Struct binius_core::poly_commit::tensor_pcs::Proof

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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>,
}
Expand description

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.

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§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§

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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,

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

Formats the value using the given formatter. Read more

Auto Trait Implementations§

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impl<U, FI, FE, VCSProof> Freeze for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static,

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impl<U, FI, FE, VCSProof> RefUnwindSafe for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static, <U as PackScalar<FE>>::Packed: RefUnwindSafe, VCSProof: RefUnwindSafe, <U as PackScalar<FI>>::Packed: RefUnwindSafe,

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impl<U, FI, FE, VCSProof> Send for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static, VCSProof: Send,

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impl<U, FI, FE, VCSProof> Sync for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static, VCSProof: Sync,

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impl<U, FI, FE, VCSProof> Unpin for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static, <U as PackScalar<FE>>::Packed: Unpin, VCSProof: Unpin, <U as PackScalar<FI>>::Packed: Unpin,

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impl<U, FI, FE, VCSProof> UnwindSafe for Proof<U, FI, FE, VCSProof>
where <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FE: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE, Output = FE, Output = FE> + for<'a> Sub<&'a FE, Output = FE, Output = FE> + for<'a> Add<&'a FE, Output = FE, Output = FE> + Product + Sum + Mul + Sub + Add + Neg<Output = FE> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FI as WithUnderlier>::Underlier: PackScalar<FI> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, FI: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FI> + for<'a> SubAssign<&'a FI> + for<'a> AddAssign<&'a FI> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FI> + for<'a> Sum<&'a FI> + for<'a> Mul<&'a FI, Output = FI, Output = FI> + for<'a> Sub<&'a FI, Output = FI, Output = FI> + for<'a> Add<&'a FI, Output = FI, Output = FI> + Product + Sum + Mul + Sub + Add + Neg<Output = FI> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, U: UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + 'static, <U as PackScalar<FE>>::Packed: UnwindSafe, VCSProof: UnwindSafe, <U as PackScalar<FI>>::Packed: UnwindSafe,

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