Nova/src/spartan/sumcheck.rs
src/spartan/sumcheck.rsRaw
1#![allow(clippy::too_many_arguments)]
2#![allow(clippy::type_complexity)]
3use super::polynomial::MultilinearPolynomial;
4use crate::errors::NovaError;
5use crate::traits::{Group, TranscriptEngineTrait, TranscriptReprTrait};
6use core::marker::PhantomData;
7use ff::Field;
8use rayon::prelude::*;
9use serde::{Deserialize, Serialize};
10
11#[derive(Clone, Debug, Serialize, Deserialize)]
12#[serde(bound = "")]
13pub(crate) struct SumcheckProof<G: Group> {
14 compressed_polys: Vec<CompressedUniPoly<G>>,
15}
16
17impl<G: Group> SumcheckProof<G> {
18 pub fn new(compressed_polys: Vec<CompressedUniPoly<G>>) -> Self {
19 Self { compressed_polys }
20 }
21
22 pub fn verify(
23 &self,
24 claim: G::Scalar,
25 num_rounds: usize,
26 degree_bound: usize,
27 transcript: &mut G::TE,
28 ) -> Result<(G::Scalar, Vec<G::Scalar>), NovaError> {
29 let mut e = claim;
30 let mut r: Vec<G::Scalar> = Vec::new();
31
32 // verify that there is a univariate polynomial for each round
33 if self.compressed_polys.len() != num_rounds {
34 return Err(NovaError::InvalidSumcheckProof);
35 }
36
37 for i in 0..self.compressed_polys.len() {
38 let poly = self.compressed_polys[i].decompress(&e);
39
40 // verify degree bound
41 if poly.degree() != degree_bound {
42 return Err(NovaError::InvalidSumcheckProof);
43 }
44
45 // we do not need to check if poly(0) + poly(1) = e, as
46 // decompress() call above already ensures that hods
47 debug_assert_eq!(poly.eval_at_zero() + poly.eval_at_one(), e);
48
49 // append the prover's message to the transcript
50 transcript.absorb(b"p", &poly);
51
52 //derive the verifier's challenge for the next round
53 let r_i = transcript.squeeze(b"c")?;
54
55 r.push(r_i);
56
57 // evaluate the claimed degree-ell polynomial at r_i
58 e = poly.evaluate(&r_i);
59 }
60
61 Ok((e, r))
62 }
63
64 pub fn prove_quad<F>(
65 claim: &G::Scalar,
66 num_rounds: usize,
67 poly_A: &mut MultilinearPolynomial<G::Scalar>,
68 poly_B: &mut MultilinearPolynomial<G::Scalar>,
69 comb_func: F,
70 transcript: &mut G::TE,
71 ) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError>
72 where
73 F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar + Sync,
74 {
75 let mut r: Vec<G::Scalar> = Vec::new();
76 let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
77 let mut claim_per_round = *claim;
78 for _ in 0..num_rounds {
79 let poly = {
80 let len = poly_A.len() / 2;
81
82 // Make an iterator returning the contributions to the evaluations
83 let (eval_point_0, eval_point_2) = (0..len)
84 .into_par_iter()
85 .map(|i| {
86 // eval 0: bound_func is A(low)
87 let eval_point_0 = comb_func(&poly_A[i], &poly_B[i]);
88
89 // eval 2: bound_func is -A(low) + 2*A(high)
90 let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
91 let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
92 let eval_point_2 = comb_func(&poly_A_bound_point, &poly_B_bound_point);
93 (eval_point_0, eval_point_2)
94 })
95 .reduce(
96 || (G::Scalar::zero(), G::Scalar::zero()),
97 |a, b| (a.0 + b.0, a.1 + b.1),
98 );
99
100 let evals = vec![eval_point_0, claim_per_round - eval_point_0, eval_point_2];
101 UniPoly::from_evals(&evals)
102 };
103
104 // append the prover's message to the transcript
105 transcript.absorb(b"p", &poly);
106
107 //derive the verifier's challenge for the next round
108 let r_i = transcript.squeeze(b"c")?;
109 r.push(r_i);
110 polys.push(poly.compress());
111
112 // Set up next round
113 claim_per_round = poly.evaluate(&r_i);
114
115 // bound all tables to the verifier's challenege
116 poly_A.bound_poly_var_top(&r_i);
117 poly_B.bound_poly_var_top(&r_i);
118 }
119
120 Ok((
121 SumcheckProof {
122 compressed_polys: polys,
123 },
124 r,
125 vec![poly_A[0], poly_B[0]],
126 ))
127 }
128
129 pub fn prove_quad_batch<F>(
130 claim: &G::Scalar,
131 num_rounds: usize,
132 poly_A_vec: &mut Vec<MultilinearPolynomial<G::Scalar>>,
133 poly_B_vec: &mut Vec<MultilinearPolynomial<G::Scalar>>,
134 coeffs: &[G::Scalar],
135 comb_func: F,
136 transcript: &mut G::TE,
137 ) -> Result<(Self, Vec<G::Scalar>, (Vec<G::Scalar>, Vec<G::Scalar>)), NovaError>
138 where
139 F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar,
