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[package]
name = "poly-commit"
version = "0.1.0"
authors = [
"Alessandro Chiesa <alexch@berkeley.edu>",
"Mary Maller <mary.maller.15@ucl.ac.uk>",
"Yuncong Hu <huyuncongh@gmail.com>",
"Pratyush Mishra <pratyush@berkeley.edu>",
"Noah Vesely <noah.vesely.18@ucl.ac.uk>",
"Nicholas Ward <npward@berkeley.edu>",
]
description = "A library for constructing polynomial commitment schemes for use in zkSNARKs"
homepage = "https://libzexe.org"
repository = "https://github.com/scipr/poly-commit"
documentation = "https://docs.rs/poly-commit/"
keywords = ["cryptography", "polynomial commitments", "elliptic curves", "pairing"]
categories = ["cryptography"]
include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
license = "MIT/Apache-2.0"
edition = "2018"
[dependencies]
algebra = { git = "https://github.com/scipr-lab/zexe/", features = [ "parallel" ] }
ff-fft = { git = "https://github.com/scipr-lab/zexe/" }
bench-utils = { git = "https://github.com/scipr-lab/zexe/" }
rand = { version = "0.4" }
rayon = { version = "1" }
derivative = { version = "1" }
[features]
timer = [ "bench-utils/timer" ]
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<h1 align="center">`poly-commit`</h1>
<p align="center">
<a href="https://travis-ci.org/scipr-lab/poly-commit"><img src="https://travis-ci.org/scipr-lab/poly-commit.svg?branch=master"></a>
<a href="https://github.com/scipr-lab/poly-commit/blob/master/AUTHORS"><img src="https://img.shields.io/badge/authors-SCIPR%20Lab-orange.svg"></a>
<a href="https://github.com/scipr-lab/poly-commit/blob/master/LICENSE-APACHE"><img src="https://img.shields.io/badge/license-APACHE-blue.svg"></a>
<a href="https://github.com/scipr-lab/poly-commit/blob/master/LICENSE-MIT"><img src="https://img.shields.io/badge/license-MIT-blue.svg"></a>
</p>
`poly-commit` is a Rust library that implements *polynomial commitment schemes*, a cryptographic primitive that enables parties to "commit" to polynomials and then provide proofs of correct evaluation for these commitments.
This library was initially developed as part of the paper *"[<span style="font-variant:small-caps;">Marlin</span>: Preprocessing zkSNARKs with Universal and Updatable SRS][marlin]"*, and it is released under the MIT License and the Apache v2 License (see [License](#license)).
**WARNING:** This is an academic proof-of-concept prototype, and in particular has not received careful code review. This implementation is NOT ready for production use.
## Overview
This library provides traits for *polynomial commitment schemes*, as well as constructions of these based on the paper *"[Polynomial Commitments][kzg10]"*. Polynomial commitment (PC) schemes allow a user to first commit to polynomials, and to then provide proofs of correct evaluation for the committed polynomials. PC schemes satisfy the following properties:
- **Hiding** - commitments and proofs should reveal no information about the committed polynomial.
- **Succinctness** - commitment and proof size should scale sublinearly with the degree of the committed polynomial. Optionally, verification time should also scale sublinearly.
- **Extractability** - there should exist an extractor *E*, which when given a commitment and a valid evaluation proof, should be able to extract a polynomial that agrees with the evaluation.
[kzg10]: http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf
## Build guide
The library compiles on the `stable` toolchain of the Rust compiler. To install the latest version of Rust, first install `rustup` by following the instructions [here](https://rustup.rs/), or via your platform's package manager. Once `rustup` is installed, install the Rust toolchain by invoking:
```bash
rustup install stable
```
After that, use `cargo`, the standard Rust build tool, to build the library:
```bash
git clone https://github.com/scipr-lab/poly-commit.git
cd poly-commit
cargo build --release
```
This library comes with some unit and integration tests. Run these tests with:
```bash
cargo test
```
Lastly, this library is instrumented with profiling infrastructure that prints detailed
profiles of execution time; to enables this, compile with `cargo build --features timer`.
## License
`poly-commit` is licensed under either of the following licenses, at your discretion.
* Apache License Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
* MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
Unless you explicitly state otherwise, any contribution submitted for inclusion in `poly-commit` by you shall be dual licensed as above (as defined in the Apache v2 License), without any additional terms or conditions.
