testudo/src/nizk/bullet.rs
src/nizk/bullet.rsRaw
1//! This module is an adaptation of code from the bulletproofs crate.
2//! See NOTICE.md for more details
3#![allow(non_snake_case)]
4#![allow(clippy::type_complexity)]
5#![allow(clippy::too_many_arguments)]
6use crate::math::Math;
7use crate::poseidon_transcript::PoseidonTranscript;
8
9use super::super::errors::ProofVerifyError;
10use super::super::group::{
11 CompressGroupElement, CompressedGroup, DecompressGroupElement, GroupElement,
12 VartimeMultiscalarMul,
13};
14use super::super::scalar::Scalar;
15use ark_ff::Field;
16use ark_serialize::*;
17use ark_std::{One, Zero};
18use core::iter;
19use std::ops::MulAssign;
20
21#[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
22pub struct BulletReductionProof {
23 L_vec: Vec<CompressedGroup>,
24 R_vec: Vec<CompressedGroup>,
25}
26
27impl BulletReductionProof {
28 /// Create an inner-product proof.
29 ///
30 /// The proof is created with respect to the bases \\(G\\).
31 ///
32 /// The `transcript` is passed in as a parameter so that the
33 /// challenges depend on the *entire* transcript (including parent
34 /// protocols).
35 ///
36 /// The lengths of the vectors must all be the same, and must all be
37 /// either 0 or a power of 2.
38 pub fn prove(
39 transcript: &mut PoseidonTranscript,
40 Q: &GroupElement,
41 G_vec: &[GroupElement],
42 H: &GroupElement,
43 a_vec: &[Scalar],
44 b_vec: &[Scalar],
45 blind: &Scalar,
46 blinds_vec: &[(Scalar, Scalar)],
47 ) -> (
48 BulletReductionProof,
49 GroupElement,
50 Scalar,
51 Scalar,
52 GroupElement,
53 Scalar,
54 ) {
55 // Create slices G, H, a, b backed by their respective
56 // vectors. This lets us reslice as we compress the lengths
57 // of the vectors in the main loop below.
58 let mut G = &mut G_vec.to_owned()[..];
59 let mut a = &mut a_vec.to_owned()[..];
60 let mut b = &mut b_vec.to_owned()[..];
61
62 // All of the input vectors must have a length that is a power of two.
63 let mut n = G.len();
64 assert!(n.is_power_of_two());
65 let lg_n = n.log_2();
66
67 // All of the input vectors must have the same length.
68 assert_eq!(G.len(), n);
69 assert_eq!(a.len(), n);
70 assert_eq!(b.len(), n);
71 assert_eq!(blinds_vec.len(), 2 * lg_n);
72
73 let mut L_vec = Vec::with_capacity(lg_n);
74 let mut R_vec = Vec::with_capacity(lg_n);
75 let mut blinds_iter = blinds_vec.iter();
76 let mut blind_fin = *blind;
77
78 while n != 1 {
79 n /= 2;
80 let (a_L, a_R) = a.split_at_mut(n);
81 let (b_L, b_R) = b.split_at_mut(n);
82 let (G_L, G_R) = G.split_at_mut(n);
83
84 let c_L = inner_product(a_L, b_R);
85 let c_R = inner_product(a_R, b_L);
86
87 let (blind_L, blind_R) = blinds_iter.next().unwrap();
88
89 let L = GroupElement::vartime_multiscalar_mul(
90 a_L.iter()
91 .chain(iter::once(&c_L))
92 .chain(iter::once(blind_L))
93 .copied()
94 .collect::<Vec<Scalar>>()
95 .as_slice(),
96 G_R.iter()
97 .chain(iter::once(Q))
98 .chain(iter::once(H))
99 .copied()
100 .collect::<Vec<GroupElement>>()
101 .as_slice(),
102 );
103
104 let R = GroupElement::vartime_multiscalar_mul(
105 a_R.iter()
106 .chain(iter::once(&c_R))
107 .chain(iter::once(blind_R))
108 .copied()
109 .collect::<Vec<Scalar>>()
110 .as_slice(),
111 G_L.iter()
112 .chain(iter::once(Q))
113 .chain(iter::once(H))
114 .copied()
115 .collect::<Vec<GroupElement>>()
116 .as_slice(),
117 );
118
119 transcript.append_point(&L.compress());
120 transcript.append_point(&R.compress());
121
122 let u = transcript.challenge_scalar();
123 let u_inv = u.inverse().unwrap();
124
125 for i in 0..n {
126 a_L[i] = a_L[i] * u + u_inv * a_R[i];
127 b_L[i] = b_L[i] * u_inv + u * b_R[i];
128 G_L[i] = GroupElement::vartime_multiscalar_mul(&[u_inv, u], &[G_L[i], G_R[i]]);
129 }
130
131 blind_fin = blind_fin + u * u * blind_L + u_inv * u_inv * blind_R;
132
133 L_vec.push(L.compress());
134 R_vec.push(R.compress());
135
136 a = a_L;
137 b = b_L;
138 G = G_L;
139 }
140
141 let Gamma_hat =
142 GroupElement::vartime_multiscalar_mul(&[a[0], a[0] * b[0], blind_fin], &[G[0], *Q, *H]);
143
144 (
145 BulletReductionProof { L_vec, R_vec },
146 Gamma_hat,
147 a[0],
148 b[0],
149 G[0],
150 blind_fin,
151 )
152 }
153
154 /// Computes three vectors of verification scalars \\([u\_{i}^{2}]\\), \\([u\_{i}^{-2}]\\) and \\([s\_{i}]\\) for combined multiscalar multiplication
155 /// in a parent protocol. See [inner product protocol notes](index.html#verification-equation) for details.
