Add KZH-k multilinear polynomial commitments

[h-hafezi]

Description

This PR adds KZH-k, a non-hiding pairing-based multilinear polynomial
commitment family parameterized by the const generic K.

The implementation follows KZH-Fold and uses the generic-opening auxiliary
commitments described by IronDict. It uses arkworks' native little-endian MLE
layout throughout and calls MultilinearExtension::fix_variables for partial
evaluation.

Highlights

• Implements the native PolynomialCommitment interface for dense and sparse
  arkworks multilinear extensions.
• Supports balanced rectangular tensor decompositions when the number of
  variables is not divisible by K.
• Stores in the commitment state only the auxiliary tables whose cached
  contraction needs fewer group-scalar terms than recommitting the partially
  evaluated polynomial in a single-polynomial opening (at most the first
  floor(K/2) layers, as in IronDict's generic opening). Tables that only
  serve free Boolean openings are not computed.
• Supports same-point batching, the framework's default multi-point and
  linear-combination APIs, and prepared verifier keys.
• Validates family markers, tensor dimensions, keys, commitments, states,
  proofs, labels, and point dimensions at operation boundaries.
• Includes commit/open/check tests for dense, sparse, and unevenly partitioned
  polynomials, a wrong-evaluation rejection test, unit tests for block
  splitting and auxiliary-table selection, and a Criterion benchmark
  (benches/kzh_times.rs) for K = 2, 3, 4, 6 at 12, 16, and 20 variables
  that also prints serialized parameter, key, state, and proof sizes.

Costs

The counts below are for N = 2^n evaluations and one polynomial. They come
from the implementation's own planner (auxiliary_prefix_lengths and
opening_work_plan in kzh/utils.rs), printed by a local, uncommitted probe
for K = 2, 3, 4, 6 and n = 12, 13, 16, 17, 20. They count MSM scalar terms, pairings, and proof
elements; they are not runtime measurements, and this PR makes no wall-clock
claims.

• Commit: at most (1 + floor(K/2)) * N MSM scalar terms, i.e. one N-term
  MSM for the commitment plus N terms per stored auxiliary table (2N for
  K = 2, 3, 3N for K = 4, 4N for K = 6 in every case above).
• Opening at a non-Boolean point: O(N) field operations plus
  O(N^(ceil(K/2)/K)) group-scalar terms, which is O(sqrt(N)) for even K
  and zero for K = 2. For odd K this is above the O(sqrt(N)) quoted in
  the papers' cost summaries (K = 3, n = 20: 8192 terms, i.e.
  8 * sqrt(N)). A same-point batch of b > 1 polynomials contracts b
  cached tables per cached layer, or recommits the layer when that is cheaper,
  so it needs more group work than a single-polynomial opening.
• Proof and verification: K - 1 layers of G1 elements plus the last block's
  field elements, i.e. O(K * N^(1/K)) elements; verification performs K - 1
  multi-pairings over those layers and K block-sized MSMs.

This PR intentionally does not add hiding commitments, strict degree bounds,
a Boolean-specialized opening API, or an R1CS verification gadget.

The most important files to review are:

• poly-commit/src/kzh/mod.rs
• poly-commit/src/kzh/data_structures.rs
• poly-commit/src/kzh/utils.rs
• poly-commit/src/kzh/tests.rs

No existing GitHub issue currently tracks this addition; the construction,
scope, costs, setup assumptions, and compatibility choices are described here
and in the module documentation.

Validation

Local runs on 79c0620 (macOS aarch64), mirroring .github/workflows/ci.yml
on stable and nightly with RUSTFLAGS=-Dwarnings:

• cargo fmt --all -- --check
• cargo check --examples --all, cargo check --examples --all-features --all
  (stable), and cargo check --all-features --examples --all --benches
  (nightly)
• cargo test --release: 118 library tests, including the 5 KZH tests, and
  4 doctests passed
• cargo build and cargo check --workspace --no-default-features --target aarch64-unknown-none --exclude ark-pcs-bench-templates

Additional KZH checks:

• cargo test --release -p ark-poly-commit --no-default-features --features std kzh:: (serial auxiliary-table path) and RAYON_NUM_THREADS=2 cargo test --release -p ark-poly-commit kzh:: (row-parallel path): 5 passed each
• cargo bench -p ark-poly-commit --bench kzh_times -- --test: all 80
  benchmark functions of the K x n matrix ran once (no timings recorded)
• RUSTDOCFLAGS=-Dwarnings cargo doc -p ark-poly-commit --no-deps --all-features: no KZH diagnostics; the 30 remaining broken-link errors
  also occur on master

---

• Targeted PR against correct branch (master)
• Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work. (Design and scope are explained above.)
• Wrote unit tests
• Updated relevant documentation in the code
• Added a relevant changelog entry to the Pending section in CHANGELOG.md
• Re-reviewed Files changed in the Github PR explorer

Edited during maintainer review (@weikengchen, with Claude Code): updated the test and validation sections for the trimmed test suite, and restated costs as operation counts from the implementation's planner.

[weikengchen]

Thanks for the PR. I am currently reviewing :)

[h-hafezi]

Hi Weikeng, I was wondering if I could follow up on this thread.

[weikengchen]

(no worries I was just a bit busy lately, but I don't think there is any blocker in merging)