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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).
118 lines
3.8 KiB
Lean4
118 lines
3.8 KiB
Lean4
/-
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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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simp [multiProtocolKeygen, sameAccessStructure]
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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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