[marlin]: https://ia.cr/2019/xxx
## Reference paper
[_<span style="font-variant:small-caps;">Marlin</span>: Preprocessing zkSNARKs with Universal and Updatable SRS_][marlin]
Alessandro Chiesa, Yuncong Hu, Mary Maller, [Pratyush Mishra](https://www.github.com/pratyush), Noah Vesely, [Nicholas Ward](https://www.github.com/npwardberkeley)
*IACR ePrint Report 2019/XXX*
## Acknowledgements
This work was supported by:
an Engineering and Physical Sciences Research Council grant (EP/N028104/1),
a Google Faculty Award,
the RISELab at UC Berkeley,
and
donations from the Ethereum Foundation and the Interchain Foundation.
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//! A crate for polynomial commitment schemes.
#![deny(unused_import_braces, unused_qualifications, trivial_casts)]
#![deny(trivial_numeric_casts, private_in_public, variant_size_differences)]
#![deny(stable_features, unreachable_pub, non_shorthand_field_patterns)]
#![deny(unused_attributes, unused_imports, unused_mut, missing_docs)]
#![deny(renamed_and_removed_lints, stable_features, unused_allocation)]
#![deny(unused_comparisons, bare_trait_objects, unused_must_use, const_err)]
#![forbid(unsafe_code)]
#[macro_use]
extern crate algebra;
#[macro_use]
extern crate derivative;
#[macro_use]
extern crate bench_utils;
use rand::Rng;
use algebra::Field;
use std::borrow::Cow;
pub use ff_fft::DensePolynomial as Polynomial;
/// Defines `SinglePolynomialCommitment` schemes that allow one to commit to
/// a single polynomial, and then provide an evaluation proof for that polynomial
/// at a single point.
pub mod single_pc;
/// Defines `MultiPolynomialCommitment` schemes that allow one to commit to
/// multiple polynomials, and then provide evaluation proofs for these polynomials
/// at many points.
pub mod multi_pc;
pub use multi_pc::MultiPolynomialCommitment;
pub use single_pc::SinglePolynomialCommitment;
/// Defines the minimal interface of committer keys for any polynomial
/// commitment scheme.
pub trait PCCommitterKey: Clone {
/// Outputs the maximum degree supported by the committer key.
fn max_degree(&self) -> usize;
}
/// Defines the minimal interface of verifier keys for any polynomial
/// commitment scheme.
pub trait PCVerifierKey: Clone {
/// Outputs the maximum degree supported by the verifier key.
fn max_degree(&self) -> usize;
}
/// Defines the minimal interface of commitments for any polynomial
/// commitment scheme.
pub trait PCCommitment: Clone + algebra::ToBytes {
/// Outputs a non-hiding commitment to the zero polynomial.
fn empty() -> Self;
/// Does this commitment have a degree bound?
fn has_degree_bound(&self) -> bool;
/// Size in bytes
fn size_in_bytes(&self) -> usize;
}
/// Defines the minimal interface of commitment randomness for any polynomial
/// commitment scheme.
pub trait PCRandomness: Clone {
/// Outputs empty randomness that does not hide the commitment.
fn empty() -> Self;
/// Outputs empty randomness that does not hide the commitment, with no degree bound.
fn empty_no_degree_bound() -> Self;
/// Samples randomness for commitments;
/// `num_queries` specifies the number of queries that the commitment will be opened at.
fn rand<R: Rng>(num_queries: usize, rng: &mut R) -> Self;
}
/// A polynomial along with other information necessary for the HIOP protocol
/// and for the polynomial commitment scheme.
#[derive(Clone)]
pub struct LabeledPolynomial<'a, F: Field> {
polynomial: Cow<'a, Polynomial<F>>,
degree_bound: Option<usize>,
hiding_bound: Option<usize>,
}
impl<'a, F: Field> std::ops::Deref for LabeledPolynomial<'a, F> {
type Target = Polynomial<F>;
fn deref(&self) -> &Self::Target {
&self.polynomial
}
}
impl<'a, F: Field> LabeledPolynomial<'a, F> {
/// Instantiate a new polynomial_context.
pub fn new_owned(polynomial: Polynomial<F>, degree_bound: Option<usize>, hiding_bound: Option<usize>) -> Self {
Self {
polynomial: Cow::Owned(polynomial),
degree_bound,
hiding_bound,
}
}
/// Instantiate a new polynomial_context.
