License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.60
URN: urn:nbn:de:0030-drops-101537
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Pietrzak, Krzysztof

Simple Verifiable Delay Functions

LIPIcs-ITCS-2019-60.pdf (0.5 MB)


We construct a verifiable delay function (VDF) by showing how the Rivest-Shamir-Wagner time-lock puzzle can be made publicly verifiable.
Concretely, we give a statistically sound public-coin protocol to prove that a tuple (N,x,T,y) satisfies y=x^{2^T} mod N where the prover doesn't know the factorization of N and its running time is dominated by solving the puzzle, that is, compute x^{2^T}, which is conjectured to require T sequential squarings. To get a VDF we make this protocol non-interactive using the Fiat-Shamir heuristic.
The motivation for this work comes from the Chia blockchain design, which uses a VDF as a key ingredient. For typical parameters (T <=2^{40},N=2048), our proofs are of size around 10KB, verification cost around three RSA exponentiations and computing the proof is 8000 times faster than solving the puzzle even without any parallelism.

BibTeX - Entry

  author =	{Krzysztof Pietrzak},
  title =	{{Simple Verifiable Delay Functions}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{60:1--60:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-101537},
  doi =		{10.4230/LIPIcs.ITCS.2019.60},
  annote =	{Keywords: Verifiable delay functions, Time-lock puzzles}

Keywords: Verifiable delay functions, Time-lock puzzles
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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