Optimize Bivariate poly math

[dvdplm]

Refactor the BivariatePoly maths to avoid generic impl and instead provide only optimized code for the shapes in actual use: vector x matrix (partial_x_eval) and matrix x vector (partial_y_eval). These are now inlined (along with the vector x vector case).

Also in this PR:

• smaller API (i.e. less pub methods)
• infallible calls no longer return Result
• a new partial_evals that compute both partial evals in one go (do note the TODO(dp) in the code though).

Note: In this PR the ndarray crate is still present and the generic matmul code is moved to matrix.rs. The follow-up PR #585 removes it entirely along with a second batch of optimizations that are unrelated to bivariate polys.

Added a few benchmarks and new tests.

This PR is ~3x faster than main on my machine for the deg 4 (i.e. 5x5 grid) case that we use in production.

group                                main                new
bivariate/evaluation/full/1          183.9±0.68ns        33.3±0.54ns    5.52x faster
bivariate/evaluation/full/4          496.5±2.57ns        147.1±4.11ns   3.37x faster <––
bivariate/evaluation/full/13         1897.6±5.13ns       999.5±4.04ns   1.90x faster

bivariate/evaluation/partial_x/1     110.5±0.65ns        23.3±0.54ns    4.73x faster
bivariate/evaluation/partial_x/4     350.1±1.08ns        118.5±7.40ns   2.95x faster <––
bivariate/evaluation/partial_x/13    1608.3±4.21ns       920.8±3.06ns   1.75x faster

bivariate/evaluation/partial_y/1     106.0±0.63ns        21.2±0.47ns    5.00x faster
bivariate/evaluation/partial_y/4     342.3±1.15ns        117.1±2.01ns   2.92x faster <––
bivariate/evaluation/partial_y/13    1574.0±7.88ns       899.2±3.62ns   1.75x faster

bivariate/from_secret/1              515.8±7.74ns        488.2±13.00ns  1.06x faster
bivariate/from_secret/4              4.0±0.03µs          3.9±0.14µs     1.03x faster
bivariate/from_secret/13             32.2±0.27µs         31.4±1.39µs    1.02x faster

[github-actions]

Consolidated Tests Results 2026-05-21 - 10:08:25

Test Results

7 passed

Details

7 tests
not captured
junit-to-ctrf
build-and-test test-reporter #2318
Optimize Bivariate poly math #576

test-reporter: Run #2318

Tests 📝	Passed ✅	Failed ❌	Skipped ⏭️	Pending ⏳	Other ❓	Flaky 🍂	Duration ⏱️
7	7	0	0	0	0	0	not captured

🎉 All tests passed!

Tests

View All Tests

Test Name	Status	Flaky	Duration
k8s_test_crs_uniqueness	✅		43.9s
k8s_test_insecure_keygen_encrypt_and_public_decrypt	✅		2m 13s
k8s_test_insecure_keygen_encrypt_multiple_types	✅		2m 20s
k8s_test_keygen_and_crs	✅		2m 10s
k8s_test_keygen_uniqueness	✅		5m 19s
k8s_test_centralized_insecure	✅		1m
nightly_full_gen_tests_default_k8s_centralized_sequential_crs	✅		1.8s

_{🍂 No flaky tests in this run.}

Github Test Reporter by CTRF 💚

🔄 This comment has been updated

[Copilot]

Pull request overview

This PR refactors bivariate polynomial evaluation to remove the prior generic/ndarray-driven evaluation path and replace it with specialized, inlined evaluation routines for the shapes used in production, while relocating the remaining generic matmul utilities into a new matrix module.

Changes:

• Reimplemented BivariatePoly storage/evaluation to use a row-major coefficient Vec plus specialized partial_x_eval, partial_y_eval, full_eval, and fused partial_evals.
• Moved generic MatrixMul + power precomputation helpers (compute_powers, compute_powers_list) into core/threshold-algebra/src/matrix.rs and updated imports/call sites.
• Updated threshold execution VSS/PRSS code to use the new infallible bivariate APIs and introduced DoublePoly::from_bivariate to leverage fused partial evaluations.

Reviewed changes

Copilot reviewed 19 out of 20 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
dylint.toml	Removes trailing formatting artifact in the config.
core/threshold-execution/src/small_execution/prss.rs	Switches power-precompute + matmul imports to algebra::matrix.
core/threshold-execution/src/malicious_execution/large_execution/malicious_vss.rs	Updates to infallible bivariate API and uses DoublePoly::from_bivariate.
core/threshold-execution/src/large_execution/vss.rs	Updates evaluation calls to new bivariate API and adds DoublePoly::from_bivariate.
core/threshold-execution/src/large_execution/single_sharing.rs	Replaces compute_powers usage with an inlined power-generation loop; updates matmul import.
core/threshold-execution/src/large_execution/double_sharing.rs	Updates matmul import to algebra::matrix.
core/threshold-algebra/src/syndrome.rs	Switches compute_powers_list import to matrix module.
core/threshold-algebra/src/matrix.rs	New module containing MatrixMul + compute_powers* helpers and associated tests.
core/threshold-algebra/src/lib.rs	Exposes the new matrix module.
core/threshold-algebra/src/galois_rings/degree_3.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/degree_4.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/degree_5.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/degree_6.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/degree_7.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/degree_8.rs	Switches compute_powers import to matrix module.
core/threshold-algebra/src/galois_rings/common.rs	Switches compute_powers_list import to matrix module.
core/threshold-algebra/src/bivariate.rs	Replaces ndarray-based bivariate representation/eval with specialized vector-based routines and new tests.
core/threshold-algebra/Cargo.toml	Adds Criterion dev-dependency and registers the new bivariate benchmark.
core/threshold-algebra/benches/bivariate.rs	New Criterion benchmark suite for bivariate sampling/evaluation paths.
Cargo.lock	Adds Criterion to the lockfile due to new benchmark dependency.

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