uzkge 0.1.2

App-specific PlonK with various gadgets & primitives
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
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222

use ark_std::ops::Mul;

use crate::{
    errors::UzkgeError,
    poly_commit::{field_polynomial::FpPolynomial, pcs::PolyComScheme},
    utils::transcript::Transcript,
};

use super::{
    constraint_system::ConstraintSystem,
    helpers::{eval_pi_poly, first_lagrange_poly, r_commitment, r_eval_zeta, PlonkChallenges},
    indexer::{PlonkProof, PlonkVerifierParams},
    transcript::transcript_init_plonk,
};

/// Verify a proof.
pub fn verifier<PCS: PolyComScheme, CS: ConstraintSystem<PCS::Field>>(
    transcript: &mut Transcript,
    pcs: &PCS,
    cs: &CS,
    verifier_params: &PlonkVerifierParams<PCS>,
    pi: &[PCS::Field],
    proof: &PlonkProof<PCS>,
) -> Result<(), UzkgeError> {
    let domain = FpPolynomial::<PCS::Field>::evaluation_domain(cs.size())
        .ok_or(UzkgeError::GroupNotFound(cs.size()))?;
    let root = domain.group_gen;

    transcript_init_plonk(transcript, verifier_params, pi, &root);
    let mut challenges = PlonkChallenges::new();
    // 1. compute all challenges such as gamma, beta, alpha, zeta and u.
    compute_challenges::<PCS>(&mut challenges, transcript, &proof);

    // 2. compute Z_h(\zeta) and L_1(\zeta).
    let (z_h_eval_zeta, first_lagrange_eval_zeta) =
        first_lagrange_poly::<PCS>(&challenges, verifier_params.cs_size as u64);

    // 3. compute PI(\zeta).
    let pi_eval_zeta = eval_pi_poly::<PCS>(
        verifier_params,
        pi,
        &z_h_eval_zeta,
        challenges.get_zeta().unwrap(),
        &root,
    );

    // 4. derive the linearization polynomial commitment.
    let r_eval_zeta = r_eval_zeta::<PCS>(
        proof,
        &challenges,
        &pi_eval_zeta,
        &first_lagrange_eval_zeta,
        verifier_params.anemoi_generator,
        verifier_params.anemoi_generator_inv,
    );

    let w_polys_eval_zeta_as_ref: Vec<&PCS::Field> = proof.w_polys_eval_zeta.iter().collect();
    #[cfg(feature = "shuffle")]
    let w_polys_eval_zeta_omega_as_ref: Vec<&PCS::Field> =
        proof.w_polys_eval_zeta_omega.iter().collect();
    #[cfg(feature = "shuffle")]
    let w_sel_polys_eval_zeta_as_ref: Vec<&PCS::Field> =
        proof.w_sel_polys_eval_zeta.iter().collect();
    let s_eval_zeta_as_ref: Vec<&PCS::Field> = proof.s_polys_eval_zeta.iter().collect();
    let cm_r = r_commitment::<PCS, CS>(
        verifier_params,
        &proof.cm_z,
        &w_polys_eval_zeta_as_ref[..],
        #[cfg(feature = "shuffle")]
        &w_sel_polys_eval_zeta_as_ref[..],
        &s_eval_zeta_as_ref[..],
        &proof.prk_3_poly_eval_zeta,
        #[cfg(feature = "shuffle")]
        &proof.q_ecc_poly_eval_zeta,
        #[cfg(feature = "shuffle")]
        &w_polys_eval_zeta_omega_as_ref[..],
        &proof.z_eval_zeta_omega,
        &challenges,
        &proof.cm_t_vec[..],
        &first_lagrange_eval_zeta,
        &z_h_eval_zeta,
        verifier_params.cs_size + 2,
    );