140 {
141 let mut e = *claim;
142 let mut r: Vec<G::Scalar> = Vec::new();
143 let mut quad_polys: Vec<CompressedUniPoly<G>> = Vec::new();
144
145 for _j in 0..num_rounds {
146 let mut evals: Vec<(G::Scalar, G::Scalar)> = Vec::new();
147
148 for (poly_A, poly_B) in poly_A_vec.iter().zip(poly_B_vec.iter()) {
149 let mut eval_point_0 = G::Scalar::zero();
150 let mut eval_point_2 = G::Scalar::zero();
151
152 let len = poly_A.len() / 2;
153 for i in 0..len {
154 // eval 0: bound_func is A(low)
155 eval_point_0 += comb_func(&poly_A[i], &poly_B[i]);
156
157 // eval 2: bound_func is -A(low) + 2*A(high)
158 let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
159 let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
160 eval_point_2 += comb_func(&poly_A_bound_point, &poly_B_bound_point);
161 }
162
163 evals.push((eval_point_0, eval_point_2));
164 }
165
166 let evals_combined_0 = (0..evals.len())
167 .map(|i| evals[i].0 * coeffs[i])
168 .fold(G::Scalar::zero(), |acc, item| acc + item);
169 let evals_combined_2 = (0..evals.len())
170 .map(|i| evals[i].1 * coeffs[i])
171 .fold(G::Scalar::zero(), |acc, item| acc + item);
172
173 let evals = vec![evals_combined_0, e - evals_combined_0, evals_combined_2];
174 let poly = UniPoly::from_evals(&evals);
175
176 // append the prover's message to the transcript
177 transcript.absorb(b"p", &poly);
178
179 // derive the verifier's challenge for the next round
180 let r_i = transcript.squeeze(b"c")?;
181 r.push(r_i);
182
183 // bound all tables to the verifier's challenege
184 for (poly_A, poly_B) in poly_A_vec.iter_mut().zip(poly_B_vec.iter_mut()) {
185 poly_A.bound_poly_var_top(&r_i);
186 poly_B.bound_poly_var_top(&r_i);
187 }
188
189 e = poly.evaluate(&r_i);
190 quad_polys.push(poly.compress());
191 }
192
193 let poly_A_final = (0..poly_A_vec.len()).map(|i| poly_A_vec[i][0]).collect();
194 let poly_B_final = (0..poly_B_vec.len()).map(|i| poly_B_vec[i][0]).collect();
195 let claims_prod = (poly_A_final, poly_B_final);
196
197 Ok((SumcheckProof::new(quad_polys), r, claims_prod))
198 }
199
200 pub fn prove_cubic_with_additive_term<F>(
201 claim: &G::Scalar,
202 num_rounds: usize,
203 poly_A: &mut MultilinearPolynomial<G::Scalar>,
204 poly_B: &mut MultilinearPolynomial<G::Scalar>,
205 poly_C: &mut MultilinearPolynomial<G::Scalar>,
206 poly_D: &mut MultilinearPolynomial<G::Scalar>,
207 comb_func: F,
208 transcript: &mut G::TE,
209 ) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError>
210 where
211 F: Fn(&G::Scalar, &G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar + Sync,
212 {
213 let mut r: Vec<G::Scalar> = Vec::new();
214 let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
215 let mut claim_per_round = *claim;
216
217 for _ in 0..num_rounds {
218 let poly = {
219 let len = poly_A.len() / 2;
220
221 // Make an iterator returning the contributions to the evaluations
222 let (eval_point_0, eval_point_2, eval_point_3) = (0..len)
223 .into_par_iter()
224 .map(|i| {
225 // eval 0: bound_func is A(low)
226 let eval_point_0 = comb_func(&poly_A[i], &poly_B[i], &poly_C[i], &poly_D[i]);
227
228 // eval 2: bound_func is -A(low) + 2*A(high)
229 let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
230 let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
231 let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
232 let poly_D_bound_point = poly_D[len + i] + poly_D[len + i] - poly_D[i];
233 let eval_point_2 = comb_func(
234 &poly_A_bound_point,
235 &poly_B_bound_point,
236 &poly_C_bound_point,
237 &poly_D_bound_point,
238 );
239
240 // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
241 let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
242 let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
243 let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
244 let poly_D_bound_point = poly_D_bound_point + poly_D[len + i] - poly_D[i];
245 let eval_point_3 = comb_func(
246 &poly_A_bound_point,
247 &poly_B_bound_point,
248 &poly_C_bound_point,
249 &poly_D_bound_point,
250 );
251 (eval_point_0, eval_point_2, eval_point_3)
252 })
253 .reduce(
254 || (G::Scalar::zero(), G::Scalar::zero(), G::Scalar::zero()),
255 |a, b| (a.0 + b.0, a.1 + b.1, a.2 + b.2),
