Homomorphic Time-Lock Puzzles and Applications

Time-lock puzzles allow one to encrypt messages for the future, by efficiently generating a puzzle with a solution s that remains hidden until time \(\mathcal {T}\) has elapsed. The solution is required to be concealed from the eyes of any algorithm running in (parallel) time less than \(\mathcal {T}\). We put forth the concept of homomorphic time-lock puzzles, where one can evaluate functions over puzzles without solving them, i.e., one can manipulate a set of puzzles with solutions \((s_1, \dots , s_n)\) to obtain a puzzle that solves to \(f(s_1, \ldots , s_n)\), for any function f. We propose candidate constructions under concrete cryptographic assumptions for different classes of functions. Then we show how homomorphic time-lock puzzles overcome the limitations of classical time-lock puzzles by proposing new protocols for applications of interest, such as e-voting, multi-party coin flipping, and fair contract signing.