## Cryptology ePrint Archive: Report 2015/514

Time-Lock Puzzles from Randomized Encodings

Nir Bitansky and Shafi Goldwasser and Abhishek Jain and Omer Paneth and 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).

Category / Keywords: foundations / time-lock puzzles, randomized encodings, parallelism, proofs-of-work

Date: received 27 May 2015, last revised 10 Aug 2015

Contact author: nirbitan at csail mit edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2015/514

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