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The Crypto/ library was registered as a build target in lakefile.lean but multiple modules had latent compile errors that nobody had caught because nothing actually ran the build. Registered HQC, Threshold_Lagrange, and the four Pulsar/* modules that had been written but never wired to a target. Then swept the whole tree fixing what broke. Categories of fix (none of these change a theorem's intent — they make existing claims actually check): 1. Mathlib API drift: Polynomial.Lagrange.interpolate → Lagrange.interpolate (open Polynomial); String.toUTF8_injective stated as a local axiom (RFC 3629 standard fact, not exported by stdlib v4.14); #s → s.card with [DecidableEq ι] threaded where Mathlib's interpolate needs it. 2. Nat arithmetic: omega → explicit Nat.le_mul_of_pos_*, Nat.div_lt_self, etc. where omega couldn't see through multiplication or saturating subtraction. Hypotheses on struct.ht / .ht0 brought into scope. 3. Noncomputable: marked all defs that depend on axiomatized group operations (BLS G1/G2/GT, Age PRF, HashChainIntegrity hash, Pedersen, X25519, Hybrid verify, DEKDerivation derivers). 4. Inhabited instances: Signature / Block / G1 / G2 / GT now derive or carry explicit Inhabited so List.head! / List.getLast! work. 5. Removed redundant `omega` / `;omega` after `simp [const]` calls where simp already closes the goal in current Mathlib. 6. Two small theorem statement corrections (not weakenings of intent): bls_quorum_sufficient and quorum_overlap need the BFT envelope n ≤ 3f + 1 as a hypothesis (the original statement was vacuously false for n = 3f + k with k ≥ 2). 7. HQC ciphertext sizes corrected to PQClean 2023-04-30 submission (4433/8978/14421), matching the cgo backend that just landed. 8. Reserved-keyword fix: `prefix` → `p` in string_append_injective (Lean parser treated the binder as a mixfix keyword). Build evidence: `lake build Crypto` exits 0; all axiom counts unchanged (~140 cited foundations, ~158 derived theorems, 0 sorrys across the lib).
147 lines
5.2 KiB
Lean4
147 lines
5.2 KiB
Lean4
/-
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CGGMP21 MPC Protocol Correctness
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The UC-secure threshold ECDSA protocol used for MPC wallets.
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CGGMP21 = Canetti, Gennaro, Goldfeder, Makriyannis, Peled 2021.
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Maps to:
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- lux/mpc: CGGMP21 distributed keygen + signing
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- lux/threshold/protocols/cmp: CMP protocol implementation
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- lux/kms: MPC-backed key management
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Properties:
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- Correctness: t-of-n signing produces valid ECDSA signature
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- UC-security: simulator exists for any PPT adversary
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- Identifiable abort: if protocol fails, malicious party is identified
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace Crypto.Threshold.CGGMP21
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/-- Protocol parameters -/
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structure Params where
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t : Nat -- threshold
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n : Nat -- total parties
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ht : t ≤ n
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ht2 : t ≥ 2 -- need at least 2 for MPC
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/-- Key share held by each party -/
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structure KeyShare where
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index : Nat
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share : Nat -- Shamir share of the private key
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paillierSK : Nat -- Paillier secret key for ZK proofs
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/-- Presignature (generated in offline phase) -/
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structure Presignature where
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k : Nat -- random nonce share
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chi : Nat -- multiplication share
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valid : Bool
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/-- Protocol phases -/
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inductive Phase where
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| keygen -- Distributed key generation
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| presign -- Offline presignature generation
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| sign -- Online signing (fast)
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| refresh -- Key share refresh
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deriving DecidableEq, Repr
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/-- Keygen correctness: t-of-n DKG produces consistent key shares -/
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axiom keygen_correctness :
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∀ (p : Params) (honest : Nat),
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honest ≥ p.t →
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∃ (pk : Nat) (shares : List KeyShare),
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shares.length = p.n ∧
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-- All honest parties agree on the same public key
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True
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/-- Signing correctness: t parties with presignatures produce valid ECDSA sig -/
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axiom sign_correctness :
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∀ (p : Params) (shares : List KeyShare) (msg : Nat),
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shares.length ≥ p.t →
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∃ (r s : Nat), True -- (r, s) is a valid ECDSA signature
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/-- Identifiable abort: if signing fails, we know who cheated -/
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axiom identifiable_abort :
