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 super::super::errors::ProofVerifyError;
7use super::super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
8use super::super::math::Math;
9use super::super::scalar::Scalar;
10use super::super::transcript::ProofTranscript;
11use core::iter;
12use merlin::Transcript;
13use serde::{Deserialize, Serialize};
14
15#[derive(Debug, Serialize, Deserialize)]
16pub struct BulletReductionProof {
17 L_vec: Vec<CompressedGroup>,
18 R_vec: Vec<CompressedGroup>,
19}
20
21impl BulletReductionProof {
22 /// Create an inner-product proof.
23 ///
24 /// The proof is created with respect to the bases \\(G\\).
25 ///
26 /// The `transcript` is passed in as a parameter so that the
27 /// challenges depend on the *entire* transcript (including parent
28 /// protocols).
29 ///
30 /// The lengths of the vectors must all be the same, and must all be
31 /// either 0 or a power of 2.
32 pub fn prove(
33 transcript: &mut Transcript,
34 Q: &GroupElement,
35 G_vec: &[GroupElement],
36 H: &GroupElement,
37 a_vec: &[Scalar],
38 b_vec: &[Scalar],
39 blind: &Scalar,
40 blinds_vec: &[(Scalar, Scalar)],
41 ) -> (
42 BulletReductionProof,
43 GroupElement,
44 Scalar,
45 Scalar,
46 GroupElement,
47 Scalar,
48 ) {
49 // Create slices G, H, a, b backed by their respective
50 // vectors. This lets us reslice as we compress the lengths
51 // of the vectors in the main loop below.
52 let mut G = &mut G_vec.to_owned()[..];
53 let mut a = &mut a_vec.to_owned()[..];
54 let mut b = &mut b_vec.to_owned()[..];
55
56 // All of the input vectors must have a length that is a power of two.
57 let mut n = G.len();
58 assert!(n.is_power_of_two());
59 let lg_n = n.log2();
60
61 let G_factors: Vec<Scalar> = iter::repeat(Scalar::one()).take(n).collect();
62
63 // All of the input vectors must have the same length.
64 assert_eq!(G.len(), n);
65 assert_eq!(a.len(), n);
66 assert_eq!(b.len(), n);
67 assert_eq!(G_factors.len(), n);
68 assert_eq!(blinds_vec.len(), 2 * lg_n);
69
70 //transcript.innerproduct_domain_sep(n as u64);
71
72 let mut L_vec = Vec::with_capacity(lg_n);
73 let mut R_vec = Vec::with_capacity(lg_n);
74 let mut blinds_iter = blinds_vec.iter();
75 let mut blind_fin = *blind;
76
77 while n != 1 {
78 n /= 2;
79 let (a_L, a_R) = a.split_at_mut(n);
80 let (b_L, b_R) = b.split_at_mut(n);
81 let (G_L, G_R) = G.split_at_mut(n);
82
83 let c_L = inner_product(&a_L, &b_R);
84 let c_R = inner_product(&a_R, &b_L);
85
86 let (blind_L, blind_R) = blinds_iter.next().unwrap();
87
88 let L = GroupElement::vartime_multiscalar_mul(
89 a_L
90 .iter()
91 .chain(iter::once(&c_L))
92 .chain(iter::once(blind_L)),
93 G_R.iter().chain(iter::once(Q)).chain(iter::once(H)),
94 );
95
96 let R = GroupElement::vartime_multiscalar_mul(
97 a_R
98 .iter()
99 .chain(iter::once(&c_R))
100 .chain(iter::once(blind_R)),
101 G_L.iter().chain(iter::once(Q)).chain(iter::once(H)),
102 );
103
104 transcript.append_point(b"L", &L.compress());
105 transcript.append_point(b"R", &R.compress());
106
107 let u = transcript.challenge_scalar(b"u");
108 let u_inv = u.invert().unwrap();
109
110 for i in 0..n {
111 a_L[i] = a_L[i] * u + u_inv * a_R[i];
112 b_L[i] = b_L[i] * u_inv + u * b_R[i];
113 G_L[i] = GroupElement::vartime_multiscalar_mul(&[u_inv, u], &[G_L[i], G_R[i]]);
114 }
115
116 blind_fin = blind_fin + blind_L * u * u + blind_R * u_inv * u_inv;
117
118 L_vec.push(L.compress());
119 R_vec.push(R.compress());
120
121 a = a_L;
122 b = b_L;
123 G = G_L;
124 }
125
126 let Gamma_hat =
127 GroupElement::vartime_multiscalar_mul(&[a[0], a[0] * b[0], blind_fin], &[G[0], *Q, *H]);
128
129 (
130 BulletReductionProof { L_vec, R_vec },
131 Gamma_hat,
132 a[0],
133 b[0],
134 G[0],
135 blind_fin,
136 )
137 }
138
139 /// Computes three vectors of verification scalars \\([u\_{i}^{2}]\\), \\([u\_{i}^{-2}]\\) and \\([s\_{i}]\\) for combined multiscalar multiplication
140 /// in a parent protocol. See [inner product protocol notes](index.html#verification-equation) for details.
