interpolate the *unique* univariate polynomial of degree *at most p_i.len()-1 passing through the y-values in p_i at x = 0,..., p_i.len()-1 and evalua

Check if the constraint system is satisfied by the given inputs

Ajtai matrix number of rows This value affects the security of the scheme.

Get the number of constraints

Get the MLEs needed for one g2 component of the sumcheck polynomial

Prepare the main linearization polynomial. $$ g(\vec{\mathbf{x}}) := eq(\vec{\beta}, \vec{\mathbf{x}}) \cdot \left( \sum\_{i=1}^{n\_s} c\_i \cdot \le

Converts the R1CS instance into a RelaxedR1CS as described in [Nova](https://eprint.iacr.org/2021/370.pdf#page=14)

Generates a valid single instance fold proof for verifier benchmarks. Creates a LinB instance, executes the lin folding protocol to generate a `CmPro

Generates a valid end-to-end proof for verifier benchmarks. Creates a complete prover setup, generates a proof by folding L instances, and prepares t

Generates a valid set check proof for verifier benchmarks. Creates input, executes the prover to generate an `Out` proof, and validates it before ret

Generates a valid range check proof for verifier benchmarks. Creates input, executes the prover to generate a `Dcom` proof, and validates it before r

Generates a valid multilinear fold proof for verifier benchmarks. Creates an `Mlin` input with L instances, executes the mlin protocol to generate a

Generates a valid decomposition proof for verifier benchmarks. Creates a LinB2 instance, executes the decomposition protocol to generate a `DecompPro

Combines evaluations of MLE into evaluation of folding sumcheck polynomial # Arguments - `vals: &[NTT]`: The evaluations of the multilinear extensio

Takes the `f_hat` value. Leaves the value in the struct as `None`.

Convert to a sparse matrix representation (R1CS)

Validates that witness size satisfies decomposition parameter constraints. Ensures the fundamental constraint: `witness_size >= κ × k × d × l × d` wh

Add a term to the linear combination

Benchmark entry point for commitment transformation prover with L scaling.

Benchmark entry point for commitment transformation verifier with L scaling.

Benchmark entry point for decomposition prover with witness size scaling.

Benchmark entry point for complete fold→decompose roundtrip cycle. Measures the full cost of folding followed by decomposition, which is the typical

Benchmark entry point for decomposition verifier with witness size scaling.

Benchmark entry point for double commitment with k-scaling.

Benchmark entry point for double commitment with witness size scaling.

Benchmark entry point for E2E prover with folding arity scaling.

Benchmark entry point for E2E prover with protocol scaling.

Benchmark entry point for E2E verifier with protocol scaling.

Benchmark entry point for single instance folding prover with witness size scaling.

Benchmark entry point for single instance folding verifier with witness size scaling.

Benchmark entry point for multilinear folding prover with k scaling.

Benchmark entry point for multilinear folding prover with κ scaling.

Benchmark entry point for multilinear folding prover with large witness scaling.

Benchmark entry point for multilinear folding prover with L scaling.

Benchmark entry point for multilinear folding verifier with L scaling.

Generic benchmark runner for prover protocols. Eliminates boilerplate by handling benchmark group creation, parameter iteration, throughput measureme

Benchmark entry point for range check prover with k-scaling.

Benchmark entry point for range check prover with κ-scaling.

Benchmark entry point for range check prover with witness size scaling.

Benchmark entry point for range check verifier with witness size scaling.

Benchmark entry point for set check prover with batching efficiency test.

Benchmark entry point for set check prover with size and batch scaling.

Benchmark entry point for set check verifier with size and batch scaling.

Benchmark entry point for split function with k_first scaling.

Benchmark entry point for split function with κ scaling.

Benchmark entry point for split function with varying parameters.

Generic benchmark runner for verifier protocols. Similar to `bench_prover_protocol` but for verification. Handles proof generation in the setup phase

Prepare MLE's of the form mle[M_i \cdot z_ccs](x), a.k.a. \sum mle[M_i](x, b) * mle[z_ccs](b).

verify the sumcheck phase, and generate the subclaim If the asserted sum is correct, then the multilinear polynomial evaluated at `subclaim.point` is

Produces a commitment from a witness Ajtai commitments are produced by multiplying an Ajtai matrix by the witness vector

Commit to a witness in the coefficient form. Performs NTT on each component of the witness and then does Ajtai commitment.

Ajtai commits to witnesses `wit_s` using Ajtai commitment scheme `scheme`.

Computes decomposition parameters for the current ring configuration. Uses FrogRing dimension and modulus to calculate optimal base and length for ga

Step 3: the mle evaluations that the prover sends to the verifier. I.e. f-hat rows mle evaluations and Mz mle evaluations.

Computes the grand sum from point 4 of the Latticefold folding protocol. # Arguments - `alpha_s: &[NTT]` A slice containing the $\alpha$ challenges.