forked from privacy-scaling-explorations/halo2
-
Notifications
You must be signed in to change notification settings - Fork 40
/
commitment.rs
415 lines (350 loc) · 13.2 KB
/
commitment.rs
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
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
//! This module contains an implementation of the polynomial commitment scheme
//! described in the [Halo][halo] paper.
//!
//! [halo]: https://eprint.iacr.org/2019/1021
use super::{Coeff, LagrangeCoeff, Polynomial, MSM};
use crate::arithmetic::{
best_fft, best_multiexp, parallelize, CurveAffine, CurveExt, Engine, FieldExt, Group,
};
use crate::helpers::CurveRead;
use ff::{Field, PrimeField};
use group::{prime::PrimeCurveAffine, Curve, Group as _, GroupEncoding};
use rand_core::OsRng;
use std::marker::PhantomData;
use std::ops::{Add, AddAssign, Mul, MulAssign};
use std::io;
/// These are the prover parameters for the polynomial commitment scheme.
#[derive(Debug)]
pub struct Params<C: CurveAffine> {
pub(crate) k: u32,
pub(crate) n: u64,
pub(crate) g: Vec<C>,
pub(crate) g_lagrange: Vec<C>,
pub(crate) additional_data: Vec<u8>,
}
/// These are the verifier parameters for the polynomial commitment scheme.
#[derive(Debug)]
pub struct ParamsVerifier<E: Engine> {
pub(crate) k: u32,
pub(crate) n: u64,
pub(crate) g1: E::G1Affine,
pub(crate) g2: E::G2Affine,
pub(crate) s_g2: E::G2Affine,
pub(crate) g_lagrange: Vec<E::G1Affine>,
}
#[cfg(test)]
mod tests {
use pairing::arithmetic::CurveAffine;
use super::Params;
impl<C: CurveAffine> Params<C> {
pub fn do_this() {}
}
}
impl<C: CurveAffine> Params<C> {
/// Initializes parameters for the curve, Draws random toxic point inside of the function
/// MUST NOT be used in production
pub fn unsafe_setup<E: Engine>(k: u32) -> Params<E::G1Affine> {
// TODO: Make this function only available in test mod
// Largest root of unity exponent of the Engine is `2^E::Scalar::S`, so we can
// only support FFTs of polynomials below degree `2^E::Scalar::S`.
assert!(k <= E::Scalar::S);
let n: u64 = 1 << k;
// Calculate g = [G1, [s] G1, [s^2] G1, ..., [s^(n-1)] G1] in parallel.
let g1 = <E::G1Affine as PrimeCurveAffine>::generator();
let s = E::Scalar::random(OsRng);
let mut g_projective = vec![E::G1::group_zero(); n as usize];
parallelize(&mut g_projective, |g, start| {
let mut current_g: E::G1 = g1.into();
current_g *= s.pow_vartime(&[start as u64]);
for g in g.iter_mut() {
*g = current_g;
current_g *= s;
}
});
let g = {
let mut g = vec![E::G1Affine::identity(); n as usize];
parallelize(&mut g, |g, starts| {
E::G1::batch_normalize(&g_projective[starts..(starts + g.len())], g);
});
g
};
let mut g_lagrange_projective = vec![E::G1::group_zero(); n as usize];
let mut root = E::Scalar::ROOT_OF_UNITY_INV.invert().unwrap();
for _ in k..E::Scalar::S {
root = root.square();
}
let n_inv = Option::<E::Scalar>::from(E::Scalar::from(n).invert())
.expect("inversion should be ok for n = 1<<k");
let multiplier = (s.pow_vartime(&[n as u64]) - E::Scalar::one()) * n_inv;
parallelize(&mut g_lagrange_projective, |g, start| {
for (idx, g) in g.iter_mut().enumerate() {
let offset = start + idx;
let root_pow = root.pow_vartime(&[offset as u64]);
let scalar = multiplier * root_pow * (s - root_pow).invert().unwrap();
*g = g1 * scalar;
}
});
let g_lagrange = {
let mut g_lagrange = vec![E::G1Affine::identity(); n as usize];
parallelize(&mut g_lagrange, |g_lagrange, starts| {
E::G1::batch_normalize(
&g_lagrange_projective[starts..(starts + g_lagrange.len())],
g_lagrange,
);
});
drop(g_lagrange_projective);
g_lagrange
};
let g2 = <E::G2Affine as PrimeCurveAffine>::generator();
let s_g2 = g2 * s;
let additional_data = Vec::from(s_g2.to_bytes().as_ref());
Params {
k,
n,
g,
g_lagrange,
additional_data,
}
}
/// This computes a commitment to a polynomial described by the provided
/// slice of coefficients. The commitment will be blinded by the blinding
/// factor `r`.
