snarkvm_algorithms/polycommit/kzg10/
data_structures.rs

1// Copyright (c) 2019-2025 Provable Inc.
2// This file is part of the snarkVM library.
3
4// Licensed under the Apache License, Version 2.0 (the "License");
5// you may not use this file except in compliance with the License.
6// You may obtain a copy of the License at:
7
8// http://www.apache.org/licenses/LICENSE-2.0
9
10// Unless required by applicable law or agreed to in writing, software
11// distributed under the License is distributed on an "AS IS" BASIS,
12// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13// See the License for the specific language governing permissions and
14// limitations under the License.
15
16use crate::{
17    AlgebraicSponge,
18    fft::{DensePolynomial, EvaluationDomain},
19};
20use snarkvm_curves::{AffineCurve, PairingCurve, PairingEngine, ProjectiveCurve};
21use snarkvm_fields::{ConstraintFieldError, ToConstraintField, Zero};
22use snarkvm_parameters::mainnet::PowersOfG;
23use snarkvm_utilities::{
24    FromBytes,
25    ToBytes,
26    error,
27    into_io_error,
28    serialize::{CanonicalDeserialize, CanonicalSerialize, Compress, SerializationError, Valid, Validate},
29};
30
31use crate::srs::{UniversalProver, UniversalVerifier};
32use anyhow::Result;
33use core::ops::{Add, AddAssign};
34use rand::RngCore;
35use std::{
36    borrow::Cow,
37    collections::BTreeMap,
38    io,
39    io::{Read, Write},
40    ops::Range,
41    sync::Arc,
42};
43
44/// `UniversalParams` are the universal parameters for the KZG10 scheme.
45#[derive(Clone, Debug)]
46pub struct UniversalParams<E: PairingEngine> {
47    /// Group elements of the form `{ \beta^i G }`, where `i` ranges from 0 to
48    /// `degree`, and group elements of the form `{ \beta^i \gamma G }`,
49    /// where `i` ranges from 0 to `degree`. This struct provides an
50    /// abstraction over the powers which are located on-disk
51    /// to reduce memory usage.
52    powers: Arc<PowersOfG<E>>,
53    /// The generator of G2.
54    pub h: E::G2Affine,
55    /// The generator of G2, prepared for use in pairings.
56    pub prepared_h: <E::G2Affine as PairingCurve>::Prepared,
57    /// \beta times the above generator of G2, prepared for use in pairings.
58    pub prepared_beta_h: <E::G2Affine as PairingCurve>::Prepared,
59}
60
61impl<E: PairingEngine> UniversalParams<E> {
62    pub fn load() -> Result<Self> {
63        let powers = Arc::new(PowersOfG::<E>::load()?);
64        let h = E::G2Affine::prime_subgroup_generator();
65        let prepared_h = h.prepare();
66        let prepared_beta_h = powers.beta_h().prepare();
67
68        Ok(Self { powers, h, prepared_h, prepared_beta_h })
69    }
70
71    pub fn download_powers_for(&self, range: Range<usize>) -> Result<()> {
72        self.powers.download_powers_for(range)
73    }
74
75    pub fn lagrange_basis(&self, domain: EvaluationDomain<E::Fr>) -> Result<Vec<E::G1Affine>> {
76        let basis = domain
77            .ifft(&self.powers_of_beta_g(0, domain.size())?.iter().map(|e| (*e).to_projective()).collect::<Vec<_>>());
78        Ok(E::G1Projective::batch_normalization_into_affine(basis))
79    }
80
81    pub fn power_of_beta_g(&self, index: usize) -> Result<E::G1Affine> {
82        self.powers.power_of_beta_g(index)
83    }
84
85    pub fn powers_of_beta_g(&self, lower: usize, upper: usize) -> Result<Vec<E::G1Affine>> {
86        self.powers.powers_of_beta_g(lower..upper)
87    }
88
89    pub fn powers_of_beta_times_gamma_g(&self) -> &BTreeMap<usize, E::G1Affine> {
90        self.powers.powers_of_beta_gamma_g()
91    }
92
93    pub fn beta_h(&self) -> E::G2Affine {
94        self.powers.beta_h()
95    }
96
97    pub fn max_degree(&self) -> usize {
98        self.powers.max_num_powers() - 1
99    }
100
101    pub fn to_universal_prover(&self) -> Result<UniversalProver<E>> {
102        Ok(UniversalProver::<E> { max_degree: self.max_degree(), _unused: None })
103    }
104
105    pub fn to_universal_verifier(&self) -> Result<UniversalVerifier<E>> {
106        let g = self.power_of_beta_g(0)?;
107        let h = self.h;
108        let beta_h = self.beta_h();
109        let gamma_g = self.powers_of_beta_times_gamma_g()[&0];
110        let prepared_h = self.prepared_h.clone();
111        let prepared_beta_h = self.prepared_beta_h.clone();
112
113        Ok(UniversalVerifier {
114            vk: VerifierKey::<E> { g, gamma_g, h, beta_h, prepared_h, prepared_beta_h },
115            prepared_negative_powers_of_beta_h: self.powers.prepared_negative_powers_of_beta_h(),
116        })
117    }
118}
119
120impl<E: PairingEngine> FromBytes for UniversalParams<E> {
121    fn read_le<R: Read>(mut reader: R) -> io::Result<Self> {
122        // Deserialize `powers`.
