Struct IdealCheckProtocol 

pub struct IdealCheckProtocol<U: Uair>(/* private fields */);

Ideal-check subprotocol.

The evaluation point $r \in F^\mu$ at which the combined polynomial MLEs are pinned down is supplied by the caller rather than squeezed from the transcript inside this subprotocol:

The protocol layer samples a single shared integer vector $r \in [0, q^*)^\mu$ once and projects it into each family’s field, so all $n + 1$ families re-use the same underlying integers (just typed in their respective fields).

Implementations

impl<U: Uair> IdealCheckProtocol<U>

pub fn prove_mle_first<C, const DEGREE_PLUS_ONE: usize>( transcript: &mut impl Transcript, trace_matrix: &ColumnMajorTrace<C::Element>, projected_scalars: &ProjectedScalars<U::Scalar, DynamicPolynomial<C::Element>>, family_idx: usize, num_constraints: usize, evaluation_point: &[C::Element], field_cfg: &C, ) -> Result<Proof<C::Element>, IdealCheckError<C::Element>>

where C: BaseFieldConfig + ProjectPrimitiveIntegersWithConfig, C::Integer: ConstTranscribable,

Prover using MLE-first evaluation (column-indexed trace).

Routes each constraint through the most efficient evaluation path:

• Linear constraints with non-zero ideals are batched through [evaluate_combined_polynomials], which evaluates trace column MLEs at the challenge point and then applies the constraints to the evaluated values.
• Non-linear constraints with non-zero ideals fall back to the row-major [evaluate_for_constraints] path; the trace is transposed on demand via column_major_to_row_major.
• Constraints with zero ideals are short-circuited to zero (their combined polynomial value is zero by construction for an honest prover).

For $F_{q_i}[X]$ constraints, trace_matrix and projected_scalars must already be projected mod $q_i$.

Parameters

• transcript: the Fiat-Shamir transcript.
• trace_matrix: input trace for the UAIR U projected to DynamicPolynomialF<F>, column-indexed: trace_matrix[col][row].
• projected_scalars: UAIR scalars projected to DynamicPolynomialF<F>.
• family_idx: which constraint family to prove. 0 -> $Q[X]$; i >= 1 -> $F_{q_{i-1}}[X]$ (i.e. UAIR-level prime_idx = i - 1).
• num_constraints: number of constraints this UAIR encodes.
• evaluation_point: pre-sampled MLE evaluation point, shared for all families of constraints ($Q[X]$ and $F_q[X]$).
• field_cfg: random field configuration sampled on the previous steps of the overall protocol.

pub fn prove_combined<C, const DEGREE_PLUS_ONE: usize>( transcript: &mut impl Transcript, trace_matrix: &RowMajorTrace<C::Element>, projected_scalars: &ProjectedScalars<U::Scalar, DynamicPolynomial<C::Element>>, family_idx: usize, num_constraints: usize, evaluation_point: &[C::Element], field_cfg: &C, ) -> Result<Proof<C::Element>, IdealCheckError<C::Element>>

where C: BaseFieldConfig + ProjectPrimitiveIntegersWithConfig, C::Integer: ConstTranscribable,

Prover for any UAIR using combined polynomial construction.

Uses row-indexed (transposed) trace for efficient row-by-row combined polynomial construction.

For $F_{q_i}[X]$ constraints, trace_matrix and projected_scalars must already be projected mod $q_i$.

Parameters

• transcript: the Fiat-Shamir transcript.
• trace_matrix: input trace for the UAIR U projected to DynamicPolynomialF<F>, row-indexed: trace_matrix[row][col].
• projected_scalars: UAIR scalars projected to DynamicPolynomialF<F>.
• family_idx: which constraint family to prove. 0 -> $Q[X]$; i >= 1 -> $F_{q_{i-1}}[X]$.
• num_constraints: number of constraints this UAIR encodes.
• evaluation_point: pre-sampled MLE evaluation point, shared for all families of constraints ($Q[X]$ and $F_q[X]$).
• field_cfg: random field configuration sampled on the previous steps of the overall protocol.

pub fn verify_as_subprotocol<'cfg, C, IdealOverF, IdealOverFFromRef, IdealOverFFromFqRef>( transcript: &mut impl Transcript, proof: Proof<C::Element>, family_idx: usize, num_constraints: usize, evaluation_point: &[C::Element], ideal_over_f_from_ref: IdealOverFFromRef, ideal_over_f_from_fq_ref: IdealOverFFromFqRef, field_cfg: &'cfg C, ) -> Result<VerifierSubclaim<C::Element>, IdealCheckError<C::Element>>

where C: BaseFieldConfig, C::Integer: ConstTranscribable, IdealOverF: Ideal + IdealCheck<DynamicPolynomialConfig<'cfg, C>>, IdealOverFFromRef: Fn(&IdealOrZero<U::Ideal>) -> IdealOverF, IdealOverFFromFqRef: Fn(&IdealOrZero<U::FqIdeal>) -> IdealOverF,

The verifier part of the ideal-check subprotocol.

Mirrors the prover: receives the prover’s combined_mle_values, absorbs them into the transcript, then checks each non-trivial constraint’s value against the corresponding lifted ideal.

Parameters

• transcript: the Fiat-Shamir transcript.
• proof: a purported proof produced by the prover.
• family_idx: which constraint family to verify. 0 -> $Q[X]$; i >= 1 -> $F_{q_{i-1}}[X]$.
• num_constraints: the number of constraints the UAIR U encodes.
• evaluation_point: pre-sampled MLE evaluation point matching the one used by the prover. The caller is responsible for ensuring transcript ordering matches the prover.
• ideal_over_f_from_ref: since the UAIR U is not aware of the field the ideal check is operating on it defines ideals over the ring IcTypes::Witness. ideal_over_f_from_ref allows to convert the ideals over IcTypes::Witness into ideals over the field IcTypes::F. Think of this as a projection for ideals.
• field_cfg: random field configuration sampled on the previous steps of the overall protocol.

Trait Implementations

impl<U: Clone + Uair> Clone for IdealCheckProtocol<U>

fn clone(&self) -> IdealCheckProtocol<U>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<U: Default + Uair> Default for IdealCheckProtocol<U>

fn default() -> IdealCheckProtocol<U>

Returns the “default value” for a type.

impl<U: Copy + Uair> Copy for IdealCheckProtocol<U>