### Time-Lock Puzzles from Randomized Encodings

Nir Bitansky, Shafi Goldwasser, Abhishek Jain, Omer Paneth, Vinod Vaikuntanathan, and Brent Waters

##### Abstract

Time-lock puzzles, introduced by May, Rivest, Shamir and Wagner, is a mechanism for sending messages to the future''. A sender can quickly generate a puzzle with a solution $s$ that remains hidden until a moderately large amount of time $t$ has elapsed. The solution $s$ should be hidden from any adversary that runs in time significantly less than $t$, including resourceful parallel adversaries with polynomially many processors. While the notion of time-lock puzzles has been around for 22 years, there has only been a *single* candidate proposed. Fifteen years ago, Rivest, Shamir and Wagner suggested a beautiful candidate time-lock puzzle based on the assumption that exponentiation modulo an RSA integer is an inherently sequential'' computation. We show that various flavors of {\em randomized encodings} give rise to time-lock puzzles of varying strengths, whose security can be shown assuming *the existence* of non-parallelizing languages, which are languages that require circuits of depth at least $t$ to decide, in the worst-case. The existence of such languages is necessary for the existence of time-lock puzzles. We instantiate the construction with different randomized encodings from the literature, where increasingly better efficiency is obtained based on increasingly stronger cryptographic assumptions, ranging from one-way functions to indistinguishability obfuscation. We also observe that time-lock puzzles imply one-way functions, and thus the reliance on some cryptographic assumption is necessary. Finally, generalizing the above, we construct other types of puzzles such as *proofs of work* from randomized encodings and a suitable worst-case hardness assumption (that is necessary for such puzzles to exist).

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
time-lock puzzlesrandomized encodingsparallelismproofs-of-work
Contact author(s)
nirbitan @ csail mit edu
History
2015-08-10: revised
See all versions
Short URL
https://ia.cr/2015/514

CC BY

BibTeX

@misc{cryptoeprint:2015/514,
author = {Nir Bitansky and Shafi Goldwasser and Abhishek Jain and Omer Paneth and Vinod Vaikuntanathan and Brent Waters},
title = {Time-Lock Puzzles from Randomized Encodings},
howpublished = {Cryptology ePrint Archive, Paper 2015/514},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/514}},
url = {https://eprint.iacr.org/2015/514}
}

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