123        let powers = Arc::new(PowersOfG::read_le(&mut reader)?);
124
125        // Deserialize `h`.
126        let h: E::G2Affine = FromBytes::read_le(&mut reader)?;
127
128        // Deserialize `prepared_h`.
129        let prepared_h: <E::G2Affine as PairingCurve>::Prepared = FromBytes::read_le(&mut reader)?;
130
131        // Deserialize `prepared_beta_h`.
132        let prepared_beta_h: <E::G2Affine as PairingCurve>::Prepared = FromBytes::read_le(&mut reader)?;
133
134        Ok(Self { powers, h, prepared_h, prepared_beta_h })
135    }
136}
137
138impl<E: PairingEngine> ToBytes for UniversalParams<E> {
139    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
140        // Serialize powers.
141        self.powers.write_le(&mut writer)?;
142
143        // Serialize `h`.
144        self.h.write_le(&mut writer)?;
145
146        // Serialize `prepared_h`.
147        self.prepared_h.write_le(&mut writer)?;
148
149        // Serialize `prepared_beta_h`.
150        self.prepared_beta_h.write_le(&mut writer)?;
151
152        Ok(())
153    }
154}
155
156/// `Powers` is used to commit to and create evaluation proofs for a given
157/// polynomial.
158#[derive(Clone, Debug, Default, Hash)]
159pub struct Powers<'a, E: PairingEngine> {
160    /// Group elements of the form `β^i G`, for different values of `i`.
161    pub powers_of_beta_g: Cow<'a, [E::G1Affine]>,
162    /// Group elements of the form `β^i γG`, for different values of `i`.
163    pub powers_of_beta_times_gamma_g: Cow<'a, [E::G1Affine]>,
164}
165
166impl<E: PairingEngine> Powers<'_, E> {
167    /// The number of powers in `self`.
168    pub fn size(&self) -> usize {
169        self.powers_of_beta_g.len()
170    }
171}
172/// `LagrangeBasis` is used to commit to and create evaluation proofs for a
173/// given polynomial.
174#[derive(Clone, Debug, Hash)]
175pub struct LagrangeBasis<'a, E: PairingEngine> {
176    /// Group elements of the form `β^i G`, for different values of `i`.
177    pub lagrange_basis_at_beta_g: Cow<'a, [E::G1Affine]>,
178    /// Group elements of the form `β^i γG`, for different values of `i`.
179    pub powers_of_beta_times_gamma_g: Cow<'a, [E::G1Affine]>,
180    /// Domain representing the multiplicative subgroup the powers
181    /// in `self.lagrange_basis_at_beta_g` are defined over.
182    pub domain: EvaluationDomain<E::Fr>,
183}
184
185impl<E: PairingEngine> LagrangeBasis<'_, E> {
186    /// The number of powers in `self`.
187    pub fn size(&self) -> usize {
188        self.lagrange_basis_at_beta_g.len()
189    }
190}
191
192/// `VerifierKey` is used to check evaluation proofs for a given commitment.
193#[derive(Clone, Debug, Default, PartialEq, Eq)]
194pub struct VerifierKey<E: PairingEngine> {
195    /// The generator of G1.
196    pub g: E::G1Affine,
197    /// The generator of G1 that is used for making a commitment hiding.
198    pub gamma_g: E::G1Affine,
199    /// The generator of G2.
200    pub h: E::G2Affine,
201    /// \beta times the above generator of G2.
202    pub beta_h: E::G2Affine,
203    /// The generator of G2, prepared for use in pairings.
204    pub prepared_h: <E::G2Affine as PairingCurve>::Prepared,
205    /// \beta times the above generator of G2, prepared for use in pairings.
