feat: batch subgroup membership testing

[yelhousni]

Description

This PR introduces batch subgroup membership for all curves. For small batches we individually check that all points are on G1/2. For large batches, for an error probability 1/2^64, we check that 64 random MSMs with coefficients in {0,1} are on G1/2. These coefficients do not kill small torsions points. For a higher probability we can redo the test. Empirically, we find that < 80 and < 160 are considered small batches for G1 and respectively G2.

Type of change

• New feature (non-breaking change which adds functionality)

How has this been tested?

TestIsInSubGroupBatchG1/2 in g1/2_test.go

How has this been benchmarked?

Please describe the benchmarks that you ran to verify your changes.

• e.g. BLS12-381 on G1:

Number of points	Naive (ms/op)	Batched (ms/op)	Speedup x
2^7	1.475	1.125	1.311
2^8	2.860	1.474	1.940
2^9	6.163	2.183	2.824
2^10	11.120	3.572	3.113
2^11	21.423	6.475	3.309
2^12	44.098	12.917	3.414
2^13	87.337	22.587	3.867
2^14	174.153	47.257	3.685
2^15	333.508	83.476	3.995
2^16	651.185	162.479	4.008
2^17	1292.244	325.368	3.972
2^18	2588.981	686.961	3.769
2^19	5184.084	1263.900	4.102
2^20	10581.648	2665.976	3.969
2^21	20680.015	5119.575	4.039
2^22	42026.034	11111.155	3.782

• e.g. BLS12-381 on G2:

Number of points	Naive (ms/op)	Batched (ms/op)	Speedup x
2^8	4.112	3.682	1.117
2^9	8.980	6.861	1.309
2^10	17.356	10.688	1.624
2^11	32.402	23.390	1.385
2^12	59.415	37.791	1.572
2^13	121.708	73.877	1.647
2^14	268.745	157.836	1.703
2^15	514.079	306.245	1.679
2^16	1017.908	570.382	1.785
2^17	1938.422	1299.176	1.492
2^18	4165.813	2623.936	1.588
2^19	8034.229	4373.636	1.837
2^20	16153.649	9258.215	1.745
2^21	33173.966	19926.421	1.665

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

---

Note

Introduce batched subgroup membership APIs for G1/G2 across curves with naive (<80/<160) and probabilistic MSM strategies, plus supporting helpers and tests; minor import cleanups.

• ECC libraries (G1/G2):
  • Add IsInSubGroupBatchG1 and IsInSubGroupBatchG2 for batched subgroup checks.
    • Use naive per-point checks for small batches (<80 for G1, <160 for G2).
    • Use probabilistic method (64 MSMs with {0,1} scalars, crypto/rand, parallel, sync/atomic) for large batches.
  • Add curve-specific helpers (e.g., fuzzCofactorOfG1/G2 for BLS12-377/381) and necessary imports.
• Tests:
  • Add TestIsInSubGroupBatchG1/TestIsInSubGroupBatchG2 covering positive and negative cases (including cofactor-torsion).
  • Expand existing subgroup tests and small import tidy-ups in various vector_test.go files.
• Codegen templates:
  • Update internal/generator/ecc/template/point.go.tmpl to generate batched subgroup APIs and required imports.
  • Update internal/generator/ecc/template/tests/point.go.tmpl to generate batch tests and cofactor checks.

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[Copilot]

Pull Request Overview

This PR adds batch subgroup membership checking for curve points across all supported ECC curves, using a naive per-point check for small batches and a probabilistic MSM-based check for larger batches. It also includes corresponding property-based tests for high-confidence validation.

• Introduce IsInSubGroupBatch*, isInSubGroupBatch*Naive, and isInSubGroupBatch*Prob functions in generator templates and per-curve implementations.
• Update imports to include crypto/rand and sync/atomic where needed.
• Add TestIsInSubGroupBatch* property tests in all curve-specific test files.

Reviewed Changes

Copilot reviewed 35 out of 35 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
internal/generator/ecc/template/tests/point.go.tmpl	Add template for TestIsInSubGroupBatch*
internal/generator/ecc/template/point.go.tmpl	Add IsInSubGroupBatch* methods and imports
ecc/stark-curve/g1.go	Add IsInSubGroupBatchG1 probabilistic batch check
ecc/secp256k1/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/secp256k1/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/grumpkin/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/grumpkin/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bw6-761/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bw6-761/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bw6-761/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bw6-761/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bw6-633/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bw6-633/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bw6-633/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bw6-633/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bn254/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bn254/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bn254/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bn254/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bls24-317/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bls24-317/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bls24-317/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bls24-317/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bls24-315/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bls24-315/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bls24-315/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bls24-315/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bls12-381/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bls12-381/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bls12-381/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bls12-381/g2_test.go	Add TestIsInSubGroupBatchG2
ecc/bls12-377/g1.go	Add IsInSubGroupBatchG1 (naive + probabilistic)
ecc/bls12-377/g1_test.go	Add TestIsInSubGroupBatchG1
ecc/bls12-377/g2.go	Add IsInSubGroupBatchG2 (naive + probabilistic)
ecc/bls12-377/g2_test.go	Add TestIsInSubGroupBatchG2

Comments suppressed due to low confidence (2)

ecc/bw6-761/g2.go:216

• The comment mentions G1 but this function checks subgroup membership for G2. Update the comment to reference G2.

// IsInSubGroupBatchG2 checks if a batch of points P_i are in G1.

internal/generator/ecc/template/point.go.tmpl:338

• The loop for j := range len(points) is invalid syntax. Replace it with for j := 0; j < len(points); j++ { or for j := range points { to iterate over the slice.

			for j := range len(points) {

[Tabaie]

Cool algo! Just one thing, the test currently only looks for false positives ("positive" being off-subgroup) but it seems pretty obvious that there can't possibly be any. It'd be more interesting imo to look for false negatives, or both at least.

[yelhousni]

Cool algo! Just one thing, the test currently only looks for false positives ("positive" being off-subgroup) but it seems pretty obvious that there can't possibly be any. It'd be more interesting imo to look for false negatives, or both at least.

Thank for the review! yeah it seems tests are not complete. I'll push something.