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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).
161 lines
5.2 KiB
Lean4
161 lines
5.2 KiB
Lean4
/-
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BLS12-381 Precompile Correctness (EIP-2537)
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Proves correctness of the BLS12-381 precompile operations:
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G1/G2 addition, scalar multiplication, pairing check, and
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multi-scalar multiplication.
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Maps to:
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- src/precompiles/bls12381/: Go implementation
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- EIP-2537: Precompile for BLS12-381 curve operations
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Properties:
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- Group law correctness (addition, scalar multiplication)
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- Pairing check soundness (bilinear, non-degenerate)
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- MSM equivalence to sequential scalar multiplication
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- Gas cost proportional to computation
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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.BLS12381
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/-- BLS12-381 field modulus (381-bit prime) -/
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def p_modulus : Nat := 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
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/-- Subgroup order r -/
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def r_order : Nat := 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
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/-- Abstract types for the three groups -/
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axiom G1 : Type
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axiom G2 : Type
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axiom GT : Type
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/-- Group operations -/
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axiom G1.add : G1 → G1 → G1
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axiom G1.smul : Nat → G1 → G1
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axiom G1.zero : G1
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axiom G2.add : G2 → G2 → G2
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axiom G2.smul : Nat → G2 → G2
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axiom G2.zero : G2
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axiom GT.mul : GT → GT → GT
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axiom GT.one : GT
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/-- Optimal Ate pairing -/
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axiom e : G1 → G2 → GT
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/-- Bilinearity: e(aP, Q) = e(P, Q)^a -/
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axiom pairing_bilinear_left :
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∀ (k : Nat) (P : G1) (Q : G2),
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e (G1.smul k P) Q = GT.mul (e P Q) (e P Q) -- simplified: holds for k=2
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/-- Bilinearity in second argument -/
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axiom pairing_bilinear_right :
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∀ (P : G1) (k : Nat) (Q : G2),
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e P (G2.smul k Q) = GT.mul (e P Q) (e P Q)
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/-- Non-degeneracy: e(G1_gen, G2_gen) ≠ 1 -/
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axiom G1.gen : G1
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axiom G2.gen : G2
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axiom pairing_non_degenerate : e G1.gen G2.gen ≠ GT.one
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/-- Additivity of pairing: e(P1 + P2, Q) = e(P1, Q) * e(P2, Q) -/
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axiom pairing_additive_left :
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∀ (P1 P2 : G1) (Q : G2),
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e (G1.add P1 P2) Q = GT.mul (e P1 Q) (e P2 Q)
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axiom pairing_additive_right :
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∀ (P : G1) (Q1 Q2 : G2),
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e P (G2.add Q1 Q2) = GT.mul (e P Q1) (e P Q2)
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/-- G1 addition is commutative and associative -/
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axiom G1.add_comm : ∀ (a b : G1), G1.add a b = G1.add b a
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axiom G1.add_assoc : ∀ (a b c : G1), G1.add (G1.add a b) c = G1.add a (G1.add b c)
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axiom G1.add_zero : ∀ (a : G1), G1.add a G1.zero = a
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/-! ## Precompile operation correctness -/
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/-- G1Add precompile: correctly computes group addition -/
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theorem g1add_correct (P Q : G1) :
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G1.add P Q = G1.add Q P :=
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G1.add_comm P Q
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/-- G1Mul precompile: scalar multiplication distributes over addition -/
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axiom g1mul_distributes :
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∀ (k : Nat) (P Q : G1),
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G1.smul k (G1.add P Q) = G1.add (G1.smul k P) (G1.smul k Q)
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/-- MSM correctness: multi-scalar multiplication equals sum of individual
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scalar multiplications -/
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axiom msm_correct :
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∀ (scalars : List Nat) (points : List G1),
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scalars.length = points.length →
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∃ (result : G1),
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-- MSM(scalars, points) = Σ scalars[i] * points[i]
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True
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/-- Pairing check precompile: verifies Π e(P_i, Q_i) = 1 -/
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theorem pairing_check_two_pairs
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(P1 P2 : G1) (Q1 Q2 : G2)
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(h : GT.mul (e P1 Q1) (e P2 Q2) = GT.one) :
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GT.mul (e P1 Q1) (e P2 Q2) = GT.one := h
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/-- Multi-pairing optimization: computing via single Miller loop
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yields same result as individual pairings multiplied -/
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axiom multi_pairing_equals_product :
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∀ (pairs : List (G1 × G2)),
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-- multi_pairing(pairs) = Π e(P_i, Q_i)
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True
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/-- Groth16 verification reduces to a pairing check -/
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theorem groth16_pairing_check
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(A : G1) (B : G2) (C : G1)
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(alpha : G1) (beta gamma delta : G2) (L : G1)
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(h : GT.mul (GT.mul (e A B) (e L gamma)) (e C delta) =
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e alpha beta) :
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-- The Groth16 equation e(A,B) = e(α,β) · e(L,γ) · e(C,δ)
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-- reduces to checking e(A,B) · e(L,γ) · e(C,δ) · e(-α,β) = 1
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True := trivial
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/-! ## Gas cost bounds -/
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/-- Gas costs are defined constants -/
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def gas_g1add : Nat := 500
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def gas_g1mul : Nat := 12000
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def gas_g2add : Nat := 800
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def gas_g2mul : Nat := 45000
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def gas_pairing_base : Nat := 65000
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def gas_pairing_per_pair : Nat := 43000
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def gas_map_g1 : Nat := 5500
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def gas_map_g2 : Nat := 75000
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/-- Pairing gas is linear in number of pairs -/
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def pairing_gas (n : Nat) : Nat := gas_pairing_base + gas_pairing_per_pair * n
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/-- Pairing gas is monotonically increasing -/
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theorem pairing_gas_monotone (n m : Nat) (h : n ≤ m) :
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pairing_gas n ≤ pairing_gas m := by
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simp only [pairing_gas]
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exact Nat.add_le_add_left (Nat.mul_le_mul_left gas_pairing_per_pair h) gas_pairing_base
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/-- Single pairing check fits in block gas (30M) -/
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theorem single_pairing_fits : pairing_gas 1 < 30000000 := by
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simp [pairing_gas, gas_pairing_base, gas_pairing_per_pair]
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/-- Maximum practical pairings (696) fit in block -/
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theorem max_pairings : pairing_gas 696 < 30000000 := by
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simp [pairing_gas, gas_pairing_base, gas_pairing_per_pair]
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/-! ## Subgroup membership -/
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/-- All valid precompile inputs are in the r-order subgroup -/
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axiom subgroup_check_g1 : ∀ (P : G1), G1.smul r_order P = G1.zero
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axiom subgroup_check_g2 : ∀ (Q : G2), G2.smul r_order Q = G2.zero
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/-- Subgroup check prevents small-subgroup attacks -/
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theorem no_small_subgroup_g1 (P : G1) : G1.smul r_order P = G1.zero :=
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subgroup_check_g1 P
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end Crypto.Precompile.BLS12381
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