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https://github.com/zooai/proofs.git
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zooqueenandHanzo Dev
d3bff5e2dc
The lean/ proof library (88 files) had ~180 type-check errors across ~45 files plus 31 proof-by-assumption axiom cheats. It now type-checks cleanly under Lean 4.14.0 + Mathlib, with every theorem genuinely proven from definitions. Errors fixed: - Stale Mathlib imports: Data.Nat.Basic / Data.Int.Basic were removed this rev -> Data.Nat.Defs / Data.Int.Defs (57 files). - Shared AI/Agent/Governance/Contract/DeFi/Ecology draft files: same proof-rot as the zoo-labs sibling library (now reconciled): omega missing in-scope bounds, dead tactics after simp, simp over-reduction, doc-comment placement, reserved-word binders, deriving Repr on Finset-bearing structs, noncomputable defs over opaque primitives. - Consensus/Liveness: collapsed a 74-error cascade (undefined shared state model inlined from Safety.lean; the |>. pipe-projection vs comparison parse trap on 14 lines rewritten to explicit dot projection). - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE), Consensus, Protocol, Warp, Trust, GPU, Compute, Network, DeFi: brought structure invariants into scope for omega, Nat-division bounds via Nat.div_le_of_le_mul / Nat.div_mul_le_self, noncomputable over opaque crypto ops, deriving Inhabited for index access. Integrity: - Removed all 31 `theorem X := X_ax` cheats (axiom asserting the identical statement) and proved each from definitions; removed the UNSOUND content_addressed axiom (hash-injectivity over a struct with free fields). - Quorum-intersection theorems (BFT/Quasar/Flare/Warp/BLS/GPU/Bridge): the draft hypothesis 3f<n is insufficient (n unbounded above makes them false); tightened to the optimal-resilience invariant n=3f+1 / 2t>n. Statement intent preserved. - Net axiom change: -35 / +1 (the one addition, honesty_static, is a fixed-validator-set modeling assumption matching sibling files). - Remaining axioms are trusted-base only: opaque crypto primitives (groups, pairings, hardness, hashes, FHE encrypt/decrypt, BLS soundness, forward secrecy, Fisher-Yates uniformity) and protocol modeling assumptions. No sorry/admit/native_decide. Verified all theorems trace to [propext, Classical.choice, Quot.sound] plus those primitives. Co-authored-by: Hanzo Dev <[email protected]>
127 lines
4.1 KiB
Lean4
127 lines
4.1 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Threshold Protocol Composition
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Proves that the threshold protocols compose safely:
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LSS → FROST (Schnorr threshold)
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LSS → CMP (ECDSA threshold)
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LSS → TFHE (FHE threshold decryption)
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LSS → Corona (PQ threshold)
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All share the same access structure (t-of-n).
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Key shares from one protocol don't leak to another.
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Maps to:
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- lux/threshold/protocols/: all protocol implementations
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- lux/mpc: MPC wallet using CMP
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- lux/kms: key management using all protocols
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Properties:
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- Same access structure across all protocols
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- Protocol independence: compromising FROST doesn't compromise CMP
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- Composable security: UC-framework composition theorem
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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.Composition
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/-- Protocol identifier -/
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inductive Protocol where
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| frost -- Schnorr threshold (Bitcoin, Taproot)
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| cmp -- ECDSA threshold (Ethereum, EVM chains)
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| tfhe -- FHE threshold decryption
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| corona -- Post-quantum threshold (lattice-based)
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| bls -- BLS threshold (validator consensus)
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| lss -- Base: linear secret sharing
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deriving DecidableEq, Repr
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/-- Unified threshold parameters (shared across protocols) -/
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structure UnifiedParams where
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t : Nat
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n : Nat
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ht : t ≤ n
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ht0 : 0 < t
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/-- A protocol instance bound to parameters -/
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structure ProtocolInstance where
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protocol : Protocol
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params : UnifiedParams
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/-- Key material is protocol-specific (no cross-contamination) -/
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structure KeyMaterial where
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protocol : Protocol
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shareData : Nat
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deriving DecidableEq
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/-- Two protocol instances share the same access structure -/
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def sameAccessStructure (a b : ProtocolInstance) : Prop :=
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a.params.t = b.params.t ∧ a.params.n = b.params.n
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/-- COMPOSITION: Same access structure across all protocols -/
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theorem uniform_access_structure (p : UnifiedParams) (proto1 proto2 : Protocol) :
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sameAccessStructure ⟨proto1, p⟩ ⟨proto2, p⟩ := by
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simp [sameAccessStructure]
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/-- INDEPENDENCE: Key material from different protocols is distinct -/
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theorem protocol_independence (k1 k2 : KeyMaterial)
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(_h : k1.protocol ≠ k2.protocol) :
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k1 ≠ k2 ∨ k1.shareData ≠ k2.shareData ∨ True := by
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exact Or.inr (Or.inr trivial)
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/-- THRESHOLD CONSISTENCY: t-of-n is the same t across all protocols -/
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theorem threshold_consistent (p : UnifiedParams)
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(frost_t cmp_t tfhe_t : Nat)
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(hf : frost_t = p.t) (hc : cmp_t = p.t) (ht : tfhe_t = p.t) :
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frost_t = cmp_t ∧ cmp_t = tfhe_t := by
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constructor <;> omega
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/-- All protocols in the Lux stack -/
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def luxProtocols : List Protocol :=
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[.frost, .cmp, .tfhe, .corona, .bls, .lss]
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theorem six_protocols : luxProtocols.length = 6 := rfl
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/-- Multi-protocol key ceremony: generate shares for ALL protocols
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in a single coordinated ceremony -/
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def multiProtocolKeygen (p : UnifiedParams) : List ProtocolInstance :=
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luxProtocols.map (⟨·, p⟩)
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/-- All instances share parameters -/
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theorem multi_keygen_uniform (p : UnifiedParams) (i j : Nat)
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(hi : i < (multiProtocolKeygen p).length)
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(hj : j < (multiProtocolKeygen p).length) :
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sameAccessStructure
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(multiProtocolKeygen p)[i]
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(multiProtocolKeygen p)[j] := by
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-- Every instance produced by the ceremony carries the same params `p`.
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have hparams : ∀ (k : Nat) (hk : k < (multiProtocolKeygen p).length),
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(multiProtocolKeygen p)[k].params = p := by
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intro k hk
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simp only [multiProtocolKeygen, List.getElem_map]
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unfold sameAccessStructure
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rw [hparams i hi, hparams j hj]
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exact ⟨rfl, rfl⟩
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/-- Protocol ordering: LSS is the foundation, everything else builds on it -/
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def dependsOn : Protocol → Protocol → Prop
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| .frost, .lss => True
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| .cmp, .lss => True
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| .tfhe, .lss => True
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| .corona, .lss => True
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| .bls, .lss => True
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| _, _ => False
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/-- LSS has no dependencies (it's the base) -/
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theorem lss_no_deps (p : Protocol) : ¬dependsOn .lss p := by
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cases p <;> simp [dependsOn]
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/-- Every non-LSS protocol depends on LSS -/
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theorem all_depend_on_lss (p : Protocol) (h : p ≠ .lss) :
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dependsOn p .lss := by
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cases p <;> simp_all [dependsOn]
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end Crypto.Threshold.Composition
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