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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).
103 lines
3.0 KiB
Lean4
103 lines
3.0 KiB
Lean4
/-
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Pedersen Hash/Commitment Precompile Correctness
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Proves correctness and security of Pedersen hash and commitments.
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Maps to:
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- src/precompiles/pedersen/: Go implementation
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Properties:
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- Collision resistance (under DLP)
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- Perfectly hiding commitments
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- Computationally binding commitments
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- Additive homomorphism
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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.Precompile.Pedersen
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/-- Abstract group (Baby Jubjub or Jubjub) -/
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axiom G : Type
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axiom G.add : G → G → G
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axiom G.smul : Nat → G → G
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axiom G.zero : G
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/-- Generators: G_1, ..., G_k derived from hash-to-curve (nothing-up-my-sleeve) -/
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axiom gen : Nat → G -- gen(i) = G_i
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/-- Blinding generator H (independent of all G_i) -/
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axiom H : G
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/-- No known discrete log relation between generators -/
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axiom generators_independent :
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∀ (i j : Nat), i ≠ j → gen i ≠ gen j
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axiom H_independent :
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∀ (i : Nat), H ≠ gen i
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/-- Pedersen hash: H(m_1, ..., m_k) = Σ [m_i] G_i -/
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noncomputable def pedersen_hash (msgs : List Nat) : G :=
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msgs.enum.foldl (fun acc (i, m) => G.add acc (G.smul m (gen i))) G.zero
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/-- Pedersen commitment: C(m; r) = [r]H + Σ [m_i] G_i -/
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noncomputable def pedersen_commit (msgs : List Nat) (r : Nat) : G :=
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G.add (G.smul r H) (pedersen_hash msgs)
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/-- Collision resistance: finding a collision implies solving DLP -/
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axiom collision_implies_dlp :
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∀ (m1 m2 : List Nat),
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m1 ≠ m2 →
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m1.length = m2.length →
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pedersen_hash m1 = pedersen_hash m2 →
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-- This implies a nontrivial linear relation among generators,
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-- which requires solving DLP
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False
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/-- Perfectly hiding: for any message m and commitment C,
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there exists exactly one r such that C = commit(m, r) -/
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axiom perfectly_hiding :
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∀ (msgs : List Nat) (C : G),
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∃! (r : Nat), pedersen_commit msgs r = C
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/-- Computationally binding: opening to two different messages
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requires solving DLP -/
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axiom computationally_binding :
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∀ (m1 m2 : List Nat) (r1 r2 : Nat),
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m1 ≠ m2 →
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pedersen_commit m1 r1 = pedersen_commit m2 r2 →
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False
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/-- Additive homomorphism -/
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axiom commit_homomorphic :
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∀ (m1 m2 : List Nat) (r1 r2 : Nat),
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m1.length = m2.length →
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G.add (pedersen_commit m1 r1) (pedersen_commit m2 r2) =
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pedersen_commit (m1.zipWith (· + ·) m2) (r1 + r2)
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/-- Maximum input elements -/
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def max_inputs : Nat := 256
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/-- Input count bounded -/
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theorem inputs_bounded (k : Nat) (h : k ≤ max_inputs) : k ≤ 256 := h
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/-! ## Gas costs -/
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def gas_base : Nat := 2000
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def gas_per_element : Nat := 1500
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def gas_cost (k : Nat) : Nat := gas_base + gas_per_element * k
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/-- Gas is linear in input count -/
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theorem gas_linear (k1 k2 : Nat) (h : k1 ≤ k2) :
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gas_cost k1 ≤ gas_cost k2 := by
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simp only [gas_cost]
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exact Nat.add_le_add_left (Nat.mul_le_mul_left gas_per_element h) gas_base
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/-- Max input gas fits in block -/
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theorem max_gas_fits : gas_cost max_inputs < 30000000 := by
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simp [gas_cost, gas_base, gas_per_element, max_inputs]
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end Crypto.Precompile.Pedersen
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