摘要：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.
