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**2018/627**

**Title:**

Simple Verifiable Delay Functions

**Authors:**
Krzysztof Pietrzak

**Abstract:**

We construct a verifable 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}\pmod 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\le 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.

**ePrint:**
https://eprint.iacr.org/2018/627

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