TEST: introduce hints for batches reconstruction

[titouantanguy]

Description of changes

First try at factoring out all the computation for common information required for reconstructing a batch of shares coming from the same set of parties.

Issue ticket number and link

PR Checklist

I attest that all checked items are satisfied. Any deviation is clearly justified above.

• Title follows conventional commits (e.g. chore: ...).
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Dependency Update Questionnaire (only if deps changed or added)

Answer in the Cargo.toml next to the dependency (or here if updating):

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More details and explanations for the checklist and dependency updates can be found in CONTRIBUTING.md

[github-actions]

Consolidated Tests Results 2026-04-30 - 10:42:18

Test Results

15 passed

Details

15 tests
not captured
junit-to-ctrf
build-and-test test-reporter #1810
TEST: introduce hints for batches reconstruction #559

test-reporter: Run #1810

Tests 📝	Passed ✅	Failed ❌	Skipped ⏭️	Pending ⏳	Other ❓	Flaky 🍂	Duration ⏱️
15	15	0	0	0	0	0	not captured

🎉 All tests passed!

Tests

View All Tests

Test Name	Status	Flaky	Duration
k8s_test_crs_uniqueness	✅		34.3s
k8s_test_insecure_keygen_encrypt_and_public_decrypt	✅		2m 16s
k8s_test_insecure_keygen_encrypt_multiple_types	✅		2m 32s
k8s_test_keygen_and_crs	✅		2m 13s
k8s_test_keygen_uniqueness	✅		5m 44s
k8s_test_crs_uniqueness	✅		34.1s
k8s_test_insecure_keygen_encrypt_and_public_decrypt	✅		2m 12s
k8s_test_insecure_keygen_encrypt_multiple_types	✅		2m 26s
k8s_test_keygen_and_crs	✅		2m 7s
k8s_test_keygen_uniqueness	✅		5m 31s
k8s_test_crs_uniqueness	✅		34.1s
k8s_test_insecure_keygen_encrypt_and_public_decrypt	✅		2m 12s
k8s_test_insecure_keygen_encrypt_multiple_types	✅		2m 26s
k8s_test_keygen_and_crs	✅		2m 7s
k8s_test_keygen_uniqueness	✅		5m 31s

_{🍂 No flaky tests in this run.}

Github Test Reporter by CTRF 💚

🔄 This comment has been updated

[titouantanguy]

Performance test don't indicate any meaningful improvement; but the whole thing was vibecoded and I didn't check in details so maybe worth coming back to the idea at some point.
Closing the PR but leaving the branch for now