pub fn new(polynomial: &'a Polynomial<F>, degree_bound: Option<usize>, hiding_bound: Option<usize>) -> Self {
Self {
polynomial: Cow::Borrowed(polynomial),
degree_bound,
hiding_bound,
}
}
/// Retrieve the polynomial from `self`.
pub fn polynomial(&self) -> &Polynomial<F> {
&self.polynomial
}
/// Evaluate the polynomial in `self`.
pub fn evaluate(&self, point: F) -> F {
self.polynomial.evaluate(point)
}
/// Retrieve the degree bound in `self`.
pub fn degree_bound(&self) -> Option<usize> {
self.degree_bound
}
/// Retrieve whether the polynomial in `self` should be hidden.
pub fn is_hiding(&self) -> bool {
self.hiding_bound.is_some()
}
/// Retrieve the hiding bound for the polynomial in `self`.
pub fn hiding_bound(&self) -> Option<usize> {
self.hiding_bound
}
}
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use algebra::Field;
use rand::Rng;
use std::borrow::Borrow;
use std::collections::{BTreeMap, BTreeSet};
use crate::*;
/// `QuerySet` is the set of queries that are to be made to a list of polynomials
/// `p` that have previously been committed. Each element of a `QuerySet` is a `(index, query)`
/// pair, where `index` is the index into `p`, and `query` is the field element
/// that `p[index]` is to be queried at.
pub type QuerySet<F> = BTreeSet<(usize, F)>;
/// `Evaluations` is the result of querying a list of polynomials `p` at a `QuerySet`
/// `Q`. It maps each element of `Q` to the resulting evaluation. That is,
/// if `(index, query)` is an element of `Q`, then `evaluation.get((index, query))`
/// should equal `p[index].evaluate(query)`.
pub type Evaluations<F> = BTreeMap<(usize, F), F>;
/// Describes the interface for a polynomial commitment scheme that allows
/// a sender to commit to multiple polynomials and later provide a succinct proof
/// of evaluation for the corresponding commitments at a query set `Q`, while
/// enforcing per-polynomial degree bounds.
pub trait MultiPolynomialCommitment<F: Field> {
/// The committer key for the scheme; used to commit to a polynomial and then
/// open the commitment to produce an evaluation proof.
type CommitterKey: PCCommitterKey;
/// The verifier key for the scheme; used to check an evaluation proof.
type VerifierKey: PCVerifierKey;
/// The commitment to a polynomial.
type Commitment: PCCommitment;
/// The commitment randomness.
type Randomness: PCRandomness;
/// The evaluation proof.
type Proof: Clone;
/// The error type for the scheme.
type Error: std::error::Error;
/// Constructs public parameters when given as input the maximum degree `degree`
/// for the polynomial commitment scheme.
fn setup<R: Rng>(degree: usize, rng: &mut R) -> Result<(Self::CommitterKey, Self::VerifierKey), Self::Error>;
/// Outputs a commitments to `polynomials`. If `hiding_bounds[i].is_some()`,
/// then the `i`-th commitment is hiding up to `hiding_bounds[i]` number of queries.
/// `rng` should not be `None` if `hiding_bounds[i].is_some()`
/// is true.
///
/// If `hiding_bounds[i].is_none()`, then the `i`-th randomness is
/// `Self::Randomness::empty()`.
// TODO: technically each iterator below can have different lifetimes, but
// that becomes quite noisy. Also, lifetime elision in argument position
// should fix this (https://github.com/rust-lang/rust/issues/49287)
fn commit<'a>(
ck: &Self::CommitterKey,
polynomials: impl IntoIterator<Item = &'a Polynomial<F>>,
degree_bounds: impl IntoIterator<Item = &'a Option<usize>>,
hiding_bounds: impl IntoIterator<Item = &'a Option<usize>>,
rng: Option<&mut dyn Rng>,
) -> Result<(Vec<Self::Commitment>, Vec<Self::Randomness>), Self::Error>;
/// On input a list of polynomials and a query set, `open` outputs a proof of evaluation
/// of the polynomials at the points in the query set.