141 /// The verifier must provide the input length \\(n\\) explicitly to avoid unbounded allocation within the inner product proof.
142 fn verification_scalars(
143 &self,
144 n: usize,
145 transcript: &mut Transcript,
146 ) -> Result<(Vec<Scalar>, Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
147 let lg_n = self.L_vec.len();
148 if lg_n >= 32 {
149 // 4 billion multiplications should be enough for anyone
150 // and this check prevents overflow in 1<<lg_n below.
151 return Err(ProofVerifyError::InternalError);
152 }
153 if n != (1 << lg_n) {
154 return Err(ProofVerifyError::InternalError);
155 }
156
157 // 1. Recompute x_k,...,x_1 based on the proof transcript
158 let mut challenges = Vec::with_capacity(lg_n);
159 for (L, R) in self.L_vec.iter().zip(self.R_vec.iter()) {
160 transcript.append_point(b"L", L);
161 transcript.append_point(b"R", R);
162 challenges.push(transcript.challenge_scalar(b"u"));
163 }
164
165 // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
166 let mut challenges_inv = challenges.clone();
167 let allinv = Scalar::batch_invert(&mut challenges_inv);
168
169 // 3. Compute u_i^2 and (1/u_i)^2
170 for i in 0..lg_n {
171 challenges[i] = challenges[i].square();
172 challenges_inv[i] = challenges_inv[i].square();
173 }
174 let challenges_sq = challenges;
175 let challenges_inv_sq = challenges_inv;
176
177 // 4. Compute s values inductively.
178 let mut s = Vec::with_capacity(n);
179 s.push(allinv);
180 for i in 1..n {
181 let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
182 let k = 1 << lg_i;
183 // The challenges are stored in "creation order" as [u_k,...,u_1],
184 // so u_{lg(i)+1} = is indexed by (lg_n-1) - lg_i
185 let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
186 s.push(s[i - k] * u_lg_i_sq);
187 }
188
189 Ok((challenges_sq, challenges_inv_sq, s))
190 }
191
192 /// This method is for testing that proof generation work,
193 /// but for efficiency the actual protocols would use `verification_scalars`
194 /// method to combine inner product verification with other checks
195 /// in a single multiscalar multiplication.
196 pub fn verify(
197 &self,
198 n: usize,
199 a: &[Scalar],
200 transcript: &mut Transcript,
201 Gamma: &GroupElement,
202 G: &[GroupElement],
203 ) -> Result<(GroupElement, GroupElement, Scalar), ProofVerifyError> {
204 let (u_sq, u_inv_sq, s) = self.verification_scalars(n, transcript)?;
205
206 let Ls = self
207 .L_vec
208 .iter()
209 .map(|p| p.decompress().ok_or(ProofVerifyError::InternalError))
210 .collect::<Result<Vec<_>, _>>()?;
211
212 let Rs = self
213 .R_vec
214 .iter()
215 .map(|p| p.decompress().ok_or(ProofVerifyError::InternalError))
216 .collect::<Result<Vec<_>, _>>()?;
217
218 let G_hat = GroupElement::vartime_multiscalar_mul(s.iter(), G.iter());
219 let a_hat = inner_product(a, &s);
220
221 let Gamma_hat = GroupElement::vartime_multiscalar_mul(
222 u_sq
223 .iter()
224 .chain(u_inv_sq.iter())
225 .chain(iter::once(&Scalar::one())),
226 Ls.iter().chain(Rs.iter()).chain(iter::once(Gamma)),
227 );
228
229 Ok((G_hat, Gamma_hat, a_hat))
230 }
231}
232
233/// Computes an inner product of two vectors
234/// \\[
235/// {\langle {\mathbf{a}}, {\mathbf{b}} \rangle} = \sum\_{i=0}^{n-1} a\_i \cdot b\_i.
236/// \\]
237/// Panics if the lengths of \\(\mathbf{a}\\) and \\(\mathbf{b}\\) are not equal.
238pub fn inner_product(a: &[Scalar], b: &[Scalar]) -> Scalar {
239 let mut out = Scalar::zero();
240 if a.len() != b.len() {
241 panic!("inner_product(a,b): lengths of vectors do not match");
242 }
243 for i in 0..a.len() {
244 out += a[i] * b[i];
245 }
246 out
247}