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::math::Math;
15use super::super::scalar::Scalar;
16use super::super::transcript::ProofTranscript;
17use ark_ff::{fields, Field};
18use ark_serialize::*;
19use ark_std::{One, Zero};
20use core::iter;
21use merlin::Transcript;
22use std::ops::MulAssign;
23
24#[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
25pub struct BulletReductionProof {
26 L_vec: Vec<CompressedGroup>,
27 R_vec: Vec<CompressedGroup>,
28}
29
30impl BulletReductionProof {
31 /// Create an inner-product proof.
32 ///
33 /// The proof is created with respect to the bases \\(G\\).
34 ///
35 /// The `transcript` is passed in as a parameter so that the
36 /// challenges depend on the *entire* transcript (including parent
37 /// protocols).
38 ///
39 /// The lengths of the vectors must all be the same, and must all be
40 /// either 0 or a power of 2.
41 pub fn prove(
42 transcript: &mut PoseidonTranscript,
43 Q: &GroupElement,
44 G_vec: &[GroupElement],
45 H: &GroupElement,
46 a_vec: &[Scalar],
47 b_vec: &[Scalar],
48 blind: &Scalar,
49 blinds_vec: &[(Scalar, Scalar)],
50 ) -> (
51 BulletReductionProof,
52 GroupElement,
53 Scalar,
54 Scalar,
55 GroupElement,
56 Scalar,
57 ) {
58 // Create slices G, H, a, b backed by their respective
59 // vectors. This lets us reslice as we compress the lengths
60 // of the vectors in the main loop below.
61 let mut G = &mut G_vec.to_owned()[..];
62 let mut a = &mut a_vec.to_owned()[..];
63 let mut b = &mut b_vec.to_owned()[..];
64
65 // All of the input vectors must have a length that is a power of two.
66 let mut n = G.len();
67 assert!(n.is_power_of_two());
68 let lg_n = n.log_2();
69
70 // All of the input vectors must have the same length.
71 assert_eq!(G.len(), n);
72 assert_eq!(a.len(), n);
73 assert_eq!(b.len(), n);
74 assert_eq!(blinds_vec.len(), 2 * lg_n);
75
76 let mut L_vec = Vec::with_capacity(lg_n);
77 let mut R_vec = Vec::with_capacity(lg_n);
78 let mut blinds_iter = blinds_vec.iter();
79 let mut blind_fin = *blind;
80
81 while n != 1 {
82 n /= 2;
83 let (a_L, a_R) = a.split_at_mut(n);
84 let (b_L, b_R) = b.split_at_mut(n);
85 let (G_L, G_R) = G.split_at_mut(n);
86
87 let c_L = inner_product(a_L, b_R);
88 let c_R = inner_product(a_R, b_L);
89
90 let (blind_L, blind_R) = blinds_iter.next().unwrap();
91
92 let L = GroupElement::vartime_multiscalar_mul(
93 a_L
94 .iter()
95 .chain(iter::once(&c_L))
96 .chain(iter::once(blind_L))
97 .map(|s| *s)
98 .collect::<Vec<Scalar>>()
99 .as_slice(),
100 G_R
101 .iter()
102 .chain(iter::once(Q))
103 .chain(iter::once(H))
104 .map(|p| *p)
105 .collect::<Vec<GroupElement>>()
106 .as_slice(),
107 );
108
109 let R = GroupElement::vartime_multiscalar_mul(
110 a_R
111 .iter()
112 .chain(iter::once(&c_R))
113 .chain(iter::once(blind_R))
114 .map(|s| *s)
115 .collect::<Vec<Scalar>>()
116 .as_slice(),
117 G_L
118 .iter()
119 .chain(iter::once(Q))
120 .chain(iter::once(H))
121 .map(|p| *p)
122 .collect::<Vec<GroupElement>>()
123 .as_slice(),
124 );
125
126 transcript.append_point(&L.compress());
127 transcript.append_point(&R.compress());
128
129 let u = transcript.challenge_scalar();
130 let u_inv = u.inverse().unwrap();
131
132 for i in 0..n {
133 a_L[i] = a_L[i] * u + u_inv * a_R[i];
134 b_L[i] = b_L[i] * u_inv + u * b_R[i];
135 G_L[i] = GroupElement::vartime_multiscalar_mul(&[u_inv, u], &[G_L[i], G_R[i]]);
136 }
137
138 blind_fin = blind_fin + u * u * blind_L + u_inv * u_inv * blind_R;
139
140 L_vec.push(L.compress());
141 R_vec.push(R.compress());
142
143 a = a_L;
144 b = b_L;
145 G = G_L;
146 }
147
148 let Gamma_hat =
149 GroupElement::vartime_multiscalar_mul(&[a[0], a[0] * b[0], blind_fin], &[G[0], *Q, *H]);
150
151 (
152 BulletReductionProof { L_vec, R_vec },
153 Gamma_hat,
154 a[0],
155 b[0],
156 G[0],
157 blind_fin,
158 )
159 }
160
161 /// Computes three vectors of verification scalars \\([u\_{i}^{2}]\\), \\([u\_{i}^{-2}]\\) and \\([s\_{i}]\\) for combined multiscalar multiplication
162 /// in a parent protocol. See [inner product protocol notes](index.html#verification-equation) for details.
