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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]>
105 lines
3.6 KiB
Lean4
105 lines
3.6 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Post-Quantum Hybrid Signature Correctness
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Models the hybrid signature scheme combining:
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- Ed25519 (classical, 32-byte keys)
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- ML-DSA-65 (FIPS 204, lattice-based, 1952-byte keys)
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- SLH-DSA-128s (FIPS 205, hash-based, 32-byte keys)
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The hybrid construction requires ALL three to verify.
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An attacker must break all three to forge — defense in depth.
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Maps to:
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- luxfi/crypto: hybrid package
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- lux/node: validator identity keys
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Properties:
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- Defense in depth: full verify ⟹ all three verify
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- Classical fallback: fast mode uses ed25519 + ML-DSA only
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- Hash-based backup: SLH-DSA protects if lattices fall
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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.Hybrid
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/-- Abstract signature verification for each scheme -/
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axiom ed25519_verify : Nat → Nat → Nat → Bool
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axiom mldsa_verify : Nat → Nat → Nat → Bool
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axiom slhdsa_verify : Nat → Nat → Nat → Bool
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/-- Hybrid public key: classical + lattice + hash-based -/
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structure HybridPK where
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ed25519 : Nat
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mldsa : Nat
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slhdsa : Nat
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/-- Hybrid signature: one from each scheme -/
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structure HybridSig where
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ed25519 : Nat
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mldsa : Nat
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slhdsa : Nat
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/-- Verification modes -/
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inductive VerifyMode where
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| fast -- ed25519 + ML-DSA (performance)
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| full -- all three (maximum security)
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| classical -- ed25519 only (fallback)
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/-- Fast verification: ed25519 ∧ ML-DSA -/
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noncomputable def verify_fast (pk : HybridPK) (msg : Nat) (sig : HybridSig) : Bool :=
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ed25519_verify pk.ed25519 msg sig.ed25519 &&
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mldsa_verify pk.mldsa msg sig.mldsa
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/-- Full verification: ed25519 ∧ ML-DSA ∧ SLH-DSA -/
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noncomputable def verify_full (pk : HybridPK) (msg : Nat) (sig : HybridSig) : Bool :=
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ed25519_verify pk.ed25519 msg sig.ed25519 &&
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mldsa_verify pk.mldsa msg sig.mldsa &&
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slhdsa_verify pk.slhdsa msg sig.slhdsa
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/-- Mode-selected verification -/
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noncomputable def verify (pk : HybridPK) (msg : Nat) (sig : HybridSig) (mode : VerifyMode) : Bool :=
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match mode with
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| .fast => verify_fast pk msg sig
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| .full => verify_full pk msg sig
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| .classical => ed25519_verify pk.ed25519 msg sig.ed25519
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/-- DEFENSE IN DEPTH: Full verification requires all three schemes.
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An attacker must break ed25519 AND ML-DSA AND SLH-DSA. -/
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theorem full_requires_all_three (pk : HybridPK) (msg : Nat) (sig : HybridSig)
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(h : verify_full pk msg sig = true) :
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ed25519_verify pk.ed25519 msg sig.ed25519 = true ∧
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mldsa_verify pk.mldsa msg sig.mldsa = true ∧
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slhdsa_verify pk.slhdsa msg sig.slhdsa = true := by
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simp only [verify_full, Bool.and_eq_true] at h
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obtain ⟨h12, h3⟩ := h
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obtain ⟨h1, h2⟩ := h12
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exact ⟨h1, h2, h3⟩
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/-- Fast mode requires both ed25519 and ML-DSA -/
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theorem fast_requires_both (pk : HybridPK) (msg : Nat) (sig : HybridSig)
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(h : verify_fast pk msg sig = true) :
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ed25519_verify pk.ed25519 msg sig.ed25519 = true ∧
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mldsa_verify pk.mldsa msg sig.mldsa = true := by
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simp only [verify_fast, Bool.and_eq_true] at h
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exact h
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/-- Full implies fast: if all three verify, the fast pair certainly does -/
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theorem full_implies_fast (pk : HybridPK) (msg : Nat) (sig : HybridSig)
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(h : verify_full pk msg sig = true) :
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verify_fast pk msg sig = true := by
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have ⟨h1, h2, _⟩ := full_requires_all_three pk msg sig h
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simp [verify_fast, h1, h2]
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/-- Full implies classical: if all three verify, ed25519 certainly does -/
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theorem full_implies_classical (pk : HybridPK) (msg : Nat) (sig : HybridSig)
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(h : verify_full pk msg sig = true) :
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verify pk msg sig .classical = true := by
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have ⟨h1, _, _⟩ := full_requires_all_three pk msg sig h
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simp [verify, h1]
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end Crypto.Hybrid
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