Paper 2015/514

Time-Lock Puzzles from Randomized Encodings

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

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).

Note: Added a comment about preprocessing TLPs and their construction from weak TLPs. Revised a statement and proof in appendix B.

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Published elsewhere. Minor revision. ITCS 2016
time-lock puzzlesrandomized encodingsparallelismproofs-of-work
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nbitansky @ gmail com
2023-09-09: last of 2 revisions
2015-05-29: received
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      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{}},
      url = {}
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