Struct Proof

pub struct Proof<U, FI, FE, VCSProof>
where
    U: PackScalar<FI> + PackScalar<FE>,
    FI: Field,
    FE: Field,
{
    pub n_polys: usize,
    pub mixed_t_prime: MultilinearExtension<PackedType<U, FE>>,
    pub vcs_proofs: VCSProofs<PackedType<U, FI>, VCSProof>,
}

Evaluation proof data for the TensorPCS polynomial commitment scheme.

Type Parameters

• PI: The packed intermediate field type.
• PE: The packed extension field type.
• VCSProof: The vector commitment scheme proof type.

Fields

n_polys: usize

Number of distinct multilinear polynomials in the batch opening proof

mixed_t_prime: MultilinearExtension<PackedType<U, FE>>

Represents a mixing of individual polynomial t_primes

Let $n$ denote n_polys. Define $l = \lceil\log_2(n)\rceil$. Let $\alpha_0, \ldots, \alpha_{l-1}$ be the sampled mixing challenges. Then $c := \otimes_{i=0}^{l-1} (1 - \alpha_i, \alpha_i)$ are the $2^l$ mixing coefficients, denoting the $i$-th coefficient by $c_i$. Let $t’i$ denote the $t’$ for the $i$-th polynomial in the batch opening proof. This value represents the multilinear polynomial such that $\forall v \in {0, 1}^{\mu}$, $v \rightarrow \sum{i=0}^{n-1} c_i * t’_i(v)$

vcs_proofs: VCSProofs<PackedType<U, FI>, VCSProof>

Opening proofs for chosen columns of the encoded matrices

Let $j_1, \ldots, j_k$ be the indices of the columns that are opened. The ith element is a tuple of:

• A vector (size=n_polys) of the $j_i$th columns (one from each polynomial’s encoded matrix)
• A proof that these columns are consistent with the vector commitment

Trait Implementations

impl<U, FI, FE, VCSProof: Debug> Debug for Proof<U, FI, FE, VCSProof>

where U: PackScalar<FI> + PackScalar<FE> + Debug, FI: Field + Debug, FE: Field + Debug,

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

Formats the value using the given formatter.