206    pub prepared_beta_h: <E::G2Affine as PairingCurve>::Prepared,
207}
208
209impl<E: PairingEngine> CanonicalSerialize for VerifierKey<E> {
210    fn serialize_with_mode<W: Write>(&self, mut writer: W, compress: Compress) -> Result<(), SerializationError> {
211        self.g.serialize_with_mode(&mut writer, compress)?;
212        self.gamma_g.serialize_with_mode(&mut writer, compress)?;
213        self.h.serialize_with_mode(&mut writer, compress)?;
214        self.beta_h.serialize_with_mode(&mut writer, compress)?;
215        Ok(())
216    }
217
218    fn serialized_size(&self, compress: Compress) -> usize {
219        self.g.serialized_size(compress)
220            + self.gamma_g.serialized_size(compress)
221            + self.h.serialized_size(compress)
222            + self.beta_h.serialized_size(compress)
223    }
224}
225
226impl<E: PairingEngine> CanonicalDeserialize for VerifierKey<E> {
227    fn deserialize_with_mode<R: Read>(
228        mut reader: R,
229        compress: Compress,
230        validate: Validate,
231    ) -> Result<Self, SerializationError> {
232        let g = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
233        let gamma_g = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
234        let h: E::G2Affine = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
235        let beta_h: E::G2Affine = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
236        let prepared_h = h.prepare();
237        let prepared_beta_h = beta_h.prepare();
238        Ok(VerifierKey { g, gamma_g, h, beta_h, prepared_h, prepared_beta_h })
239    }
240}
241
242impl<E: PairingEngine> Valid for VerifierKey<E> {
243    fn check(&self) -> Result<(), SerializationError> {
244        Valid::check(&self.g)?;
245        Valid::check(&self.gamma_g)?;
246        Valid::check(&self.h)?;
247        Valid::check(&self.beta_h)?;
248        Ok(())
249    }
250
251    fn batch_check<'a>(batch: impl Iterator<Item = &'a Self> + Send) -> Result<(), SerializationError>
252    where
253        Self: 'a,
254    {
255        let batch: Vec<_> = batch.collect();
256        Valid::batch_check(batch.iter().map(|v| &v.g))?;
257        Valid::batch_check(batch.iter().map(|v| &v.gamma_g))?;
258        Valid::batch_check(batch.iter().map(|v| &v.h))?;
259        Valid::batch_check(batch.iter().map(|v| &v.beta_h))?;
260        Ok(())
261    }
262}
263
264impl<E: PairingEngine> FromBytes for VerifierKey<E> {
265    fn read_le<R: Read>(mut reader: R) -> io::Result<Self> {
266        CanonicalDeserialize::deserialize_compressed(&mut reader)
267            .map_err(|_| error("could not deserialize VerifierKey"))
268    }
269}
270
271impl<E: PairingEngine> ToBytes for VerifierKey<E> {
272    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
273        CanonicalSerialize::serialize_compressed(self, &mut writer)
274            .map_err(|_| error("could not serialize VerifierKey"))
275    }
276}
277
278/// `KZGCommitment` commits to a polynomial. It is output by `KZG10::commit`.
279#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Hash, CanonicalSerialize, CanonicalDeserialize)]
280pub struct KZGCommitment<E: PairingEngine>(
281    /// The commitment is a group element.
282    pub E::G1Affine,
283);
284
285impl<E: PairingEngine> FromBytes for KZGCommitment<E> {
286    fn read_le<R: Read>(mut reader: R) -> io::Result<Self> {
287        CanonicalDeserialize::deserialize_compressed(&mut reader)
288            .map_err(|_| error("could not deserialize KZGCommitment"))
289    }
290}
291
292impl<E: PairingEngine> ToBytes for KZGCommitment<E> {
293    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
294        CanonicalSerialize::serialize_compressed(self, &mut writer)
295            .map_err(|_| error("could not serialize KZGCommitment"))
296    }
297}
298
299impl<E: PairingEngine> KZGCommitment<E> {
300    #[inline]
301    pub fn empty() -> Self {
302        KZGCommitment(E::G1Affine::zero())
303    }
304
305    pub fn has_degree_bound(&self) -> bool {
306        false
307    }
308
309    pub fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool {
310        self.0.is_in_correct_subgroup_assuming_on_curve()
311    }
312}
313
314impl<E: PairingEngine> ToConstraintField<E::Fq> for KZGCommitment<E> {
315    fn to_field_elements(&self) -> Result<Vec<E::Fq>, ConstraintFieldError> {
316        self.0.to_field_elements()
317    }
318}
319
320/// `KZGRandomness` hides the polynomial inside a commitment. It is output by
321/// `KZG10::commit`.
322#[derive(Clone, Debug, Default, PartialEq, Eq, Hash, CanonicalSerialize, CanonicalDeserialize)]
323pub struct KZGRandomness<E: PairingEngine> {
324    /// For KZG10, the commitment randomness is a random polynomial.
