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_sum<F>(
130 claim: &G::Scalar,
131 num_rounds: usize,
132 poly_A: &mut MultilinearPolynomial<G::Scalar>,
133 poly_B: &mut MultilinearPolynomial<G::Scalar>,
134 poly_C: &mut MultilinearPolynomial<G::Scalar>,
135 poly_D: &mut MultilinearPolynomial<G::Scalar>,
136 comb_func: F,
137 transcript: &mut G::TE,
138 ) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError>
139 where
140 F: Fn(&G::Scalar, &G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar + Sync,
141 {
142 let mut r: Vec<G::Scalar> = Vec::new();
143 let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
144 let mut claim_per_round = *claim;
145 for _ in 0..num_rounds {
146 let poly = {
147 let len = poly_A.len() / 2;
148
149 // Make an iterator returning the contributions to the evaluations
150 let (eval_point_0, eval_point_2) = (0..len)
151 .into_par_iter()
152 .map(|i| {
153 // eval 0: bound_func is A(low)
154 let eval_point_0 = comb_func(&poly_A[i], &poly_B[i], &poly_C[i], &poly_D[i]);
155
156 // eval 2: bound_func is -A(low) + 2*A(high)
157 let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
158 let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
159 let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
160 let poly_D_bound_point = poly_D[len + i] + poly_D[len + i] - poly_D[i];
161 let eval_point_2 = comb_func(
162 &poly_A_bound_point,
163 &poly_B_bound_point,
164 &poly_C_bound_point,
165 &poly_D_bound_point,
166 );
167 (eval_point_0, eval_point_2)
168 })
169 .reduce(
170 || (G::Scalar::zero(), G::Scalar::zero()),
171 |a, b| (a.0 + b.0, a.1 + b.1),
172 );
173
174 let evals = vec![eval_point_0, claim_per_round - eval_point_0, eval_point_2];
175 UniPoly::from_evals(&evals)
176 };
177
178 // append the prover's message to the transcript
179 transcript.absorb(b"p", &poly);
180
181 // derive the verifier's challenge for the next round
182 let r_i = transcript.squeeze(b"c")?;
183 r.push(r_i);
184 polys.push(poly.compress());
185
186 // Set up next round
187 claim_per_round = poly.evaluate(&r_i);
188
189 // bound all tables to the verifier's challenege
190 poly_A.bound_poly_var_top(&r_i);
191 poly_B.bound_poly_var_top(&r_i);
192 poly_C.bound_poly_var_top(&r_i);
193 poly_D.bound_poly_var_top(&r_i);
194 }
195
196 Ok((
197 SumcheckProof {
198 compressed_polys: polys,
199 },
200 r,
201 vec![poly_A[0], poly_B[0], poly_C[0], poly_D[0]],
202 ))
203 }
204
205 pub fn prove_cubic_with_additive_term<F>(
206 claim: &G::Scalar,
207 num_rounds: usize,
208 poly_A: &mut MultilinearPolynomial<G::Scalar>,
209 poly_B: &mut MultilinearPolynomial<G::Scalar>,
210 poly_C: &mut MultilinearPolynomial<G::Scalar>,
211 poly_D: &mut MultilinearPolynomial<G::Scalar>,
212 comb_func: F,
213 transcript: &mut G::TE,
214 ) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError>
215 where
216 F: Fn(&G::Scalar, &G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar + Sync,
217 {
218 let mut r: Vec<G::Scalar> = Vec::new();
219 let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
220 let mut claim_per_round = *claim;
221
222 for _ in 0..num_rounds {
223 let poly = {
224 let len = poly_A.len() / 2;
225
226 // Make an iterator returning the contributions to the evaluations
227 let (eval_point_0, eval_point_2, eval_point_3) = (0..len)
228 .into_par_iter()
229 .map(|i| {
230 // eval 0: bound_func is A(low)
231 let eval_point_0 = comb_func(&poly_A[i], &poly_B[i], &poly_C[i], &poly_D[i]);
232
233 // eval 2: bound_func is -A(low) + 2*A(high)
234 let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
235 let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
236 let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
237 let poly_D_bound_point = poly_D[len + i] + poly_D[len + i] - poly_D[i];
238 let eval_point_2 = comb_func(
239 &poly_A_bound_point,
240 &poly_B_bound_point,
241 &poly_C_bound_point,
242 &poly_D_bound_point,
243 );
244
245 // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
246 let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
247 let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
248 let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
249 let poly_D_bound_point = poly_D_bound_point + poly_D[len + i] - poly_D[i];
250 let eval_point_3 = comb_func(
251 &poly_A_bound_point,
252 &poly_B_bound_point,
253 &poly_C_bound_point,
254 &poly_D_bound_point,