fn open(
ck: &Self::CommitterKey,
polynomials: &[impl Borrow<Polynomial<F>>],
degree_bounds: &[Option<usize>],
query_set: &QuerySet<F>,
opening_challenge: F,
r: &[impl Borrow<Self::Randomness>],
) -> Result<Self::Proof, Self::Error>;
/// Checks that `values` are the true evaluations at `query_set` of the polynomials
/// committed in `comm`.
fn check<R: Rng>(
vk: &Self::VerifierKey,
comm: &[Self::Commitment],
degree_bounds: &[Option<usize>],
query_set: &QuerySet<F>,
values: &Evaluations<F>,
proof: &Self::Proof,
opening_challenge: F,
rng: &mut R,
) -> Result<bool, Self::Error>;
/// Commit to labeled polynomials.
fn commit_labeled<'a>(
ck: &Self::CommitterKey,
labeled_polynomials: impl Iterator<Item = &'a LabeledPolynomial<'a, F>>,
rng: Option<&mut dyn Rng>,
) -> Result<(Vec<Self::Commitment>, Vec<Self::Randomness>), Self::Error> {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
let mut hiding_bounds = Vec::new();
for labeled_poly in labeled_polynomials {
polynomials.push(labeled_poly.polynomial());
degree_bounds.push(labeled_poly.degree_bound());
hiding_bounds.push(labeled_poly.hiding_bound());
}
Self::commit(
ck,
polynomials,
&degree_bounds,
&hiding_bounds,
rng,
)
}
/// Open labeled polynomials.
fn open_labeled<'a>(
ck: &Self::CommitterKey,
labeled_polynomials: impl Iterator<Item = &'a LabeledPolynomial<'a, F>>,
query_set: &QuerySet<F>,
opening_challenge: F,
rands: &[Self::Randomness],
) -> Result<Self::Proof, Self::Error> {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
let mut hiding_bounds = Vec::new();
for labeled_poly in labeled_polynomials {
polynomials.push(labeled_poly.polynomial());
degree_bounds.push(labeled_poly.degree_bound());
hiding_bounds.push(labeled_poly.hiding_bound());
}
Self::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)
}
}
/// Generic construction of a `MultiPolynomialCommitment` scheme from a
/// `SinglePolynomialCommitment` scheme whenever the commitment and randomness of the
/// `SinglePolynomialCommitment` scheme are additively homomorphic.
/// Specifically, we require `C = MultiPolynomialCommitment::Commitment`
/// to satisfy `for<'a> C: AddAssign<(F, &'a C)>.
///
/// The construction follows the blueprint laid out in [CHMMVW19](insert eprint link).
pub mod mpc_from_spc;
#[cfg(test)]
pub mod tests {
use crate::multi_pc::*;
use algebra::Field;
use rand::{distributions::Sample, thread_rng, Rand};
pub fn single_poly_test<F, MultiPC>() -> Result<(), MultiPC::Error>
where
F: Field,
MultiPC: MultiPolynomialCommitment<F>,
{
let rng = &mut thread_rng();
let max_degree = rand::distributions::Range::new(1, 64).sample(rng);;
let (ck, vk) = MultiPC::setup(max_degree, rng)?;
for _ in 0..100 {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
// Generate polynomials
for _ in 0..1 {
let degree = max_degree;
polynomials.push(Polynomial::rand(degree, rng));
degree_bounds.push(None);
}
let num_points_in_query_set = 1;
let hiding_bounds = vec![Some(num_points_in_query_set); 1];
let (comms, rands) = MultiPC::commit(
&ck,
&polynomials,
&degree_bounds,
&hiding_bounds,
Some(rng),
)?;
// Construct query set
let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for _ in 0..num_points_in_query_set {
let point = F::rand(rng);
for i in 0..1 {
query_set.insert((i, point));
let value = polynomials[i].evaluate(point);
values.insert((i, point), value);
}
}
let opening_challenge = F::rand(rng);
let proof = MultiPC::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)?;
assert!(
MultiPC::check(
&vk,
&comms,
&degree_bounds,
&query_set,
&values,
&proof,
opening_challenge,
rng
)?,
"proof was incorrect"
);
}
Ok(())
}
pub fn single_poly_degree_bound_test<F, MultiPC>() -> Result<(), MultiPC::Error>
where
F: Field,
MultiPC: MultiPolynomialCommitment<F>,
{
let rng = &mut thread_rng();
let max_degree = rand::distributions::Range::new(1, 64).sample(rng);;
let (ck, vk) = MultiPC::setup(max_degree, rng)?;
