cryptid 0.2.8

An implementation of the threshold ElGamal cryptosystem with zero-knowledge proofs, using Curve25519 as the group.
Documentation 
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
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180

use serde::{Serialize, Deserialize};

use crate::elgamal::CryptoContext;
use crate::curve::CurveElem;
use crate::{CryptoError, Hasher, Scalar};

#[derive(Copy, Clone, PartialEq, Eq, Debug, Serialize, Deserialize)]
pub struct PrfKnowDlog {
    pub(crate) g: CurveElem,
    y: CurveElem,
    a: CurveElem,
    r: Scalar,
}

impl PrfKnowDlog {
    fn challenge(g: &CurveElem, y: &CurveElem, a: &CurveElem) -> Scalar {
        Hasher::sha_256()
            .update(&g.as_bytes())
            .update(&y.as_bytes())
            .update(&a.as_bytes())
            .finish_scalar()
    }

    /// Proves that we know x such that y = g^x
    pub fn new(ctx: &mut CryptoContext, g: &CurveElem, x: &Scalar, y: &CurveElem) -> Result<Self, CryptoError> {
        // Choose random commitment
        let z = ctx.random_power()?;
        let a = g.scaled(&z);
        // Calculate the challenge
        let c = Self::challenge(g, y, &a);
        let r = Scalar(z.0 + c.0 * x.0);

        Ok(Self {
            g: g.clone(),
            y: y.clone(),
            a,
            r,
        })
    }

    pub fn verify(&self) -> Result<bool, CryptoError> {
        let c = Self::challenge(&self.g, &self.y, &self.a);
        Ok(self.g.scaled(&self.r) == &self.a + &self.y.scaled(&c))
    }
}

// TODO: this is a big-ass proof
#[derive(Clone, PartialEq, Eq, Debug, Serialize, Deserialize)]
pub struct PrfEqDlogs {
    pub v: CurveElem,
    pub f: CurveElem,
    pub w: CurveElem,
    pub h: CurveElem,
    a: CurveElem,
    b: CurveElem,
    r: Scalar,
}

impl PrfEqDlogs {
    fn challenge(f: &CurveElem,
                 h: &CurveElem,
                 v: &CurveElem,
                 w: &CurveElem,
                 a: &CurveElem,
                 b: &CurveElem) -> Scalar {
        Hasher::sha_256()
            .update(&f.as_bytes())
            .update(&h.as_bytes())
            .update(&v.as_bytes())
            .update(&w.as_bytes())
            .update(&a.as_bytes())
            .update(&b.as_bytes())
            .finish_scalar()
    }

    /// Prove that v = f^x and w = h^x, i.e. that dlog_f v = dlog_h w for a secret x
    pub fn new(ctx: &mut CryptoContext,
               f: &CurveElem,
               h: &CurveElem,
               v: &CurveElem,
               w: &CurveElem,
               x: &Scalar) -> Result<Self, CryptoError> {
        let z = ctx.random_power()?;
        let a = f.scaled(&z);
        let b = h.scaled(&z);
        let c = Self::challenge(&f, &h, &v, &w, &a, &b);
        let r = Scalar(z.0 + c.0 * x.0);
        Ok(Self {
            v: v.clone(),
            f: f.clone(),
            w: w.clone(),
            h: h.clone(),
            a,
            b,
            r
        })
    }

    pub fn verify(&self) -> Result<bool, CryptoError> {
        let c = Self::challenge(&self.f, &self.h, &self.v, &self.w, &self.a, &self.b);
        Ok(self.f.scaled(&self.r) == &self.a + &self.v.scaled(&c)
            && self.h.scaled(&self.r) == &self.b + &self.w.scaled(&c))
    }
}

#[cfg(test)]
mod tests {
    use crate::elgamal::CryptoContext;
    use crate::zkp::{PrfKnowDlog, PrfEqDlogs};
    use crate::{DalekScalar, Scalar};

    #[test]
    fn test_exp_sum() {
        let mut ctx = CryptoContext::new();
        let a = ctx.random_power().unwrap();
        let b = ctx.random_power().unwrap();
        let r = Scalar(a.0 + b.0);

        let x = ctx.g_to(&r);
        let y = ctx.g_to(&a) + ctx.g_to(&b);
        assert_eq!(x, y);
    }

    #[test]
    fn test_prf_know_dlog_complete() {
        let mut ctx = CryptoContext::new();
        let x = ctx.random_power().unwrap();
        let y = ctx.g_to(&x);
        let g = ctx.generator();
        let proof = PrfKnowDlog::new(&mut ctx, &g, &x, &y).unwrap();

        assert!(proof.verify().unwrap());
    }

    #[test]
    fn test_prof_know_dlog_sound() {
        let mut ctx = CryptoContext::new();
        let x = ctx.random_power().unwrap();
        let y = ctx.g_to(&x);
        let g = ctx.generator();
        let mut proof = PrfKnowDlog::new(&mut ctx, &g, &x, &y).unwrap();
        proof.r.0 += &DalekScalar::one();

        assert!(!proof.verify().unwrap());
    }

    #[test]
    fn test_prf_eq_dlogs_complete() {
        let mut ctx = CryptoContext::new();
        let x1 = ctx.random_power().unwrap();
        let f = ctx.g_to(&x1);
        let x2 = ctx.random_power().unwrap();
        let h = ctx.g_to(&x2);

        let x = ctx.random_power().unwrap();
        let v = f.scaled(&x);
        let w = h.scaled(&x);

        let proof = PrfEqDlogs::new(&mut ctx, &f, &h, &v, &w, &x).unwrap();
        assert!(proof.verify().unwrap());
    }

    #[test]
    fn test_prf_eq_dlogs_sound() {
        let mut ctx = CryptoContext::new();
        let x1 = ctx.random_power().unwrap();
        let f = ctx.g_to(&x1);
        let x2 = ctx.random_power().unwrap();
        let h = ctx.g_to(&x2);

        let x = ctx.random_power().unwrap();
        let v = f.scaled(&x);
        let w = h.scaled(&x);

        let mut proof = PrfEqDlogs::new(&mut ctx, &f, &h, &v, &w, &x).unwrap();
        proof.r.0 += &DalekScalar::one();

        assert!(!proof.verify().unwrap());
    }
}