325    pub blinding_polynomial: DensePolynomial<E::Fr>,
326}
327impl<E: PairingEngine> FromBytes for KZGRandomness<E> {
328    fn read_le<R: Read>(mut reader: R) -> io::Result<Self> {
329        CanonicalDeserialize::deserialize_compressed(&mut reader)
330            .map_err(|_| error("could not deserialize KZGRandomness"))
331    }
332}
333
334impl<E: PairingEngine> ToBytes for KZGRandomness<E> {
335    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
336        CanonicalSerialize::serialize_compressed(self, &mut writer)
337            .map_err(|_| error("could not serialize KZGRandomness"))
338    }
339}
340
341impl<E: PairingEngine> KZGRandomness<E> {
342    /// Does `self` provide any hiding properties to the corresponding
343    /// commitment? `self.is_hiding() == true` only if the underlying
344    /// polynomial is non-zero.
345    #[inline]
346    pub fn is_hiding(&self) -> bool {
347        !self.blinding_polynomial.is_zero()
348    }
349
350    /// What is the degree of the hiding polynomial for a given hiding bound?
351    #[inline]
352    pub fn calculate_hiding_polynomial_degree(hiding_bound: usize) -> usize {
353        hiding_bound + 1
354    }
355}
356
357impl<E: PairingEngine> KZGRandomness<E> {
358    pub fn empty() -> Self {
359        Self { blinding_polynomial: DensePolynomial::zero() }
360    }
361
362    pub fn rand<R: RngCore>(hiding_bound: usize, _: bool, rng: &mut R) -> Self {
363        let mut randomness = KZGRandomness::empty();
364        let hiding_poly_degree = Self::calculate_hiding_polynomial_degree(hiding_bound);
365        randomness.blinding_polynomial = DensePolynomial::rand(hiding_poly_degree, rng);
366        randomness
367    }
368}
369
370impl<'a, E: PairingEngine> Add<&'a KZGRandomness<E>> for KZGRandomness<E> {
371    type Output = Self;
372
373    #[inline]
374    fn add(mut self, other: &'a Self) -> Self {
375        self.blinding_polynomial += &other.blinding_polynomial;
376        self
377    }
378}
379
380impl<'a, E: PairingEngine> Add<(E::Fr, &'a KZGRandomness<E>)> for KZGRandomness<E> {
381    type Output = Self;
382
383    #[inline]
384    fn add(mut self, other: (E::Fr, &'a KZGRandomness<E>)) -> Self {
385        self += other;
386        self
387    }
388}
389
390impl<'a, E: PairingEngine> AddAssign<&'a KZGRandomness<E>> for KZGRandomness<E> {
391    #[inline]
392    fn add_assign(&mut self, other: &'a Self) {
393        self.blinding_polynomial += &other.blinding_polynomial;
394    }
395}
396
397impl<'a, E: PairingEngine> AddAssign<(E::Fr, &'a KZGRandomness<E>)> for KZGRandomness<E> {
398    #[inline]
399    fn add_assign(&mut self, (f, other): (E::Fr, &'a KZGRandomness<E>)) {
400        self.blinding_polynomial += (f, &other.blinding_polynomial);
401    }
402}
403
404/// `KZGProof` is an evaluation proof that is output by `KZG10::open`.
405#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Hash, CanonicalSerialize, CanonicalDeserialize)]
406pub struct KZGProof<E: PairingEngine> {
407    /// This is a commitment to the witness polynomial; see [\[KZG10\]][kzg] for
408    /// more details.
409    ///
410    /// [kzg]: http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf
411    pub w: E::G1Affine,
412    /// This is the evaluation of the random polynomial at the point for which
413    /// the evaluation proof was produced.
414    pub random_v: Option<E::Fr>,
415}
416
417impl<E: PairingEngine> KZGProof<E> {
418    pub fn absorb_into_sponge(&self, sponge: &mut impl AlgebraicSponge<E::Fq, 2>) {
419        sponge.absorb_native_field_elements(&self.w.to_field_elements().unwrap());
420        if let Some(random_v) = self.random_v {
421            sponge.absorb_nonnative_field_elements([random_v]);
422        }
423    }
424}
425
426impl<E: PairingEngine> FromBytes for KZGProof<E> {
427    fn read_le<R: Read>(mut reader: R) -> io::Result<Self> {
428        CanonicalDeserialize::deserialize_compressed(&mut reader)
429            .map_err(|err| into_io_error(anyhow::Error::from(err).context("could not deserialize KZG proof")))
430    }
431}
432
433impl<E: PairingEngine> ToBytes for KZGProof<E> {
434    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
435        CanonicalSerialize::serialize_compressed(self, &mut writer)
436            .map_err(|err| into_io_error(anyhow::Error::from(err).context("could not serialize KZG proof")))
437    }
438}
439
440impl<E: PairingEngine> KZGProof<E> {
441    pub fn is_hiding(&self) -> bool {
442        self.random_v.is_some()
443    }
444}
snarkvm_algorithms/polycommit/kzg10/data_structures.rs

snarkvm_algorithms/polycommit/kzg10/
data_structures.rs