pub fn commit(&self, poly: &Polynomial<C::Scalar, Coeff>) -> C::Curve {
let mut scalars = Vec::with_capacity(poly.len());
scalars.extend(poly.iter());
let bases = &self.g;
let size = scalars.len();
assert!(bases.len() >= size);
best_multiexp(&scalars, &bases[0..size])
}
/// This commits to a polynomial using its evaluations over the $2^k$ size
/// evaluation domain. The commitment will be blinded by the blinding factor
/// `r`.
pub fn commit_lagrange(&self, poly: &Polynomial<C::Scalar, LagrangeCoeff>) -> C::Curve {
let mut scalars = Vec::with_capacity(poly.len());
scalars.extend(poly.iter());
let bases = &self.g_lagrange;
let size = scalars.len();
assert!(bases.len() >= size);
best_multiexp(&scalars, &bases[0..size])
}
/// Generates an empty multiscalar multiplication struct using the
/// appropriate params.
pub fn empty_msm(&self) -> MSM<C> {
MSM::new()
}
/// Getter for g generators
pub fn get_g(&self) -> Vec<C> {
self.g.clone()
}
/// Writes params to a buffer.
pub fn write<W: io::Write>(&self, writer: &mut W) -> io::Result<()> {
writer.write_all(&self.k.to_le_bytes())?;
for el in &self.g {
writer.write_all(el.to_bytes().as_ref())?;
}
for el in &self.g_lagrange {
writer.write_all(el.to_bytes().as_ref())?;
}
let additional_data_len = self.additional_data.len() as u32;
writer.write_all(&additional_data_len.to_le_bytes())?;
writer.write_all(&self.additional_data)?;
Ok(())
}
/// Reads params from a buffer.
pub fn read<R: io::Read>(mut reader: R) -> io::Result<Self> {
let mut k = [0u8; 4];
reader.read_exact(&mut k[..])?;
let k = u32::from_le_bytes(k);
let n = 1 << k;
let load_points_from_file_parallelly = |reader: &mut R| -> io::Result<Vec<C>> {
let mut points_compressed: Vec<C::Repr> = vec![C::Repr::default(); n];
for points_compressed in points_compressed.iter_mut() {
reader.read_exact((*points_compressed).as_mut())?;
}
let mut points = vec![C::default(); n];
parallelize(&mut points, |points, chunks| {
for (i, point) in points.iter_mut().enumerate() {
*point = Option::from(C::from_bytes(&points_compressed[chunks + i])).unwrap();
}
});
Ok(points)
};
let g = load_points_from_file_parallelly(&mut reader)?;
let g_lagrange = load_points_from_file_parallelly(&mut reader)?;
let mut additional_data_len = [0u8; 4];
reader.read_exact(&mut additional_data_len[..])?;
let additional_data_len = u32::from_le_bytes(additional_data_len);
let mut additional_data = vec![0u8; additional_data_len as usize];
reader.read_exact(&mut additional_data[..])?;
Ok(Params {
k,
n: n as u64,
g,
g_lagrange,
additional_data,
})
}
/// Returns verifier params with size of Lagrange bases equal to number of public inputs
pub fn verifier<E: Engine<G1Affine = C>>(
&self,
public_inputs_size: usize,
) -> io::Result<ParamsVerifier<E>> {
assert!(public_inputs_size < self.n as usize);
let g_lagrange = self.g_lagrange[..public_inputs_size].to_vec();
let g2 = <E::G2Affine as PrimeCurveAffine>::generator();
let additional_data = self.additional_data.clone();
let s_g2 = E::G2Affine::read(&mut additional_data.as_slice())?;
Ok(ParamsVerifier {
k: self.k,
n: self.n,
g1: self.g[0],
g_lagrange,
g2,
s_g2,
})
}
}
/// Wrapper type around a blinding factor.
#[derive(Copy, Clone, Eq, PartialEq, Debug)]
pub struct Blind<F>(pub F);
impl<F: FieldExt> Default for Blind<F> {
fn default() -> Self {
Blind(F::one())
}
}
impl<F: FieldExt> Add for Blind<F> {
type Output = Self;
fn add(self, rhs: Blind<F>) -> Self {
Blind(self.0 + rhs.0)
}
}
impl<F: FieldExt> Mul for Blind<F> {
type Output = Self;
fn mul(self, rhs: Blind<F>) -> Self {
Blind(self.0 * rhs.0)
}
}
impl<F: FieldExt> AddAssign for Blind<F> {
fn add_assign(&mut self, rhs: Blind<F>) {
self.0 += rhs.0;
}
}
impl<F: FieldExt> MulAssign for Blind<F> {
fn mul_assign(&mut self, rhs: Blind<F>) {
self.0 *= rhs.0;
}
}
impl<F: FieldExt> AddAssign<F> for Blind<F> {
fn add_assign(&mut self, rhs: F) {
self.0 += rhs;
}
}
impl<F: FieldExt> MulAssign<F> for Blind<F> {
fn mul_assign(&mut self, rhs: F) {
self.0 *= rhs;
}
}
impl<E: Engine> ParamsVerifier<E> {
/// Returns maximum public input size allowed
pub fn public_inputs_size(&self) -> usize {
self.g_lagrange.len()
}
/// Generates an empty multiscalar multiplication struct using the
/// appropriate params.