for _ in 0..100 {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
// Generate polynomials
for _ in 0..1 {
let degree = rand::distributions::Range::new(1, max_degree).sample(rng);
polynomials.push(Polynomial::rand(degree, rng));
let mut range = rand::distributions::Range::new(degree, max_degree);
let degree_bound = Some(range.sample(rng));
degree_bounds.push(degree_bound);
}
let num_points_in_query_set = 1;
let hiding_bounds = vec![Some(num_points_in_query_set); 1];
let (comms, rands) = MultiPC::commit(
&ck,
&polynomials,
&degree_bounds,
&hiding_bounds,
Some(rng),
)?;
println!("Committed");
// Construct query set
let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for _ in 0..num_points_in_query_set {
let point = F::rand(rng);
for i in 0..1 {
query_set.insert((i, point));
let value = polynomials[i].evaluate(point);
values.insert((i, point), value);
}
}
println!("Generated query set");
let opening_challenge = F::rand(rng);
let proof = MultiPC::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)?;
println!("Opened");
assert!(
MultiPC::check(
&vk,
&comms,
&degree_bounds,
&query_set,
&values,
&proof,
opening_challenge,
rng
)?,
"proof was incorrect"
);
}
Ok(())
}
pub fn single_poly_degree_bound_multiple_queries_test<F, MultiPC>() -> Result<(), MultiPC::Error>
where
F: Field,
MultiPC: MultiPolynomialCommitment<F>,
{
let rng = &mut thread_rng();
let max_degree = rand::distributions::Range::new(1, 64).sample(rng);;
let (ck, vk) = MultiPC::setup(max_degree, rng)?;
for _ in 0..100 {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
// Generate polynomials
for _ in 0..1 {
let degree = rand::distributions::Range::new(1, max_degree).sample(rng);
polynomials.push(Polynomial::rand(degree, rng));
let mut range = rand::distributions::Range::new(degree, max_degree);
let degree_bound = Some(range.sample(rng));
degree_bounds.push(degree_bound);
}
let num_points_in_query_set = 2;
let hiding_bounds = vec![Some(num_points_in_query_set); 1];
let (comms, rands) = MultiPC::commit(
&ck,
&polynomials,
&degree_bounds,
&hiding_bounds,
Some(rng),
)?;
// Construct query set
let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for _ in 0..num_points_in_query_set {
let point = F::rand(rng);
for i in 0..1 {
query_set.insert((i, point));
let value = polynomials[i].evaluate(point);
values.insert((i, point), value);
}
}
let opening_challenge = F::rand(rng);
let proof = MultiPC::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)?;
assert!(
MultiPC::check(
&vk,
&comms,
&degree_bounds,
&query_set,
&values,
&proof,
opening_challenge,
rng
)?,
"proof was incorrect"
);
}
Ok(())
}
pub fn two_polys_degree_bound_single_query_test<F, MultiPC>() -> Result<(), MultiPC::Error>
where
F: Field,
MultiPC: MultiPolynomialCommitment<F>,
{
let rng = &mut thread_rng();
let max_degree = 10;
let (ck, vk) = MultiPC::setup(max_degree, rng)?;
for _ in 0..100 {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
// Generate polynomials
for _ in 0..2 {
let degree = rand::distributions::Range::new(1, max_degree).sample(rng);
polynomials.push(Polynomial::rand(degree, rng));
let mut range = rand::distributions::Range::new(degree, max_degree);
let degree_bound = Some(range.sample(rng));
degree_bounds.push(degree_bound);
}
let num_points_in_query_set = 1;
let hiding_bounds = vec![Some(num_points_in_query_set); 2];
let (comms, rands) = MultiPC::commit(
&ck,
&polynomials,
&degree_bounds,
&hiding_bounds,
Some(rng),
)?;
// Construct query set
let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for _ in 0..num_points_in_query_set {
let point = F::rand(rng);
for i in 0..2 {
query_set.insert((i, point));
let value = polynomials[i].evaluate(point);
values.insert((i, point), value);
}
}
let opening_challenge = F::rand(rng);
let proof = MultiPC::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)?;
assert!(
MultiPC::check(
&vk,
&comms,
&degree_bounds,
&query_set,
