auctions, fair contract signing, and so on. The time required to generate a time-lock puzzle and the time needed to solve it are asymmetric, making the verification of a time-lock puzzle crucial. Before solving the puzzle, the solver needs to verify the validity of the puzzle to avoid computing invalid time-lock puzzles. After the puzzle has been solved, it is essential for a third party to confirm the correctness of the solution. This paper proposes a framework for time-lock puzzles, providing both pre-verification and post-verification functionalities, and outlines the security requirements of this framework. Furthermore, we present a practical construction based on iterated squaring in the RSA group and analyze the security of the specific construction. Finally, we implement this construction in Python and demonstrate its efficiency in different settings when implemented in practice.