256 );
257
258 let evals = vec![
259 eval_point_0,
260 claim_per_round - eval_point_0,
261 eval_point_2,
262 eval_point_3,
263 ];
264 UniPoly::from_evals(&evals)
265 };
266
267 // append the prover's message to the transcript
268 transcript.absorb(b"p", &poly);
269
270 //derive the verifier's challenge for the next round
271 let r_i = transcript.squeeze(b"c")?;
272 r.push(r_i);
273 polys.push(poly.compress());
274
275 // Set up next round
276 claim_per_round = poly.evaluate(&r_i);
277
278 // bound all tables to the verifier's challenege
279 poly_A.bound_poly_var_top(&r_i);
280 poly_B.bound_poly_var_top(&r_i);
281 poly_C.bound_poly_var_top(&r_i);
282 poly_D.bound_poly_var_top(&r_i);
283 }
284
285 Ok((
286 SumcheckProof {
287 compressed_polys: polys,
288 },
289 r,
290 vec![poly_A[0], poly_B[0], poly_C[0], poly_D[0]],
291 ))
292 }
293}
294
295// ax^2 + bx + c stored as vec![a,b,c]
296// ax^3 + bx^2 + cx + d stored as vec![a,b,c,d]
297#[derive(Debug)]
298pub struct UniPoly<G: Group> {
299 coeffs: Vec<G::Scalar>,
300}
301
302// ax^2 + bx + c stored as vec![a,c]
303// ax^3 + bx^2 + cx + d stored as vec![a,c,d]
304#[derive(Clone, Debug, Serialize, Deserialize)]
305pub struct CompressedUniPoly<G: Group> {
306 coeffs_except_linear_term: Vec<G::Scalar>,
307 _p: PhantomData<G>,
308}
309
310impl<G: Group> UniPoly<G> {
311 pub fn from_evals(evals: &[G::Scalar]) -> Self {
312 // we only support degree-2 or degree-3 univariate polynomials
313 assert!(evals.len() == 3 || evals.len() == 4);
314 let coeffs = if evals.len() == 3 {
315 // ax^2 + bx + c
316 let two_inv = G::Scalar::from(2).invert().unwrap();
317
318 let c = evals[0];
319 let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
320 let b = evals[1] - c - a;
321 vec![c, b, a]
322 } else {
323 // ax^3 + bx^2 + cx + d
324 let two_inv = G::Scalar::from(2).invert().unwrap();
325 let six_inv = G::Scalar::from(6).invert().unwrap();
326
327 let d = evals[0];
328 let a = six_inv
329 * (evals[3] - evals[2] - evals[2] - evals[2] + evals[1] + evals[1] + evals[1] - evals[0]);
330 let b = two_inv
331 * (evals[0] + evals[0] - evals[1] - evals[1] - evals[1] - evals[1] - evals[1]
332 + evals[2]
333 + evals[2]
334 + evals[2]
335 + evals[2]
336 - evals[3]);
337 let c = evals[1] - d - a - b;
338 vec![d, c, b, a]
339 };
340
341 UniPoly { coeffs }
342 }
343
344 pub fn degree(&self) -> usize {
345 self.coeffs.len() - 1
346 }
347
348 pub fn eval_at_zero(&self) -> G::Scalar {
349 self.coeffs[0]
350 }
351
352 pub fn eval_at_one(&self) -> G::Scalar {
353 (0..self.coeffs.len())
354 .into_par_iter()
355 .map(|i| self.coeffs[i])
356 .reduce(G::Scalar::zero, |a, b| a + b)
357 }
358
359 pub fn evaluate(&self, r: &G::Scalar) -> G::Scalar {
360 let mut eval = self.coeffs[0];
361 let mut power = *r;
362 for coeff in self.coeffs.iter().skip(1) {
363 eval += power * coeff;
364 power *= r;
365 }
366 eval
367 }
368
369 pub fn compress(&self) -> CompressedUniPoly<G> {
370 let coeffs_except_linear_term = [&self.coeffs[0..1], &self.coeffs[2..]].concat();
371 assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
372 CompressedUniPoly {
373 coeffs_except_linear_term,
374 _p: Default::default(),
375 }
376 }
377}
378
379impl<G: Group> CompressedUniPoly<G> {
380 // we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
381 // linear_term = hint - 2 * constant_term - deg2 term - deg3 term
382 pub fn decompress(&self, hint: &G::Scalar) -> UniPoly<G> {
383 let mut linear_term =
384 *hint - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
385 for i in 1..self.coeffs_except_linear_term.len() {
386 linear_term -= self.coeffs_except_linear_term[i];
387 }
388
389 let mut coeffs: Vec<G::Scalar> = Vec::new();
390 coeffs.extend(vec![&self.coeffs_except_linear_term[0]]);
391 coeffs.extend(vec![&linear_term]);
392 coeffs.extend(self.coeffs_except_linear_term[1..].to_vec());
393 assert_eq!(self.coeffs_except_linear_term.len() + 1, coeffs.len());
394 UniPoly { coeffs }
395 }
396}
397
398impl<G: Group> TranscriptReprTrait<G> for UniPoly<G> {
399 fn to_transcript_bytes(&self) -> Vec<u8> {
400 let coeffs = self.compress().coeffs_except_linear_term;
401 coeffs.as_slice().to_transcript_bytes()
402 }
403}