163 /// The verifier must provide the input length \\(n\\) explicitly to avoid unbounded allocation within the inner product proof.
164 fn verification_scalars(
165 &self,
166 n: usize,
167 transcript: &mut PoseidonTranscript,
168 ) -> Result<(Vec<Scalar>, Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
169 let lg_n = self.L_vec.len();
170 if lg_n >= 32 {
171 // 4 billion multiplications should be enough for anyone
172 // and this check prevents overflow in 1<<lg_n below.
173 return Err(ProofVerifyError::InternalError);
174 }
175 if n != (1 << lg_n) {
176 return Err(ProofVerifyError::InternalError);
177 }
178
179 // 1. Recompute x_k,...,x_1 based on the proof transcript
180 let mut challenges = Vec::with_capacity(lg_n);
181 for (L, R) in self.L_vec.iter().zip(self.R_vec.iter()) {
182 transcript.append_point(L);
183 transcript.append_point(R);
184 challenges.push(transcript.challenge_scalar());
185 }
186
187 // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
188 let mut challenges_inv: Vec<Scalar> = challenges.clone();
189
190 ark_ff::fields::batch_inversion(&mut challenges_inv);
191 let mut allinv: Scalar = Scalar::one();
192 for c in challenges.iter().filter(|s| !s.is_zero()) {
193 allinv.mul_assign(c);
194 }
195 allinv = allinv.inverse().unwrap();
196
197 // 3. Compute u_i^2 and (1/u_i)^2
198 for i in 0..lg_n {
199 challenges[i] = challenges[i].square();
200 challenges_inv[i] = challenges_inv[i].square();
201 }
202 let challenges_sq = challenges;
203 let challenges_inv_sq = challenges_inv;
204
205 // 4. Compute s values inductively.
206 let mut s = Vec::with_capacity(n);
207 s.push(allinv);
208 for i in 1..n {
209 let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
210 let k = 1 << lg_i;
211 // The challenges are stored in "creation order" as [u_k,...,u_1],
212 // so u_{lg(i)+1} = is indexed by (lg_n-1) - lg_i
213 let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
214 s.push(s[i - k] * u_lg_i_sq);
215 }
216
217 Ok((challenges_sq, challenges_inv_sq, s))
218 }
219
220 /// This method is for testing that proof generation work,
221 /// but for efficiency the actual protocols would use `verification_scalars`
222 /// method to combine inner product verification with other checks
223 /// in a single multiscalar multiplication.
224 pub fn verify(
225 &self,
226 n: usize,
227 a: &[Scalar],
228 transcript: &mut PoseidonTranscript,
229 Gamma: &GroupElement,
230 G: &[GroupElement],
231 ) -> Result<(GroupElement, GroupElement, Scalar), ProofVerifyError> {
232 let (u_sq, u_inv_sq, s) = self.verification_scalars(n, transcript)?;
233
234 let Ls = self
235 .L_vec
236 .iter()
237 .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
238 .collect::<Result<Vec<_>, _>>()?;
239
240 let Rs = self
241 .R_vec
242 .iter()
243 .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
244 .collect::<Result<Vec<_>, _>>()?;
245
246 let G_hat = GroupElement::vartime_multiscalar_mul(s.as_slice(), G);
247 let a_hat = inner_product(a, &s);
248
249 let Gamma_hat = GroupElement::vartime_multiscalar_mul(
250 u_sq
251 .iter()
252 .chain(u_inv_sq.iter())
253 .chain(iter::once(&Scalar::one()))
254 .map(|s| *s)
255 .collect::<Vec<Scalar>>()
256 .as_slice(),
257 Ls.iter()
258 .chain(Rs.iter())
259 .chain(iter::once(Gamma))
260 .map(|p| *p)
261 .collect::<Vec<GroupElement>>()
262 .as_slice(),
263 );
264
265 Ok((G_hat, Gamma_hat, a_hat))
266 }
267}
268
269/// Computes an inner product of two vectors
270/// \\[
271/// {\langle {\mathbf{a}}, {\mathbf{b}} \rangle} = \sum\_{i=0}^{n-1} a\_i \cdot b\_i.
272/// \\]
273/// Panics if the lengths of \\(\mathbf{a}\\) and \\(\mathbf{b}\\) are not equal.
274pub fn inner_product(a: &[Scalar], b: &[Scalar]) -> Scalar {
275 assert!(
276 a.len() == b.len(),
277 "inner_product(a,b): lengths of vectors do not match"
278 );
279 let mut out = Scalar::zero();
280 for i in 0..a.len() {
281 out += a[i] * b[i];
282 }
283 out
284}