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zeekay e6c6417d52 proofs/cmp: Tier A EC theories + Lean bridges + Jasmin CT scaffolds

Adds the Tier A formal-artifact cluster for protocols/cmp (Lux profile
of CGGMP21 threshold ECDSA, CCS '21 / ePrint 2021/060). Mirrors
luxfi/pulsar's Tier A structure adapted to CCS '21's 4-round keygen +
3-round presign + 1-round online sign decomposition.

- proofs/easycrypt/CGGMP21_N1.ec — Class N1 byte-equality reduction
- proofs/easycrypt/CGGMP21_N1_Refinement.ec — keygen/presign/sign refinement
- proofs/easycrypt/CGGMP21_Paillier.ec — Paillier additive homomorphism
- proofs/easycrypt/CGGMP21_ZK.ec — 17 ZK subprotocol cluster obligation
- proofs/easycrypt/CGGMP21_N4.ec — refresh / proactive rotation
- proofs/easycrypt/lemmas/CGGMP21_CT.ec — constant-time obligations
- proofs/easycrypt/AXIOM-INVENTORY.md — honest enumeration
- proofs/lean-easycrypt-bridge.md — Lean↔EC bridge map
- jasmin/lib/ + jasmin/single-party/ + jasmin/presign/ + jasmin/threshold/

Admit budget: 1/1 (same one-line group-identity admit as FROST_N4).
ZK cluster obligation surface honest: 17 subprotocols enumerated,
mechanization is multi-year program documented in
AXIOM-INVENTORY.md §closure roadmap.

2026-05-19 08:34:25 -07:00

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CGGMP21 EasyCrypt axiom inventory

Honest enumeration of every axiom and admit in the CGGMP21 EC theories. Mirrors ~/work/lux/pulsar/AXIOM-INVENTORY.md structure.

Status

Category	Count
Lean-bridged algebraic axioms (Lagrange / Paillier)	6
Section-local declared axioms (byte-walk, ZK)	4
Refinement-obligation axioms (presign R1/R2/R3 + sign vs honest spec)	4
CT obligations (concrete-impl-dependent declared axioms)	4
`admit`s in proof bodies	1

Lean-bridged axioms (6)

Lagrange / Shamir over F_n (4)

#	EC axiom	EC file:line	Lean theorem	Lean file
1	`scalar_add_zeroR`	`CGGMP21_N1.ec:120`	`AddCommMonoid` instance	(Mathlib auto-derived)
2	`reconstruct_linear`	`CGGMP21_N1.ec:125`	`combine_distributes_over_sum`	`Crypto/Threshold_Lagrange.lean:81`
3	`lagrange_inverse_eval`	`CGGMP21_N1.ec:135`	`shamir_correct_at_target`	`Crypto/Pulsar/Shamir.lean:76`
4	`derive_pk_homomorphism` (N4)	`CGGMP21_N4.ec:64`	`derive_pk_homomorphism`	`Crypto/CGGMP21.lean` (Lux profile extension)

Paillier algebra (2)

#	EC axiom	EC file:line	Lean theorem	Lean file
5	`paillier_add_homomorphism`	`CGGMP21_Paillier.ec:56`	`paillier_add_homomorphism`	`Crypto/CGGMP21.lean:200`
6	`paillier_scalar_homomorphism`	`CGGMP21_Paillier.ec:69`	`paillier_mul_homomorphism`	`Crypto/CGGMP21.lean:212`

Section-local declared axioms (4)

The Combine/Sign byte-walk axiom mirrors Pulsar's combine_body_compute_sig_spec. The three ZK security axioms (zk_completeness, zk_soundness, zk_zero_knowledge) are parameterized over the 17 ZK subprotocols in ~/work/lux/threshold/pkg/zk/.

#	EC axiom	EC file:line	Discharge target
7	`cggmp21_dispatches_to_ecdsa`	`CGGMP21_N1.ec:218`	`jasmin/{presign,sign}/` extraction
8	`zk_completeness`	`CGGMP21_ZK.ec:62`	Per-protocol completeness (17 subprotocols)
9	`zk_soundness`	`CGGMP21_ZK.ec:69`	Per-protocol soundness (17 subprotocols)
10	`zk_zero_knowledge`	`CGGMP21_ZK.ec:77`	Per-protocol ZK simulator (17 subprotocols)

Refinement-obligation axioms (4)

Stated as deferred obligations in CGGMP21_N1_Refinement.ec. The presign refinement is gated on a libjade-port-of-Paillier; the sign refinement is the simpler one-line scalar arithmetic step.

#	EC axiom	EC file:line	Discharge target
10a	`presign_round1_refinement_axiom`	`CGGMP21_N1_Refinement.ec:115`	`jasmin/presign/round1.jazz`
10b	`presign_round2_refinement_axiom`	`CGGMP21_N1_Refinement.ec:144`	`jasmin/presign/round2.jazz`
10c	`presign_round3_refinement_axiom`	`CGGMP21_N1_Refinement.ec:161`	`jasmin/presign/round3.jazz`
10d	`sign_online_refinement_axiom`	`CGGMP21_N1_Refinement.ec:175`	`jasmin/threshold/sign_online.jazz`

CT obligations (4)

#	EC axiom	EC file:line	Discharge target
11	`presign_round1_constant_time`	`lemmas/CGGMP21_CT.ec:73`	`jasmin/presign/round1.jazz`
12	`presign_round2_constant_time`	`lemmas/CGGMP21_CT.ec:93`	`jasmin/presign/round2.jazz` (Paillier dec)
13	`presign_round3_constant_time`	`lemmas/CGGMP21_CT.ec:113`	`jasmin/presign/round3.jazz`
14	`sign_online_constant_time`	`lemmas/CGGMP21_CT.ec:132`	`jasmin/threshold/sign_online.jazz`

`admit`s (1)

#	Location	Closure
15	`CGGMP21_N4.ec` `cggmp21_n4_pk_preservation_honest`	Same one-line group-identity rewrite as FROST_N4 / Pulsar_N4. Closure: add `derive_pk_group_identity` to `Crypto.CGGMP21.lean`.

Closure roadmap

Axioms 1-4 (Lagrange): Closed in Lean, bridged via the high-assurance gate.
Axioms 5-6 (Paillier): Stated in EC; mechanizable in Lean via Mathlib's commutative-ring tactic + CRT machinery. Estimated 4-6 weeks Lean work.
Axiom 7 (byte-walk): Discharged Jasmin-side once the presign+sign extraction lands.
Axioms 8-10 (ZK): Each of the 17 ZK subprotocols requires its own EC theory (completeness + soundness + ZK simulator). Estimated 3-6 months per subprotocol; the cluster is a Tier A multi-year program (the same scale as the lurk-rs / arkworks foundational ZK formal-methods program).
Axioms 11-14 (CT): Discharged by jasminc -checkCT on the threshold-layer Jasmin sources.
Admit 15: One-line Lean lemma.

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