    // 5. verify opening proofs.
    let mut commitments: Vec<&PCS::Commitment> = proof
        .cm_w_vec
        .iter()
        .chain(
            verifier_params
                .cm_s_vec
                .iter()
                .take(CS::n_wires_per_gate() - 1),
        )
        .collect();
    commitments.push(&verifier_params.cm_prk_vec[2]);
    commitments.push(&verifier_params.cm_prk_vec[3]);
    #[cfg(feature = "shuffle")]
    {
        commitments.push(&verifier_params.cm_q_ecc);
        for cm_w_sel in proof.cm_w_sel_vec.iter() {
            commitments.push(cm_w_sel);
        }
    }
    commitments.push(&cm_r);

    let mut values: Vec<PCS::Field> = proof
        .w_polys_eval_zeta
        .iter()
        .chain(proof.s_polys_eval_zeta.iter())
        .cloned()
        .collect();
    values.push(proof.prk_3_poly_eval_zeta);
    values.push(proof.prk_4_poly_eval_zeta);
    #[cfg(feature = "shuffle")]
    {
        values.push(proof.q_ecc_poly_eval_zeta);
        for w_sel_eval_zeta in proof.w_sel_polys_eval_zeta.iter() {
            values.push(*w_sel_eval_zeta);
        }
    }
    values.push(r_eval_zeta);

    let zeta = challenges.get_zeta().unwrap();
    let zeta_omega = zeta.mul(&root);

    let (comm, val) = pcs.batch(
        transcript,
        &commitments[..],
        verifier_params.cs_size + 2,
        &zeta,
        &values[..],
    );

    let (comm_omega, val_omega) = pcs.batch(
        transcript,
        &[
            &proof.cm_z,
            &proof.cm_w_vec[0],
            &proof.cm_w_vec[1],
            &proof.cm_w_vec[2],
        ],
        verifier_params.cs_size + 2,
        &zeta_omega,
        &[
            proof.z_eval_zeta_omega,
            proof.w_polys_eval_zeta_omega[0],
            proof.w_polys_eval_zeta_omega[1],
            proof.w_polys_eval_zeta_omega[2],
        ],
    );

    pcs.batch_verify_diff_points(
        &[comm, comm_omega],
        &[zeta.clone(), zeta_omega.clone()],
        &[val, val_omega],
        &[
            proof.opening_witness_zeta.clone(),
            proof.opening_witness_zeta_omega.clone(),
        ],
        challenges.get_u().unwrap(),
    )
    .map_err(|_| UzkgeError::VerificationError)
}

fn compute_challenges<PCS: PolyComScheme>(
    challenges: &mut PlonkChallenges<PCS::Field>,
    transcript: &mut Transcript,
    proof: &PlonkProof<PCS>,
) {
    // 1. compute gamma and beta challenges.
    for cm_w in proof.cm_w_vec.iter() {
        transcript.append_commitment::<PCS::Commitment>(cm_w);
    }

    #[cfg(feature = "shuffle")]
    for cm_w_sel in proof.cm_w_sel_vec.iter() {
        transcript.append_commitment::<PCS::Commitment>(cm_w_sel);
    }

    let beta = transcript.get_challenge_field_elem(b"beta");
    transcript.append_single_byte(b"gamma", 0x01);
    let gamma = transcript.get_challenge_field_elem(b"gamma");
    challenges.insert_beta_gamma(beta, gamma).unwrap();

    // 2. compute alpha challenge.
    transcript.append_commitment::<PCS::Commitment>(&proof.cm_z);
    let alpha = transcript.get_challenge_field_elem(b"alpha");
    challenges.insert_alpha(alpha).unwrap();
    for cm_t in &proof.cm_t_vec {
        transcript.append_commitment::<PCS::Commitment>(&cm_t);
    }

    // 3. compute zeta challenge.
    let zeta = transcript.get_challenge_field_elem(b"zeta");
    challenges.insert_zeta(zeta).unwrap();
    for eval_zeta in proof
        .w_polys_eval_zeta
        .iter()
        .chain(proof.s_polys_eval_zeta.iter())
    {
        transcript.append_challenge(eval_zeta);
    }
    #[cfg(feature = "shuffle")]
    {
        for eval_zeta in proof.w_sel_polys_eval_zeta.iter() {
            transcript.append_challenge(eval_zeta);
        }
    }
    transcript.append_challenge(&proof.prk_3_poly_eval_zeta);
    transcript.append_challenge(&proof.prk_4_poly_eval_zeta);
    transcript.append_challenge(&proof.z_eval_zeta_omega);
    #[cfg(feature = "shuffle")]
    transcript.append_challenge(&proof.q_ecc_poly_eval_zeta);
    for eval_zeta_omega in proof.w_polys_eval_zeta_omega.iter() {
        transcript.append_challenge(eval_zeta_omega);
    }

    // 4. compute u challenge.
    let u = transcript.get_challenge_field_elem(b"u");
    challenges.insert_u(u).unwrap();
}