1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162

#![allow(non_snake_case)]

use crate::utilities::ErrorReason;
use curv::arithmetic::traits::Modulo;
use curv::arithmetic::traits::Samplable;
use curv::arithmetic::{traits::*, BigInt};
use serde::{Deserialize, Serialize};
use utilities::{compute_rsa_modulus, h_g, hash_to_prime};

const BIT_LENGTH: usize = 4096;
const SEED_LENGTH: usize = 256;
pub mod utilities;

pub struct ElGamal;
pub struct ExponentElGamal;

/// Wesolowski VDF, based on https://eprint.iacr.org/2018/712.pdf.
/// Original paper: https://eprint.iacr.org/2018/623.pdf
///
#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
pub struct SolvedVDF {
    vdf_instance: UnsolvedVDF,
    pub y: BigInt,
    pub pi: BigInt,
}

#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
pub struct SetupForVDF {
    pub t: BigInt,
    pub N: BigInt,
}

#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
pub struct UnsolvedVDF {
    pub x: BigInt,
    pub setup: SetupForVDF,
}

impl SetupForVDF {
    pub fn public_setup(t: &BigInt) -> Self {
        // todo: setup can also be used to define H_G. for example pick random domain separator
        let N = compute_rsa_modulus(BIT_LENGTH);
        SetupForVDF { t: t.clone(), N }
    }

    pub fn pick_challenge(setup: &SetupForVDF) -> UnsolvedVDF {
        let x = BigInt::sample(SEED_LENGTH);
        UnsolvedVDF {
            x,
            setup: setup.clone(),
        }
    }
}

impl UnsolvedVDF {
    //algorithm 3 from https://eprint.iacr.org/2018/623.pdf
    pub fn eval(unsolved_vdf: &UnsolvedVDF) -> SolvedVDF {
        let N = unsolved_vdf.setup.N.clone();
        let x = unsolved_vdf.x.clone();
        let t = unsolved_vdf.setup.t.clone();

        let g = h_g(&N, &x);
        let mut y = g.clone();
        let mut i = BigInt::zero();

        while i < t {
            y = BigInt::mod_mul(&y, &y, &N);
            i = i + BigInt::one();
        }
        let l = hash_to_prime(&unsolved_vdf.setup, &g, &y);

        //algorithm 4 from https://eprint.iacr.org/2018/623.pdf
        // long division TODO: consider alg 5 instead
        let mut i = BigInt::zero();
        let mut b: BigInt;
        let mut r = BigInt::one();
        let mut r2: BigInt;
        let two = BigInt::from(2);
        let mut pi = BigInt::one();
        let mut g_b: BigInt;

        while i < t {
            r2 = &r * &two;
            b = r2.div_floor(&l);
            r = r2.mod_floor(&l);
            g_b = BigInt::mod_pow(&g, &b, &N);
            pi = BigInt::mod_mul(&pi, &pi, &N);
            pi = BigInt::mod_mul(&pi, &g_b, &N);
            i = i + BigInt::one();
        }

        let vdf = SolvedVDF {
            vdf_instance: unsolved_vdf.clone(),
            y,
            pi,
        };
        vdf
    }
}

impl SolvedVDF {
    //algorithm 2 from https://eprint.iacr.org/2018/623.pdf
    pub fn verify(&self, unsolved_vdf: &UnsolvedVDF) -> Result<(), ErrorReason> {
        // we first check the solution received is for VDF generated by us
        if &self.vdf_instance != unsolved_vdf {
            return Err(ErrorReason::MisMatchedVDF);
        }
        let N = self.vdf_instance.setup.N.clone();
        let g = h_g(&self.vdf_instance.setup.N, &self.vdf_instance.x);

        // test that y is element in the group : https://eprint.iacr.org/2018/712.pdf 2.1 line 0
        if &self.y >= &N || &self.pi >= &N {
            return Err(ErrorReason::VDFVerifyError);
        }

        let l = hash_to_prime(&self.vdf_instance.setup, &g, &self.y);

        let r = BigInt::mod_pow(&BigInt::from(2), &self.vdf_instance.setup.t, &l);
        let pi_l = BigInt::mod_pow(&self.pi, &l, &N);
        let g_r = BigInt::mod_pow(&g, &r, &N);
        let pi_l_g_r = BigInt::mod_mul(&pi_l, &g_r, &N);

        match pi_l_g_r == self.y {
            true => return Ok(()),
            false => return Err(ErrorReason::VDFVerifyError),
        }
    }
}

#[cfg(test)]
mod tests {
    use super::SetupForVDF;
    use super::UnsolvedVDF;
    use curv::arithmetic::traits::Samplable;
    use curv::BigInt;
    use std::time::Instant;

    #[test]
    fn test_vdf_valid_proof() {
        let t = BigInt::sample(13);
        let setup = SetupForVDF::public_setup(&t);

        let mut i = 0;
        while i < 10 {
            let unsolved_vdf = SetupForVDF::pick_challenge(&setup);
            let start = Instant::now();
            let solved_vdf = UnsolvedVDF::eval(&unsolved_vdf);
            let duration1 = start.elapsed();
            let start = Instant::now();
            // here unsolved_vdf is the version that was kept by the challenger
            let res = solved_vdf.verify(&unsolved_vdf);
            let duration2 = start.elapsed();
            i = i + 1;

            // todo: compute mean and std
            println!("eval time: {:?}", duration1);
            println!("verify time: {:?}", duration2);

            assert!(res.is_ok());
        }
    }
}