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zooqueenandHanzo Dev
ac9676a47a
The formal/lean library (53 files — a separate formalization from lean/) had ~110 type-check errors across 38 files and had never had its Mathlib oleans built. It now verifies at 0 errors under the project's strict setting: `lake env lean -D autoImplicit=false`, all 53 files. Fixed the same families as the sibling lean/ tree (the content is diverged, so each was repaired directly): - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE/Verkle): omega needs in-scope structure invariants; Nat-division bounds; noncomputable over opaque verifiers; Fin n index → Nat; deriving Inhabited. - DeFi (AMM/staking/fees/flashloan/HFT/router): constant-product invariant and fee bounds via Nat.div_mul_le_self / Nat.div_le_of_le_mul; dead tactics. - Protocol/Consensus/Warp/Bridge: BFT quorum theorems tightened to n=3f+1; pipe-projection parse fixes; split-after-simp; dead tactics; built the Consensus/Safety + ThresholdProof dependency oleans from clean source. - Network/Compute/Trust/Build: record-projection opacity (unfold+split), foldl-min monotonicity, BEq parse parens. - autoImplicit=false: declared previously auto-bound variables (explicit binders / variable blocks); the lakefile sets autoImplicit:=false. Integrity: no sorry/admit/native_decide; no proof-by-assumption axiom cheats. Statement changes only tightened false/trivial draft theorems to true invariants. Remaining axioms are trusted-base only (opaque crypto primitives, protocol modeling / honesty-static, build determinism). Co-authored-by: Hanzo Dev <[email protected]>
106 lines
3.8 KiB
Lean4
106 lines
3.8 KiB
Lean4
/-
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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` because the per-scheme verifiers are abstract axioms. -/
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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` because the per-scheme verifiers are abstract axioms. -/
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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` because the per-scheme verifiers are abstract axioms. -/
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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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