&values,
&proof,
opening_challenge,
rng
)?,
"proof was incorrect"
);
}
Ok(())
}
pub fn full_end_to_end_test<F, MultiPC>() -> Result<(), MultiPC::Error>
where
F: Field,
MultiPC: MultiPolynomialCommitment<F>,
{
let rng = &mut thread_rng();
let max_degree = rand::distributions::Range::new(2, 64).sample(rng);;
let (ck, vk) = MultiPC::setup(max_degree, rng)?;
for _ in 0..10 {
let mut polynomials = Vec::new();
let mut degree_bounds = Vec::new();
// Generate polynomials
for _ in 0..10 {
let degree = rand::distributions::Range::new(1, max_degree).sample(rng);
polynomials.push(Polynomial::rand(degree, rng));
let mut range = rand::distributions::Range::new(degree, max_degree);
let degree_bound = Some(range.sample(rng));
degree_bounds.push(degree_bound);
}
let num_points_in_query_set = rand::distributions::Range::new(1, 5).sample(rng);
let hiding_bounds = vec![Some(num_points_in_query_set); 10];
let (comms, rands) = MultiPC::commit(
&ck,
&polynomials,
&degree_bounds,
&hiding_bounds,
Some(rng),
)?;
// Construct query set
let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for _ in 0..num_points_in_query_set {
let point = F::rand(rng);
for i in 0..10 {
let should_be_queried = bool::rand(rng);
if should_be_queried {
query_set.insert((i, point));
let value = polynomials[i].evaluate(point);
values.insert((i, point), value);
}
}
}
let opening_challenge = F::rand(rng);
let proof = MultiPC::open(
&ck,
&polynomials,
&degree_bounds,
&query_set,
opening_challenge,
&rands,
)?;
let result = MultiPC::check(
&vk,
&comms,
&degree_bounds,
&query_set,
&values,
&proof,
opening_challenge,
rng
)?;
if !result {
println!("Failed with 10 polynomials, num_points_in_query_set: {:?}", num_points_in_query_set);
}
assert!(result, "proof was incorrect");
}
Ok(())
}
}
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use crate::*;
use algebra::Field;
use rand::Rng;
/// Describes the interface for a polynomial commitment scheme that allows
/// a sender to commit to a single polynomial and later provide a succinct proof
/// of evaluation for that commitment.
/// ```compile_fail
///
/// let rng = &mut thread_rng();
/// // Generate committer and verifier keys for a maximum polynomial degree
/// // of 10.
/// let degree = 10;
/// let (ck, vk) = SinglePC::setup(degree, rng);
///
/// // Generate a random degree-10 polynomial.
/// let p = Polynomial::rand(degree, rng);;
/// let hiding_bound = Some(1);
///
/// // Commit to this polynomial
/// let (comm, rand) = SinglePC::commit(&ck, &p, hiding_bound, rng)?;
///
/// // Evaluate the polynomial at a random point, and generate an evaluation
/// // proof.
/// let point = F::rand(rng);
/// let value = p.evaluate(point);
/// let proof = SinglePC::open(&ck, &p, point, &rand)?;
///
/// // Verify the evaluation proof.
/// assert!(SinglePC::check(&vk, &comm, point, value, &proof)?, "proof was incorrect");
/// ```
pub trait SinglePolynomialCommitment<F: Field> {
/// The committer key for the scheme; used to commit to a polynomial and then
/// open the commitment to produce an evaluation proof.
type CommitterKey: PCCommitterKey;
/// The verifier key for the scheme; used to check an evaluation proof.
type VerifierKey: PCVerifierKey;
/// The commitment to a polynomial.
type Commitment: PCCommitment;
/// The commitment randomness.
type Randomness: PCRandomness;
/// The evaluation proof.
type Proof: Clone;
/// The error type for the scheme.
type Error: std::error::Error;
/// Constructs public parameters when given as input the maximum degree `degree`
/// for the polynomial commitment scheme.
fn setup<R: Rng>(degree: usize, rng: &mut R) -> Result<(Self::CommitterKey, Self::VerifierKey), Self::Error>;
/// Outputs a commitment to `polynomial`. If `hiding_bound.is_some()`, then the
/// resulting commitment is hiding up to `hiding_bound.unwrap()` number of queries.
/// `rng` should not be `None` if `hiding_bound.is_some()`.
