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11

First, you need more than just a signature, because a VRF produces both an output and a proof. To an observer, the output is uniformly distributed unless the observer also has the proof, which can be used to verify the output. With a signature scheme and a random oracle $H$, you could use a signature $s$ on a message $m$ as a proof and $h = H(s)$ as an ...

5

Sharon Goldberg's research group at Boston University has a web site on VRFs with research references and applications, including key transparency in CONIKS, authenticated enumeration-resistant denial of existence in DNSSEC with NSEC5, and the Byzantine agreement protocol Algorand. Here's a quick history of how negative answers work in DNS and DNSSEC. The ...

4

Ed25519 is a typical elliptic-curve signature scheme, in a group of large prime order $\ell \approx 2^{252}$ on a curve over the field $\mathbb F_p$ for $p = 2^{255} - 19$. A secret key is a uniform random 32-byte string; a signature is a 64-byte string encoding a point $R$ on the curve generated by the standard base point, and encoding a scalar $s \in \... 1 Yes, in the random oracle model, the hash of a BLS signature makes a VRF essentially as secure as the BLS signature scheme (provided the verifier accepts only the unique canonical encoding of each signature). This works because BLS signatures are unique. Fix a pairing$e\colon G_1 \times G_2 \to G_T$on groups$G_1$and$G_2\$ of prime order. For any fixed ...

1

Sure VRFs can be used for sortition. One can say that a party is selected if the output of his VRF satisifies some property. The VRF outputs two things - a random output and a proof that the output is computed correctly. It is not always the case that if the output of a VRF is f(x) the corresponding proof is x. For example, the VRF could simply output a ...

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