Add two-group signing with group-tagged binding factors

[keenan-lightspark]

What

Adds frost_core::two_group: FROST signing where the second participant group (Spark: the user side) is itself a t-of-n FROST group with its own identifier space, per the settled F2 design (SP-2884).

• Collections are keyed by (group, identifier); sub-user positions may numerically collide with operator identifiers and never alias.
• Binding-factor preimage is domain-separated by a one-byte group tag (0x00 primary / 0x01 secondary), present both in each signer's preimage and in every commitment-list entry hashed by H5:

  rho_i = H1(tag(group(i)) || vk || H4(msg) || H5(commitment_list) || id(i))
  commitment_list = concat over signers sorted by (tag, id) of tag || id || hiding || binding
  

• Lagrange coefficients stay within the signer's own group (same rule as the deployed participant-groups scheme); aggregate only sums shares.
• Group commitment R, challenge, share computation/verification, and BIP-340 even-Y handling reuse the Ciphersuite hooks unchanged — even-Y parity is decided by the single R over both groups' commitments.
• Aggregation takes verifying shares for the primary group only: primary shares get share-level blame (InvalidSignatureShare); a failure attributable to the secondary group (no verifying material on the wire by design) is reported as InvalidSignature without blame.
• No changes to existing entry points — deployed single-party byte behavior is untouched; callers select this scheme explicitly by calling the new module.

Tests

frost-secp256k1-tr/tests/two_group_tests.rs:

• (3-of-5)×(2-of-3) sign+aggregate verifies, repeated until both parities of the aggregate nonce R have actually occurred; default identifier lists make cross-group identifier collisions the default case
• colliding identifiers get distinct tagged binding factors (tag is the only preimage difference)
• tampered primary share → blamed by identifier; tampered secondary share → InvalidSignature without blame
• a secondary signer binding a divergent primary commitment set fails loudly at the aggregate check
• taproot-tweaked flow under the deployed key convention (primary pre-normalized to the untweaked combined key's parity carrying the tweaked VK; secondary applies tweak() at signing so the taptweak scalar enters the sum exactly once), repeated until all four combinations of the untweaked key's parity and R's parity have occurred
• the tagged scheme produces a different (still valid) signature than the flat participant-groups scheme over identical commitments and nonces

Note: serialization_tests::check_signing_package_postcard_serialization fails on main before this PR (stale upstream snapshot vs the fork's added SigningPackage fields); not addressed here.

[greptile-apps]

Greptile Summary

Adds an explicit two-group FROST signing scheme with group-tagged binding factors.

• Introduces independent primary and secondary identifier spaces and canonical tagged commitment encoding.
• Adds two-group share generation, aggregation, primary-share blame, and secp256k1-tr parity/tweak handling.
• Adds integration tests for identifier collisions, tampering, divergent commitment views, Taproot tweaking, and compatibility boundaries.

Confidence Score: 4/5

The PR appears safe to merge, with a non-blocking test-coverage gap around deterministic exercise of both aggregate-nonce parities.

The implementation consistently hashes and aggregates both tagged groups, while the only accepted concern is that one randomized test can pass without covering both parity branches it claims to exercise.

Files Needing Attention: frost-secp256k1-tr/tests/two_group_tests.rs

Important Files Changed

Filename	Overview
frost-core/src/two_group.rs	Implements tagged two-group packages, binding factors, per-group interpolation, signing, aggregation, and primary-share verification.
frost-secp256k1-tr/tests/two_group_tests.rs	Adds broad two-group coverage, but its randomized loop does not guarantee the claimed coverage of both aggregate-nonce parities.
frost-core/src/lib.rs	Exposes the new two_group module through the public frost-core API.

Sequence Diagram

sequenceDiagram
    participant P as Primary signers
    participant S as Secondary signers
    participant A as Aggregator
    P->>A: Tagged commitments (0x00, id)
    S->>A: Tagged commitments (0x01, id)
    A-->>P: TwoGroupSigningPackage
    A-->>S: TwoGroupSigningPackage
    P->>P: Compute tagged binding factor and primary-group Lagrange coefficient
    S->>S: Compute tagged binding factor and secondary-group Lagrange coefficient
    P->>A: Primary signature shares
    S->>A: Secondary signature shares
    A->>A: Sum all shares and verify combined signature
    alt Aggregate invalid
        A->>A: Verify primary shares for blame
    end

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Prompt To Fix All With AI

Fix the following 1 code review issue. Work through them one at a time, proposing concise fixes.

---

### Issue 1 of 1
frost-secp256k1-tr/tests/two_group_tests.rs:121
**Parity coverage is nondeterministic**

The fixed random loop never records the aggregate commitment parity, so all eight iterations can exercise the same branch while the test still passes, leaving a parity-specific regression undetected.

_{Reviews (1): Last reviewed commit: "Add two-group signing with group-tagged ..." | Re-trigger Greptile}

[greptile-apps]

Parity coverage is nondeterministic

The fixed random loop never records the aggregate commitment parity, so all eight iterations can exercise the same branch while the test still passes, leaving a parity-specific regression undetected.

Prompt To Fix With AI

This is a comment left during a code review.
Path: frost-secp256k1-tr/tests/two_group_tests.rs
Line: 121

Comment:
**Parity coverage is nondeterministic**

The fixed random loop never records the aggregate commitment parity, so all eight iterations can exercise the same branch while the test still passes, leaving a parity-specific regression undetected.

How can I resolve this? If you propose a fix, please make it concise.

[keenan-lightspark]

@faraday