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unipoly.rs
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182 lines (156 loc) · 5.41 KB
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use super::commitments::{Commitments, MultiCommitGens};
use super::group::GroupElement;
use super::scalar::{Scalar, ScalarFromPrimitives};
use super::transcript::{AppendToTranscript, ProofTranscript};
use merlin::Transcript;
use serde::{Deserialize, Serialize};
// ax^2 + bx + c stored as vec![c,b,a]
// ax^3 + bx^2 + cx + d stored as vec![d,c,b,a]
#[derive(Debug)]
pub struct UniPoly {
coeffs: Vec<Scalar>,
}
// ax^2 + bx + c stored as vec![c,a]
// ax^3 + bx^2 + cx + d stored as vec![d,b,a]
#[derive(Serialize, Deserialize, Debug)]
pub struct CompressedUniPoly {
coeffs_except_linear_term: Vec<Scalar>,
}
impl UniPoly {
pub fn from_evals(evals: &[Scalar]) -> Self {
// we only support degree-2 or degree-3 univariate polynomials
assert!(evals.len() == 3 || evals.len() == 4);
let coeffs = if evals.len() == 3 {
// ax^2 + bx + c
let two_inv = (2_usize).to_scalar().invert().unwrap();
let c = evals[0];
let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
let b = evals[1] - c - a;
vec![c, b, a]
} else {
// ax^3 + bx^2 + cx + d
let two_inv = (2_usize).to_scalar().invert().unwrap();
let six_inv = (6_usize).to_scalar().invert().unwrap();
let d = evals[0];
let a = six_inv
* (evals[3] - evals[2] - evals[2] - evals[2] + evals[1] + evals[1] + evals[1] - evals[0]);
let b = two_inv
* (evals[0] + evals[0] - evals[1] - evals[1] - evals[1] - evals[1] - evals[1]
+ evals[2]
+ evals[2]
+ evals[2]
+ evals[2]
- evals[3]);
let c = evals[1] - d - a - b;
vec![d, c, b, a]
};
UniPoly { coeffs }
}
pub fn degree(&self) -> usize {
self.coeffs.len() - 1
}
pub fn as_vec(&self) -> Vec<Scalar> {
self.coeffs.clone()
}
pub fn eval_at_zero(&self) -> Scalar {
self.coeffs[0]
}
pub fn eval_at_one(&self) -> Scalar {
(0..self.coeffs.len()).map(|i| self.coeffs[i]).sum()
}
pub fn evaluate(&self, r: &Scalar) -> Scalar {
let mut eval = self.coeffs[0];
let mut power = *r;
for i in 1..self.coeffs.len() {
eval += power * self.coeffs[i];
power *= r;
}
eval
}
pub fn compress(&self) -> CompressedUniPoly {
let coeffs_except_linear_term = [&self.coeffs[..1], &self.coeffs[2..]].concat();
assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
CompressedUniPoly {
coeffs_except_linear_term,
}
}
pub fn commit(&self, gens: &MultiCommitGens, blind: &Scalar) -> GroupElement {
self.coeffs.commit(blind, gens)
}
}
impl CompressedUniPoly {
// we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
// linear_term = hint - 2 * constant_term - deg2 term - deg3 term
pub fn decompress(&self, hint: &Scalar) -> UniPoly {
let mut linear_term =
hint - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
for i in 1..self.coeffs_except_linear_term.len() {
linear_term -= self.coeffs_except_linear_term[i];
}
let mut coeffs = vec![self.coeffs_except_linear_term[0], linear_term];
coeffs.extend(&self.coeffs_except_linear_term[1..]);
assert_eq!(self.coeffs_except_linear_term.len() + 1, coeffs.len());
UniPoly { coeffs }
}
}
impl AppendToTranscript for UniPoly {
fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
transcript.append_message(label, b"UniPoly_begin");
for i in 0..self.coeffs.len() {
transcript.append_scalar(b"coeff", &self.coeffs[i]);
}
transcript.append_message(label, b"UniPoly_end");
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_from_evals_quad() {
// polynomial is 2x^2 + 3x + 1
let e0 = Scalar::one();
let e1 = (6_usize).to_scalar();
let e2 = (15_usize).to_scalar();
let evals = vec![e0, e1, e2];
let poly = UniPoly::from_evals(&evals);
assert_eq!(poly.eval_at_zero(), e0);
assert_eq!(poly.eval_at_one(), e1);
assert_eq!(poly.coeffs.len(), 3);
assert_eq!(poly.coeffs[0], Scalar::one());
assert_eq!(poly.coeffs[1], (3_usize).to_scalar());
assert_eq!(poly.coeffs[2], (2_usize).to_scalar());
let hint = e0 + e1;
let compressed_poly = poly.compress();
let decompressed_poly = compressed_poly.decompress(&hint);
for i in 0..decompressed_poly.coeffs.len() {
assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
}
let e3 = (28_usize).to_scalar();
assert_eq!(poly.evaluate(&(3_usize).to_scalar()), e3);
}
#[test]
fn test_from_evals_cubic() {
// polynomial is x^3 + 2x^2 + 3x + 1
let e0 = Scalar::one();
let e1 = (7_usize).to_scalar();
let e2 = (23_usize).to_scalar();
let e3 = (55_usize).to_scalar();
let evals = vec![e0, e1, e2, e3];
let poly = UniPoly::from_evals(&evals);
assert_eq!(poly.eval_at_zero(), e0);
assert_eq!(poly.eval_at_one(), e1);
assert_eq!(poly.coeffs.len(), 4);
assert_eq!(poly.coeffs[0], Scalar::one());
assert_eq!(poly.coeffs[1], (3_usize).to_scalar());
assert_eq!(poly.coeffs[2], (2_usize).to_scalar());
assert_eq!(poly.coeffs[3], (1_usize).to_scalar());
let hint = e0 + e1;
let compressed_poly = poly.compress();
let decompressed_poly = compressed_poly.decompress(&hint);
for i in 0..decompressed_poly.coeffs.len() {
assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
}
let e4 = (109_usize).to_scalar();
assert_eq!(poly.evaluate(&(4_usize).to_scalar()), e4);
}
}