255 );
256 (eval_point_0, eval_point_2, eval_point_3)
257 })
258 .reduce(
259 || (G::Scalar::zero(), G::Scalar::zero(), G::Scalar::zero()),
260 |a, b| (a.0 + b.0, a.1 + b.1, a.2 + b.2),
261 );
262
263 let evals = vec![
264 eval_point_0,
265 claim_per_round - eval_point_0,
266 eval_point_2,
267 eval_point_3,
268 ];
269 UniPoly::from_evals(&evals)
270 };
271
272 // append the prover's message to the transcript
273 transcript.absorb(b"p", &poly);
274
275 //derive the verifier's challenge for the next round
276 let r_i = transcript.squeeze(b"c")?;
277 r.push(r_i);
278 polys.push(poly.compress());
279
280 // Set up next round
281 claim_per_round = poly.evaluate(&r_i);
282
283 // bound all tables to the verifier's challenege
284 poly_A.bound_poly_var_top(&r_i);
285 poly_B.bound_poly_var_top(&r_i);
286 poly_C.bound_poly_var_top(&r_i);
287 poly_D.bound_poly_var_top(&r_i);
288 }
289
290 Ok((
291 SumcheckProof {
292 compressed_polys: polys,
293 },
294 r,
295 vec![poly_A[0], poly_B[0], poly_C[0], poly_D[0]],
296 ))
297 }
298}
299
300// ax^2 + bx + c stored as vec![a,b,c]
301// ax^3 + bx^2 + cx + d stored as vec![a,b,c,d]
302#[derive(Debug)]
303pub struct UniPoly<G: Group> {
304 coeffs: Vec<G::Scalar>,
305}
306
307// ax^2 + bx + c stored as vec![a,c]
308// ax^3 + bx^2 + cx + d stored as vec![a,c,d]
309#[derive(Clone, Debug, Serialize, Deserialize)]
310pub struct CompressedUniPoly<G: Group> {
311 coeffs_except_linear_term: Vec<G::Scalar>,
312 _p: PhantomData<G>,
313}
314
315impl<G: Group> UniPoly<G> {
316 pub fn from_evals(evals: &[G::Scalar]) -> Self {
317 // we only support degree-2 or degree-3 univariate polynomials
318 assert!(evals.len() == 3 || evals.len() == 4);
319 let coeffs = if evals.len() == 3 {
320 // ax^2 + bx + c
321 let two_inv = G::Scalar::from(2).invert().unwrap();
322
323 let c = evals[0];
324 let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
325 let b = evals[1] - c - a;
326 vec![c, b, a]
327 } else {
328 // ax^3 + bx^2 + cx + d
329 let two_inv = G::Scalar::from(2).invert().unwrap();
330 let six_inv = G::Scalar::from(6).invert().unwrap();
331
332 let d = evals[0];
333 let a = six_inv
334 * (evals[3] - evals[2] - evals[2] - evals[2] + evals[1] + evals[1] + evals[1] - evals[0]);
335 let b = two_inv
336 * (evals[0] + evals[0] - evals[1] - evals[1] - evals[1] - evals[1] - evals[1]
337 + evals[2]
338 + evals[2]
339 + evals[2]
340 + evals[2]
341 - evals[3]);
342 let c = evals[1] - d - a - b;
343 vec![d, c, b, a]
344 };
345
346 UniPoly { coeffs }
347 }
348
349 pub fn degree(&self) -> usize {
350 self.coeffs.len() - 1
351 }
352
353 pub fn eval_at_zero(&self) -> G::Scalar {
354 self.coeffs[0]
355 }
356
357 pub fn eval_at_one(&self) -> G::Scalar {
358 (0..self.coeffs.len())
359 .into_par_iter()
360 .map(|i| self.coeffs[i])
361 .reduce(G::Scalar::zero, |a, b| a + b)
362 }
363
364 pub fn evaluate(&self, r: &G::Scalar) -> G::Scalar {
365 let mut eval = self.coeffs[0];
366 let mut power = *r;
367 for coeff in self.coeffs.iter().skip(1) {
368 eval += power * coeff;
369 power *= r;
370 }
371 eval
372 }
373
374 pub fn compress(&self) -> CompressedUniPoly<G> {
375 let coeffs_except_linear_term = [&self.coeffs[0..1], &self.coeffs[2..]].concat();
376 assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
377 CompressedUniPoly {
378 coeffs_except_linear_term,
379 _p: Default::default(),
380 }
381 }
382}
383
384impl<G: Group> CompressedUniPoly<G> {
385 // we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
386 // linear_term = hint - 2 * constant_term - deg2 term - deg3 term
387 pub fn decompress(&self, hint: &G::Scalar) -> UniPoly<G> {
388 let mut linear_term =
389 *hint - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
390 for i in 1..self.coeffs_except_linear_term.len() {
391 linear_term -= self.coeffs_except_linear_term[i];
392 }
393
394 let mut coeffs: Vec<G::Scalar> = Vec::new();
395 coeffs.extend(vec![&self.coeffs_except_linear_term[0]]);
396 coeffs.extend(vec![&linear_term]);
397 coeffs.extend(self.coeffs_except_linear_term[1..].to_vec());
398 assert_eq!(self.coeffs_except_linear_term.len() + 1, coeffs.len());
399 UniPoly { coeffs }
400 }
401}
402
403impl<G: Group> TranscriptReprTrait<G> for UniPoly<G> {
404 fn to_transcript_bytes(&self) -> Vec<u8> {
405 let coeffs = self.compress().coeffs_except_linear_term;
406 coeffs.as_slice().to_transcript_bytes()
407 }
408}