Struct RoundProof

pub struct RoundProof<F: Field>(pub RoundCoeffs<F>);

A sumcheck round proof is a univariate polynomial in monomial basis with the coefficient of the highest-degree term truncated off.

Since the verifier knows the claimed sum of the polynomial values at the points 0 and 1, the high-degree term coefficient can be easily recovered. Truncating the coefficient off saves a small amount of proof data.

Tuple Fields

0: RoundCoeffs<F>

Implementations

impl<F: Field> RoundProof<F>

pub fn recover(self, sum: F) -> RoundCoeffs<F>

Recovers all univariate polynomial coefficients from the compressed round proof.

The prover has sent coefficients for the purported ith round polynomial $r_i(X) = \sum_{j=0}^d a_j * X^j$. However, the prover has not sent the highest degree coefficient $a_d$. The verifier will need to recover this missing coefficient.

Let $s$ denote the current round’s claimed sum. The verifier expects the round polynomial $r_i$ to satisfy the identity $s = r_i(0) + r_i(1)$. Using $r_i(0) = a_0$ $r_i(1) = \sum_{j=0}^d a_j$ There is a unique $a_d$ that allows $r_i$ to satisfy the above identity. Specifically $a_d = s - a_0 - \sum_{j=0}^{d-1} a_j$

Not sending the whole round polynomial is an optimization. In the unoptimized version of the protocol, the verifier will halt and reject if given a round polynomial that does not satisfy the above identity.

pub fn coeffs(&self) -> &[F]

The truncated polynomial coefficients.

pub fn isomorphic<FI: Field + From<F>>(self) -> RoundProof<FI>

Representation in an isomorphic field

Trait Implementations

impl<F: Clone + Field> Clone for RoundProof<F>

fn clone(&self) -> RoundProof<F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F: Debug + Field> Debug for RoundProof<F>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F: Default + Field> Default for RoundProof<F>

fn default() -> RoundProof<F>

Returns the “default value” for a type.

impl<F: PartialEq + Field> PartialEq for RoundProof<F>

fn eq(&self, other: &RoundProof<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F: Eq + Field> Eq for RoundProof<F>

impl<F: Field> StructuralPartialEq for RoundProof<F>