pub fn empty_msm(&self) -> MSM<E::G1Affine> {
MSM::new()
}
/// Commits to a polynomial using its evaluations over the $2^k$ size
/// evaluation domain.
pub fn commit_lagrange(&self, scalars: Vec<E::Scalar>) -> E::G1 {
let bases = &self.g_lagrange;
let size = scalars.len();
assert!(bases.len() >= size);
best_multiexp(&scalars, &bases[0..size])
}
/// Writes params to a buffer.
pub fn write<W: io::Write>(&self, writer: &mut W) -> io::Result<()> {
writer.write_all(&self.k.to_le_bytes())?;
let public_inputs_size = self.public_inputs_size() as u32;
writer.write_all(&public_inputs_size.to_le_bytes())?;
writer.write_all(self.g1.to_bytes().as_ref())?;
writer.write_all(self.g2.to_bytes().as_ref())?;
writer.write_all(self.s_g2.to_bytes().as_ref())?;
for el in &self.g_lagrange {
writer.write_all(el.to_bytes().as_ref())?;
}
Ok(())
}
/// Reads params from a buffer.
pub fn read<R: io::Read>(mut reader: R) -> io::Result<Self> {
let mut k = [0u8; 4];
reader.read_exact(&mut k[..])?;
let k = u32::from_le_bytes(k);
let mut public_inputs_size = [0u8; 4];
reader.read_exact(&mut public_inputs_size[..])?;
let public_inputs_size = u32::from_le_bytes(public_inputs_size);
let n = 1 << k;
let g1 = E::G1Affine::read(&mut reader)?;
let g2 = E::G2Affine::read(&mut reader)?;
let s_g2 = E::G2Affine::read(&mut reader)?;
let g_lagrange: Vec<E::G1Affine> = (0..public_inputs_size)
.map(|_| E::G1Affine::read(&mut reader))
.collect::<Result<_, _>>()?;
Ok(ParamsVerifier {
k,
n,
g1,
g2,
s_g2,
g_lagrange,
})
}
}
#[cfg(test)]
use pairing::bn256::{Bn256, Fr, G1Affine};
#[test]
fn test_parameter_serialization() {
const K: u32 = 4;
let params0: Params<G1Affine> = Params::<G1Affine>::unsafe_setup::<Bn256>(K);
let mut data: Vec<u8> = Vec::new();
params0.write(&mut data).unwrap();
let params1: Params<G1Affine> = Params::read(&data[..]).unwrap();
assert_eq!(params0.k, params1.k);
assert_eq!(params0.n, params1.n);
assert_eq!(params0.g.len(), params1.g.len());
assert_eq!(params0.g_lagrange.len(), params1.g_lagrange.len());
assert_eq!(params0.g, params1.g);
assert_eq!(params0.g_lagrange, params1.g_lagrange);
assert_eq!(params0.additional_data, params1.additional_data);
let public_inputs_size = 2;
let verifier_params0: ParamsVerifier<Bn256> = params0.verifier(public_inputs_size).unwrap();
assert_eq!(verifier_params0.k, params1.k);
assert_eq!(verifier_params0.n, params1.n);
assert_eq!(verifier_params0.g_lagrange.len(), public_inputs_size);
assert_eq!(
verifier_params0.s_g2.to_bytes().as_ref(),
params0.additional_data
);
let mut data: Vec<u8> = Vec::new();
verifier_params0.write(&mut data).unwrap();
let verifier_params1: ParamsVerifier<Bn256> = ParamsVerifier::read(&data[..]).unwrap();
assert_eq!(verifier_params0.k, verifier_params1.k);
assert_eq!(verifier_params0.n, verifier_params1.n);
assert_eq!(verifier_params0.g1, verifier_params1.g1);
assert_eq!(verifier_params0.g2, verifier_params1.g2);
assert_eq!(verifier_params0.s_g2, verifier_params1.s_g2);
assert_eq!(verifier_params0.g_lagrange, verifier_params1.g_lagrange);
}
#[test]
fn test_commit_lagrange() {
const K: u32 = 6;
let params: Params<G1Affine> = Params::<G1Affine>::unsafe_setup::<Bn256>(K);
let domain = super::EvaluationDomain::new(1, K);
let mut a = domain.empty_lagrange();
for (i, a) in a.iter_mut().enumerate() {
*a = Fr::from(i as u64);
}
let b = domain.lagrange_to_coeff(a.clone());
assert_eq!(params.commit(&b), params.commit_lagrange(&a));
}