testudo/src/nizk/bullet.rs
src/nizk/bullet.rsRaw
1#![allow(non_snake_case)]
2
3use super::super::errors::ProofVerifyError;
4use super::super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
5use super::super::math::Math;
6use super::super::scalar::Scalar;
7use super::super::transcript::ProofTranscript;
8use merlin::Transcript;
9use serde::{Deserialize, Serialize};
10use std::iter;
11
12#[derive(Debug, Serialize, Deserialize)]
13pub struct BulletReductionProof {
14 L_vec: Vec<CompressedGroup>,
15 R_vec: Vec<CompressedGroup>,
16}
17
18impl BulletReductionProof {
19 /// Create an inner-product proof.
20 ///
21 /// The proof is created with respect to the bases \\(G\\).
22 ///
23 /// The `transcript` is passed in as a parameter so that the
24 /// challenges depend on the *entire* transcript (including parent
25 /// protocols).
26 ///
27 /// The lengths of the vectors must all be the same, and must all be
28 /// either 0 or a power of 2.
29 pub fn prove(
30 transcript: &mut Transcript,
31 Q: &GroupElement,
32 G_vec: &Vec<GroupElement>,
33 H: &GroupElement,
34 a_vec: &Vec<Scalar>,
35 b_vec: &Vec<Scalar>,
36 blind: &Scalar,
37 blinds_vec: &Vec<(Scalar, Scalar)>,
38 ) -> (
39 BulletReductionProof,
40 GroupElement,
41 Scalar,
42 Scalar,
43 GroupElement,
44 Scalar,
45 ) {
46 // Create slices G, H, a, b backed by their respective
47 // vectors. This lets us reslice as we compress the lengths
48 // of the vectors in the main loop below.
49 let mut G = &mut G_vec.clone()[..];
50 let mut a = &mut a_vec.clone()[..];
51 let mut b = &mut b_vec.clone()[..];
52
53 // All of the input vectors must have a length that is a power of two.
54 let mut n = G.len();
55 assert!(n.is_power_of_two());
56 let lg_n = n.log2();
57
58 let G_factors: Vec<Scalar> = iter::repeat(Scalar::one()).take(n).collect();
59
60 // All of the input vectors must have the same length.
61 assert_eq!(G.len(), n);
62 assert_eq!(a.len(), n);
63 assert_eq!(b.len(), n);
64 assert_eq!(G_factors.len(), n);
65 assert_eq!(blinds_vec.len(), 2 * lg_n);
66
67 //transcript.innerproduct_domain_sep(n as u64);
68
69 let mut L_vec = Vec::with_capacity(lg_n);
70 let mut R_vec = Vec::with_capacity(lg_n);
71 let mut blinds_iter = blinds_vec.iter();
72 let mut blind_fin = *blind;
73
74 while n != 1 {
75 n = n / 2;
76 let (a_L, a_R) = a.split_at_mut(n);
77 let (b_L, b_R) = b.split_at_mut(n);
78 let (G_L, G_R) = G.split_at_mut(n);
79
80 let c_L = inner_product(&a_L, &b_R);
81 let c_R = inner_product(&a_R, &b_L);
82
83 let (blind_L, blind_R) = blinds_iter.next().unwrap();
84
85 let L = GroupElement::vartime_multiscalar_mul(
86 a_L
87 .iter()
88 .chain(iter::once(&c_L))
89 .chain(iter::once(blind_L)),
90 G_R.iter().chain(iter::once(Q)).chain(iter::once(H)),
91 );
92
93 let R = GroupElement::vartime_multiscalar_mul(
94 a_R
95 .iter()
96 .chain(iter::once(&c_R))
97 .chain(iter::once(blind_R)),
98 G_L.iter().chain(iter::once(Q)).chain(iter::once(H)),
99 );
100
101 transcript.append_point(b"L", &L.compress());
102 transcript.append_point(b"R", &R.compress());
103
104 let u = transcript.challenge_scalar(b"u");
105 let u_inv = u.invert().unwrap();
106
107 for i in 0..n {
108 a_L[i] = a_L[i] * u + u_inv * a_R[i];
109 b_L[i] = b_L[i] * u_inv + u * b_R[i];
110 G_L[i] = GroupElement::vartime_multiscalar_mul(&[u_inv, u], &[G_L[i], G_R[i]]);
111 }
112
113 blind_fin = blind_fin + blind_L * &u * &u + blind_R * &u_inv * &u_inv;
114
115 L_vec.push(L.compress());
116 R_vec.push(R.compress());
117
118 a = a_L;
119 b = b_L;
120 G = G_L;
121 }
122
123 let Gamma_hat =
124 GroupElement::vartime_multiscalar_mul(&[a[0], a[0] * b[0], blind_fin], &[G[0], *Q, *H]);
125
126 (
127 BulletReductionProof {
128 L_vec: L_vec,
129 R_vec: R_vec,
130 },
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);
152 }
153 if n != (1 << lg_n) {
154 return Err(ProofVerifyError);
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] * challenges[i];
172 challenges_inv[i] = challenges_inv[i] * challenges_inv[i];
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: &Vec<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))
210 .collect::<Result<Vec<_>, _>>()?;
211
212 let Rs = self
213 .R_vec
214 .iter()
215 .map(|p| p.decompress().ok_or(ProofVerifyError))
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}