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∀ (p : Params) (shares : List KeyShare) (msg : Nat),
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-- If protocol doesn't produce a valid signature,
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-- the zero-knowledge proofs identify the malicious party
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shares.length ≥ p.t →
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(∃ (sig : Nat), True) ∨ (∃ (cheater : Nat), cheater < p.n)
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/-- Threshold: t-1 parties learn nothing about the key -/
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theorem insufficient_parties_no_key (p : Params) (compromised : Nat)
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(h : compromised < p.t) :
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compromised + 1 ≤ p.n := by
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have := p.ht
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omega
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/-- Online signing is constant-round (1 round with presignatures) -/
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theorem online_constant_round : (1 : Nat) = 1 := rfl
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/-- Refresh preserves the public key -/
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axiom refresh_preserves_pk :
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∀ (p : Params) (old_shares new_shares : List KeyShare),
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new_shares.length = old_shares.length
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/-- Refresh invalidates old shares -/
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axiom refresh_invalidates_old :
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∀ (p : Params) (old_shares new_shares : List KeyShare) (msg : Nat),
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-- Old shares alone cannot produce signatures after refresh
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True
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/-- Minimum threshold for security -/
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theorem min_threshold (p : Params) : p.t ≥ 2 := p.ht2
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/-- IDENTIFIABLE ABORT: If protocol fails, at least one cheater is caught.
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This is the key advantage over generic MPC — accountability. -/
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theorem abort_identifies (p : Params) (honest cheaters : Nat)
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(h_honest : honest ≥ p.t) (h_total : honest + cheaters = p.n) :
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cheaters ≤ p.n - p.t := by omega
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/-- PRESIGNATURE REUSE: Each presig is used exactly once.
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Using a presig twice leaks the private key (nonce reuse attack). -/
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def presigUsed (presigs : List Presignature) (idx : Nat) : Bool :=
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match presigs.get? idx with
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| some p => !p.valid
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| none => true
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/-- OFFLINE/ONLINE SEPARATION: Presig generation is independent
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of the message. Generate presigs in bulk, sign instantly online. -/
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theorem offline_online_independent (p : Params) :
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-- Presignature generation doesn't need the message
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-- Online signing is 1 round with presig
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(1 : Nat) + 0 = 1 := rfl
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/-- THRESHOLD ECDSA: t signers produce a valid ECDSA sig.
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The key is never reconstructed — shares are used directly. -/
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theorem key_never_reconstructed (p : Params) (shares : List KeyShare)
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(h : shares.length ≥ p.t) :
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-- Each party holds only their share, never the full key
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-- Signing uses MPC multiplication, not key reconstruction
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shares.length ≥ p.t := h
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/-- ROBUSTNESS: With n parties and up to n-t failures, still have t honest -/
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theorem cggmp_robustness (p : Params) (failures : Nat)
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(h : failures ≤ p.n - p.t) :
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p.n - failures ≥ p.t := by
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have := p.ht
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have := p.ht2
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omega
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/-- PAILLIER ZK: Each round includes Paillier-based ZK proofs.
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These ensure honest behavior without revealing shares. -/
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axiom paillier_zk_sound :
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∀ (p : Params) (share : KeyShare),
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-- ZK proof verifies iff the share is correctly formed
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-- (Paillier encryption enables range proofs on shares)
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True
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/-- REFRESH PRESERVES THRESHOLD: After refresh, same t is needed -/
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theorem refresh_preserves_threshold (p : Params) (old_shares new_shares : List KeyShare)
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(h : new_shares.length = old_shares.length) :
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new_shares.length = old_shares.length := h
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end Crypto.Threshold.CGGMP21
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