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Small optimisations for IPA verification #27

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merged 2 commits into from
Sep 27, 2023
Merged

Small optimisations for IPA verification #27

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9128f5e
remove `G_0_prime` from proof`
kilic Sep 25, 2023
c862fad
commit suggestion: compute scaled h poly
kilic Sep 27, 2023
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26 changes: 10 additions & 16 deletions plonkish_backend/src/pcs/multilinear/ipa.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -235,7 +235,6 @@ where
zs.truncate(mid);
}

transcript.write_commitment(&bases[0])?;
transcript.write_field_element(&coeffs[0])?;

Ok(())
Expand Down Expand Up @@ -289,25 +288,20 @@ where
.collect::<Result<Vec<_>, _>>()?
.into_iter()
.multiunzip::<(Vec<_>, Vec<_>, Vec<_>)>();
let g_k = transcript.read_commitment()?;
let c = transcript.read_field_element()?;
let neg_c = -transcript.read_field_element()?;

let xi_invs = {
let mut xi_invs = xis.clone();
xi_invs.iter_mut().batch_invert();
xi_invs
};
let eval_prime = xi_0 * eval;
let c_k = variable_base_msm(
chain![&xi_invs, &xis, Some(&eval_prime)],
chain![&ls, &rs, Some(vp.h())],
) + comm.0;
let h = MultilinearPolynomial::new(h_coeffs(&xis));

(c_k == variable_base_msm(&[c, c * h.evaluate(point) * xi_0], [&g_k, vp.h()])
&& g_k == variable_base_msm(h.evals(), vp.g()).to_affine())
.then_some(())
.ok_or_else(|| Error::InvalidPcsOpen("Invalid multilinear IPA open".to_string()))
let neg_c_h = MultilinearPolynomial::new(h_coeffs(neg_c, &xis));
let u = &(xi_0 * (neg_c_h.evaluate(point) + eval));
let scalars = chain![&xi_invs, &xis, neg_c_h.evals(), Some(u)];
let bases = chain![&ls, &rs, vp.g(), Some(vp.h())];
bool::from((variable_base_msm(scalars, bases) + comm.0).is_identity())
.then_some(())
.ok_or_else(|| Error::InvalidPcsOpen("Invalid multilinear IPA open".to_string()))
}

fn batch_verify<'a>(
Expand All @@ -322,11 +316,11 @@ where
}
}

fn h_coeffs<F: Field>(xi: &[F]) -> Vec<F> {
fn h_coeffs<F: Field>(scalar: F, xi: &[F]) -> Vec<F> {
assert!(!xi.is_empty());

let mut coeffs = vec![F::ZERO; 1 << xi.len()];
coeffs[0] = F::ONE;
coeffs[0] = scalar;

for (len, xi) in xi.iter().rev().enumerate().map(|(i, xi)| (1 << i, xi)) {
let (left, right) = coeffs.split_at_mut(len);
Expand Down
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