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 T has elapsed. The solution is required to be concealed from the eyes of any algorithm running in (parallel) time less than 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,.. ., s_n) to obtain a puzzle that solves to f(s_1,..., 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.
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