156 /// The verifier must provide the input length \\(n\\) explicitly to avoid unbounded allocation within the inner product proof.
157 fn verification_scalars(
158 &self,
159 n: usize,
160 transcript: &mut PoseidonTranscript,
161 ) -> Result<(Vec<Scalar>, Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
162 let lg_n = self.L_vec.len();
163 if lg_n >= 32 {
164 // 4 billion multiplications should be enough for anyone
165 // and this check prevents overflow in 1<<lg_n below.
166 return Err(ProofVerifyError::InternalError);
167 }
168 if n != (1 << lg_n) {
169 return Err(ProofVerifyError::InternalError);
170 }
171
172 // 1. Recompute x_k,...,x_1 based on the proof transcript
173 let mut challenges = Vec::with_capacity(lg_n);
174 for (L, R) in self.L_vec.iter().zip(self.R_vec.iter()) {
175 transcript.append_point(L);
176 transcript.append_point(R);
177 challenges.push(transcript.challenge_scalar());
178 }
179
180 // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
181 let mut challenges_inv: Vec<Scalar> = challenges.clone();
182
183 ark_ff::fields::batch_inversion(&mut challenges_inv);
184 let mut allinv: Scalar = Scalar::one();
185 for c in challenges.iter().filter(|s| !s.is_zero()) {
186 allinv.mul_assign(c);
187 }
188 allinv = allinv.inverse().unwrap();
189
190 // 3. Compute u_i^2 and (1/u_i)^2
191 for i in 0..lg_n {
192 challenges[i] = challenges[i].square();
193 challenges_inv[i] = challenges_inv[i].square();
194 }
195 let challenges_sq = challenges;
196 let challenges_inv_sq = challenges_inv;
197
198 // 4. Compute s values inductively.
199 let mut s = Vec::with_capacity(n);
200 s.push(allinv);
201 for i in 1..n {
202 let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
203 let k = 1 << lg_i;
204 // The challenges are stored in "creation order" as [u_k,...,u_1],
205 // so u_{lg(i)+1} = is indexed by (lg_n-1) - lg_i
206 let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
207 s.push(s[i - k] * u_lg_i_sq);
208 }
209
210 Ok((challenges_sq, challenges_inv_sq, s))
211 }
212
213 /// This method is for testing that proof generation work,
214 /// but for efficiency the actual protocols would use `verification_scalars`
215 /// method to combine inner product verification with other checks
216 /// in a single multiscalar multiplication.
217 pub fn verify(
218 &self,
219 n: usize,
220 a: &[Scalar],
221 transcript: &mut PoseidonTranscript,
222 Gamma: &GroupElement,
223 G: &[GroupElement],
224 ) -> Result<(GroupElement, GroupElement, Scalar), ProofVerifyError> {
225 let (u_sq, u_inv_sq, s) = self.verification_scalars(n, transcript)?;
226
227 let Ls = self
228 .L_vec
229 .iter()
230 .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
231 .collect::<Result<Vec<_>, _>>()?;
232
233 let Rs = self
234 .R_vec
235 .iter()
236 .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
237 .collect::<Result<Vec<_>, _>>()?;
238
239 let G_hat = GroupElement::vartime_multiscalar_mul(s.as_slice(), G);
240 let a_hat = inner_product(a, &s);
241
242 let Gamma_hat = GroupElement::vartime_multiscalar_mul(
243 u_sq.iter()
244 .chain(u_inv_sq.iter())
245 .chain(iter::once(&Scalar::one()))
246 .copied()
247 .collect::<Vec<Scalar>>()
248 .as_slice(),
249 Ls.iter()
250 .chain(Rs.iter())
251 .chain(iter::once(Gamma))
252 .copied()
253 .collect::<Vec<GroupElement>>()
254 .as_slice(),
255 );
256
257 Ok((G_hat, Gamma_hat, a_hat))
258 }
259}
260
261/// Computes an inner product of two vectors
262/// \\[
263/// {\langle {\mathbf{a}}, {\mathbf{b}} \rangle} = \sum\_{i=0}^{n-1} a\_i \cdot b\_i.
264/// \\]
265/// Panics if the lengths of \\(\mathbf{a}\\) and \\(\mathbf{b}\\) are not equal.
266pub fn inner_product(a: &[Scalar], b: &[Scalar]) -> Scalar {
267 assert!(
268 a.len() == b.len(),
269 "inner_product(a,b): lengths of vectors do not match"
270 );
271 let mut out = Scalar::zero();
272 for i in 0..a.len() {
273 out += a[i] * b[i];
274 }
275 out
276}