VRFs (Verifiable random functions) are great tools in decentralized systems because they can introduce random oracles into a protocol without the fear of data manipulation from a trusted party. These oracle functions are proven to be as hard to manipulate as breaking a particular cryptographic trapdoor.

See more in Micali's groundbreaking publication: https://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Pseudo%20Randomness/Verifiable_Random_Functions.pdf

This elliptic curve instantiation was originally subject to exhaustive research in order to improve DNSSEC and proven to have the Trusted Uniqueness and Selective Pseudorandomness properties: https://eprint.iacr.org/2014/905.pdf

An even more naive explanation of VRFs is that they are HMACs where the key is asymmetric. The parties agree on a pseudorandom function (SHA3) and exchange a proof with the same pseudorandomness that binds to the input but doesn't serve as the only witness (which is the case with simple SHA).

    extern crate rand_os;
    extern crate ec_vrf;
    use curve25519_dalek::scalar::{Scalar};
    use curve25519_dalek::constants::ED25519_BASEPOINT_POINT as g;
    use curve25519_dalek::constants::RISTRETTO_BASEPOINT_POINT as rg;
    use rand_os::OsRng;

   
    fn main() {
        let mut csprng: OsRng = OsRng::new().unwrap();
        let privkey: Scalar = Scalar::random(&mut csprng);
        let input = vec![1,2,3,4,5,6,7,8];
		// using curve25519
        let pubkey = g*privkey;
        let (output, proof) = ec_vrf::curve25519::prove(&input, privkey);
        assert!(ec_vrf::curve25519::verify(&input, pubkey, output, proof));

		// using ristretto
        let pubkey2 = rg*privkey;
        let (output2, proof2) = ec_vrf::ristretto::prove(&input, privkey);
        assert!(ec_vrf::ristretto::verify(&input, pubkey2, output2, proof2));
    }
}

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