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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).
102 lines
2.8 KiB
Lean4
102 lines
2.8 KiB
Lean4
/-
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Curve25519 Precompile Correctness
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Proves correctness of Curve25519 point operations.
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Foundation for X25519, Ed25519, and VRF.
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Maps to:
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- src/precompiles/curve25519/: Go implementation
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Properties:
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- Montgomery ladder constant-time execution
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- Birational equivalence to Edwards25519
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- Field reduction correctness (mod 2^255 - 19)
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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.Curve25519
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/-- Field modulus: 2^255 - 19 (pseudo-Mersenne prime) -/
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def p : Nat := 2^255 - 19
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/-- Subgroup order -/
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def ell : Nat := 2^252 + 27742317777372353535851937790883648493
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/-- Cofactor -/
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def cofactor : Nat := 8
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/-- Montgomery parameter A = 486662 -/
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def A_param : Nat := 486662
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/-- p is positive -/
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theorem p_pos : 0 < p := by simp [p]
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/-- p is odd (required for field arithmetic) -/
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theorem p_odd : p % 2 = 1 := by simp [p]
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/-- Abstract point type (extended Edwards coordinates) -/
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axiom Point : Type
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axiom Point.add : Point → Point → Point
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axiom Point.smul : Nat → Point → Point
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axiom Point.identity : Point
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/-- Montgomery ladder function (u-coordinate only) -/
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axiom montgomery_ladder : Nat → Nat → Nat
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/-- Edwards addition is complete for Edwards25519 -/
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axiom edwards_add_complete :
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∀ (P Q : Point), ∃ (R : Point), Point.add P Q = R
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/-- Scalar multiplication via Montgomery ladder is constant-time:
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always executes exactly 255 iterations -/
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def ladder_iterations : Nat := 255
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theorem ladder_constant_steps : ladder_iterations = 255 := rfl
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/-- Montgomery ladder agrees with Edwards scalar multiplication
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on the u-coordinate -/
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axiom ladder_agrees_edwards :
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∀ (k : Nat) (u : Nat),
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u < p →
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montgomery_ladder k u < p
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/-- Reduction mod p: for a < 2p, reduce to [0, p) -/
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def field_reduce (a : Nat) : Nat := a % p
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theorem field_reduce_bounded (a : Nat) : field_reduce a < p := by
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simp [field_reduce, p]
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omega
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/-- Multiplication by 19 for fast reduction: 2^255 ≡ 19 (mod p) -/
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theorem fast_reduce : 2^255 % p = 19 := by simp [p]
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/-- Field element fits in 256 bits -/
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theorem field_element_bits (a : Nat) (ha : a < p) : a < 2^256 := by
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have hp : p < 2^256 := by simp [p]
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omega
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/-- Subgroup order divides curve order -/
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theorem order_divides : cofactor * ell = 8 * ell := by simp [cofactor]
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/-- Cofactor clearing projects to prime-order subgroup -/
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axiom cofactor_clears :
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∀ (P : Point), Point.smul ell (Point.smul cofactor P) = Point.identity
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/-! ## Gas costs -/
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def gas_add : Nat := 120
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def gas_mul : Nat := 5000
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def gas_decompress : Nat := 200
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/-- Scalar mul gas justified by 255 ladder steps -/
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theorem gas_per_step : gas_mul / ladder_iterations = 19 := by
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simp [gas_mul, ladder_iterations]
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/-- Operations fit in block gas -/
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theorem all_ops_fit : gas_add + gas_mul + gas_decompress < 30000000 := by
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simp [gas_add, gas_mul, gas_decompress]
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end Crypto.Precompile.Curve25519
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