Simple Verifiable Delay Functions

Author Krzysztof Pietrzak

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Krzysztof Pietrzak
  • Institute of Science and Technology Austria, Austria

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Krzysztof Pietrzak. Simple Verifiable Delay Functions. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 60:1-60:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Interactive proof systems
  • Verifiable delay functions
  • Time-lock puzzles


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