/// If `hiding_bound.is_none()`, then the randomness is `Self::Randomness::empty()`.
fn commit(
ck: &Self::CommitterKey,
polynomial: &Polynomial<F>,
hiding_bound: Option<usize>,
rng: Option<&mut dyn Rng>,
) -> Result<(Self::Commitment, Self::Randomness), Self::Error>;
/// On input a polynomial `p` and a point `point` in the field `F`,
/// `open` outputs an evaluation proof for `p` at `point`.
fn open(
ck: &Self::CommitterKey,
p: &Polynomial<F>,
point: F,
r: &Self::Randomness,
) -> Result<Self::Proof, Self::Error>;
/// Verifies that `value` is the evaluation at `point` of the polynomial
/// committed inside `comm`.
fn check(
vk: &Self::VerifierKey,
comm: &Self::Commitment,
point: F,
value: F,
proof: &Self::Proof,
) -> Result<bool, Self::Error>;
/// Check a batch of proofs
fn batch_check<R: Rng>(
vk: &Self::VerifierKey,
commitments: &[Self::Commitment],
points: &[F],
values: &[F],
proofs: &[Self::Proof],
rng: &mut R,
) -> Result<bool, Self::Error>;
/// Commit to a labeled polynomial.
fn commit_labeled(
ck: &Self::CommitterKey,
labeled_polynomial: &LabeledPolynomial<F>,
rng: Option<&mut dyn Rng>,
) -> Result<(Self::Commitment, Self::Randomness), Self::Error> {
Self::commit(
ck,
labeled_polynomial.polynomial(),
labeled_polynomial.hiding_bound(),
rng,
)
}
/// Open a labeled polynomial.
fn open_labeled<'a>(
ck: &Self::CommitterKey,
labeled_polynomial: &LabeledPolynomial<F>,
point: F,
rand: &Self::Randomness,
) -> Result<Self::Proof, Self::Error> {
Self::open(
&ck,
labeled_polynomial.polynomial(),
point,
&rand,
)
}
}
/// Implements the [KZG10](kzg10) construction that satisfies the `SinglePolynomialCommitment`
/// trait.
///
/// [kzg10]: http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf
pub mod kzg10;
#[cfg(test)]
pub mod tests {
use crate::*;
use algebra::Field;
use rand::{thread_rng, Rand};
pub fn end_to_end_test<F, SinglePC>() -> Result<(), SinglePC::Error>
where
F: Field,
SinglePC: SinglePolynomialCommitment<F>,
{
let rng = &mut thread_rng();
for _ in 0..100 {
let mut degree = 0;
while degree <= 1 {
degree = usize::rand(rng) % 20;
}
let (ck, vk) = SinglePC::setup(degree, rng)?;
let p = Polynomial::rand(degree, rng);;
let hiding_bound = Some(1);
let (comm, rand) = SinglePC::commit(&ck, &p, hiding_bound, Some(rng))?;
let point = F::rand(rng);
let value = p.evaluate(point);
let proof = SinglePC::open(&ck, &p, point, &rand)?;
assert!(
SinglePC::check(&vk, &comm, point, value, &proof)?,
"proof was incorrect for max_degree = {}, polynomial_degree = {}, hiding_bound = {:?}",
degree,
p.degree(),
hiding_bound,
);
}
Ok(())
}
pub fn batch_check_test<F, SinglePC>() -> Result<(), SinglePC::Error>
where
F: Field,
SinglePC: SinglePolynomialCommitment<F>,
{
let rng = &mut thread_rng();
for _ in 0..10 {
let mut degree = 0;
while degree <= 1 {
degree = usize::rand(rng) % 20;
}
let (ck, vk) = SinglePC::setup(degree, rng)?;
let mut comms = Vec::new();
let mut values = Vec::new();
let mut points = Vec::new();
let mut proofs = Vec::new();
for _ in 0..10 {
let p = Polynomial::rand(degree, rng);;
let hiding_bound = Some(1);
let (comm, rand) = SinglePC::commit(&ck, &p, hiding_bound, Some(rng))?;
let point = F::rand(rng);
let value = p.evaluate(point);
let proof = SinglePC::open(&ck, &p, point, &rand)?;
assert!(SinglePC::check(&vk, &comm, point, value, &proof)?);
comms.push(comm);
values.push(value);
points.push(point);
proofs.push(proof);
}
assert!(SinglePC::batch_check(&vk, &comms, &points, &values, &proofs, rng)?);
}
Ok(())
}
}
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