mirror of
https://github.com/luxfi/proofs.git
synced 2026-10-30 15:21:05 +00:00
zeekay
5ccdd345c9
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).
103 lines
3.6 KiB
Lean4
103 lines
3.6 KiB
Lean4
/-
|
|
Post-Quantum Hybrid Signature Correctness
|
|
|
|
Models the hybrid signature scheme combining:
|
|
- Ed25519 (classical, 32-byte keys)
|
|
- ML-DSA-65 (FIPS 204, lattice-based, 1952-byte keys)
|
|
- SLH-DSA-128s (FIPS 205, hash-based, 32-byte keys)
|
|
|
|
The hybrid construction requires ALL three to verify.
|
|
An attacker must break all three to forge — defense in depth.
|
|
|
|
Maps to:
|
|
- luxfi/crypto: hybrid package
|
|
- lux/node: validator identity keys
|
|
|
|
Properties:
|
|
- Defense in depth: full verify ⟹ all three verify
|
|
- Classical fallback: fast mode uses ed25519 + ML-DSA only
|
|
- Hash-based backup: SLH-DSA protects if lattices fall
|
|
-/
|
|
|
|
import Mathlib.Data.Nat.Defs
|
|
import Mathlib.Tactic
|
|
|
|
namespace Crypto.Hybrid
|
|
|
|
/-- Abstract signature verification for each scheme -/
|
|
axiom ed25519_verify : Nat → Nat → Nat → Bool
|
|
axiom mldsa_verify : Nat → Nat → Nat → Bool
|
|
axiom slhdsa_verify : Nat → Nat → Nat → Bool
|
|
|
|
/-- Hybrid public key: classical + lattice + hash-based -/
|
|
structure HybridPK where
|
|
ed25519 : Nat
|
|
mldsa : Nat
|
|
slhdsa : Nat
|
|
|
|
/-- Hybrid signature: one from each scheme -/
|
|
structure HybridSig where
|
|
ed25519 : Nat
|
|
mldsa : Nat
|
|
slhdsa : Nat
|
|
|
|
/-- Verification modes -/
|
|
inductive VerifyMode where
|
|
| fast -- ed25519 + ML-DSA (performance)
|
|
| full -- all three (maximum security)
|
|
| classical -- ed25519 only (fallback)
|
|
|
|
/-- Fast verification: ed25519 ∧ ML-DSA -/
|
|
noncomputable def verify_fast (pk : HybridPK) (msg : Nat) (sig : HybridSig) : Bool :=
|
|
ed25519_verify pk.ed25519 msg sig.ed25519 &&
|
|
mldsa_verify pk.mldsa msg sig.mldsa
|
|
|
|
/-- Full verification: ed25519 ∧ ML-DSA ∧ SLH-DSA -/
|
|
noncomputable def verify_full (pk : HybridPK) (msg : Nat) (sig : HybridSig) : Bool :=
|
|
ed25519_verify pk.ed25519 msg sig.ed25519 &&
|
|
mldsa_verify pk.mldsa msg sig.mldsa &&
|
|
slhdsa_verify pk.slhdsa msg sig.slhdsa
|
|
|
|
/-- Mode-selected verification -/
|
|
noncomputable def verify (pk : HybridPK) (msg : Nat) (sig : HybridSig) (mode : VerifyMode) : Bool :=
|
|
match mode with
|
|
| .fast => verify_fast pk msg sig
|
|
| .full => verify_full pk msg sig
|
|
| .classical => ed25519_verify pk.ed25519 msg sig.ed25519
|
|
|
|
/-- DEFENSE IN DEPTH: Full verification requires all three schemes.
|
|
An attacker must break ed25519 AND ML-DSA AND SLH-DSA. -/
|
|
theorem full_requires_all_three (pk : HybridPK) (msg : Nat) (sig : HybridSig)
|
|
(h : verify_full pk msg sig = true) :
|
|
ed25519_verify pk.ed25519 msg sig.ed25519 = true ∧
|
|
mldsa_verify pk.mldsa msg sig.mldsa = true ∧
|
|
slhdsa_verify pk.slhdsa msg sig.slhdsa = true := by
|
|
simp only [verify_full, Bool.and_eq_true] at h
|
|
obtain ⟨h12, h3⟩ := h
|
|
obtain ⟨h1, h2⟩ := h12
|
|
exact ⟨h1, h2, h3⟩
|
|
|
|
/-- Fast mode requires both ed25519 and ML-DSA -/
|
|
theorem fast_requires_both (pk : HybridPK) (msg : Nat) (sig : HybridSig)
|
|
(h : verify_fast pk msg sig = true) :
|
|
ed25519_verify pk.ed25519 msg sig.ed25519 = true ∧
|
|
mldsa_verify pk.mldsa msg sig.mldsa = true := by
|
|
simp only [verify_fast, Bool.and_eq_true] at h
|
|
exact h
|
|
|
|
/-- Full implies fast: if all three verify, the fast pair certainly does -/
|
|
theorem full_implies_fast (pk : HybridPK) (msg : Nat) (sig : HybridSig)
|
|
(h : verify_full pk msg sig = true) :
|
|
verify_fast pk msg sig = true := by
|
|
have ⟨h1, h2, _⟩ := full_requires_all_three pk msg sig h
|
|
simp [verify_fast, h1, h2]
|
|
|
|
/-- Full implies classical: if all three verify, ed25519 certainly does -/
|
|
theorem full_implies_classical (pk : HybridPK) (msg : Nat) (sig : HybridSig)
|
|
(h : verify_full pk msg sig = true) :
|
|
verify pk msg sig .classical = true := by
|
|
have ⟨h1, _, _⟩ := full_requires_all_three pk msg sig h
|
|
simp [verify, h1]
|
|
|
|
end Crypto.Hybrid
|