chore: Extract algebra into its own crate

[dvdplm]

Most of the diff is mechanical import rewiring. Focus review on the new crates and the open questions below.

What this does

Extracts the pure-algebra layer out of threshold-fhe into its own crate – threshold-algebra, abbreviated as algebra – along with three smaller utility crates.
The goal is to make threshold-fhe thinner and thus allow for more compilation parallelism. Smaller code units provides a clear(-er) dependency boundary (no IO, no async, no tokio). This is the first step of several.

New crates

Crate	Path	What it contains
threshold-algebra	core/threshold-algebra/	base_ring, bivariate, galois_fields, galois_rings, poly, error_correction, syndrome, structure_traits — plus role, sharing and the PRSSConversions trait (see open questions)
threshold-hashing	core/threshold-hashing/	hash_element, unsafe_hash_list, DomainSep, DIGEST_BYTES etc. — extracted from threshold-fhe
error-utils	core/error-utils/	anyhow_error_and_log / anyhow_error_and_warn_log helpers (lived in threshold-fhe's internal error module)
thread-handles	core/thread-handles/	Threading utilities extracted from threshold-fhe and some cleanup&tests

Other notable changes

• gen → ggen rename in choreography::grpc and networking — avoids clashing with the Rust gen reserved keyword. While we are still on the 2021 edition, tools like rust-analyzer flags gen as a syntax error. Suggestions for a better rename welcome!
• Role is no longer re-exported from execution — consumers now import from algebra::role directly.
• sharing is no longer re-exported from execution — consumers import from algebra::sharing.
• Test and dev Cargo profiles: disabled full debug info (632a6e7f) after seeing the compiler spend a lot of time and RAM generating full debug info. The downside is that inspecting lvars during debugging is not possible with the partial debug info; backtraces are however intact.

Open questions for reviewers

1. Should Role (and RoleTrait, RoleKind, TwoSetsRole, DualRole) live in its own crate?
   I moved it from threshold-fhe into threshold-algebra, but several types in execution::runtime (sessions, party) still depend on it heavily. Some role-related pieces are still left in execution, which is a bit of a code smell. A standalone threshold-role crate might make the dependency graph cleaner. Thoughts?

2. Same question for sharing::{shamir, share}.
   ShamirSharings, Share, InputOp, RevealOp are now in threshold-algebra, but they're really protocol-level types used by execution. Should they stay in algebra or be extracted to a mini-crate? Currently there is code left in execution/sharing, which is not great.

3. PRSSConversions trait is now defined in threshold-algebra/src/lib.rs.
   It exists so that galois ring types can implement it, but it's a protocol thing more than an algebra concern. Where should it live? It's re-exported in execution::small_execution::prf. This is a tricky one, ideas welcome.

Outstanding TODOs

Location	Note
threshold-algebra/Cargo.toml:14	Get rid of lazy_static dep (kms-internal#2907)
threshold-algebra/Cargo.toml:30	Are all these feature flags actually needed now that the crate does no IO? non-wasm might be unnecessary.
threshold-algebra/src/role.rs:107	Used derive_more before — still needed?
threshold-algebra/src/structure_traits.rs:140,159	embed_role_to_exceptional_sequence and Derive trait could take 1-based indexes instead of Role — simplify? Can we get rid of Role and the other types fromalgebra?
threshold-algebra/src/sharing/shamir.rs:629	A test that should move back to threshold-fhe.
threshold-algebra/src/lib.rs:12-16	Notes on why shamir/PRSSConversions ended up here.
threshold-hashing/src/lib.rs:7	DomainSep/DSEP_LEN/DIGEST_BYTES constants — own "types and consts" crate?

[github-actions]

Consolidated Tests Results 2026-02-25 - 17:24:58

Test Results

14 passed

Details

14 tests
not captured
junit-to-ctrf
build-and-test test-reporter #591
chore: Extract algebra into its own crate #434

test-reporter: Run #591

Tests 📝	Passed ✅	Failed ❌	Skipped ⏭️	Pending ⏳	Other ❓	Flaky 🍂	Duration ⏱️
14	14	0	0	0	0	0	not captured

🎉 All tests passed!

Tests

View All Tests

Test Name	Status	Flaky	Duration
full_gen_tests_k8s_default_threshld_sequential_crs	✅		32.6s
test_k8s_threshld_insecure	✅		3m 16s
k8s_test_crs_uniqueness	✅		32.5s
k8s_test_keygen_and_crs	✅		3m 19s
k8s_test_keygen_uniqueness	✅		8m 58s
full_gen_tests_k8s_default_threshld_sequential_crs	✅		32.4s
test_k8s_threshld_insecure	✅		3m 18s
k8s_test_crs_uniqueness	✅		32.5s
k8s_test_keygen_and_crs	✅		3m 18s
k8s_test_keygen_uniqueness	✅		9m 7s
full_gen_tests_k8s_default_centralzd_sequential_crs	✅		1.8s
test_k8s_centralzd_insecure	✅		1m 3s
full_gen_tests_default_k8s_centralized_sequential_crs	✅		1.8s
k8s_test_centralized_insecure	✅		1m 3s

_{🍂 No flaky tests in this run.}

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