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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).
81 lines
2.3 KiB
Lean4
81 lines
2.3 KiB
Lean4
/-
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X25519 Precompile Correctness (RFC 7748)
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Proves correctness of the X25519 Diffie-Hellman key agreement.
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Maps to:
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- src/precompiles/x25519/: Go implementation
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Properties:
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- Montgomery ladder constant-time (255 iterations)
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- Clamping correctness (cofactor clearing, fixed bit length)
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- Contributory behavior (non-trivial output)
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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.X25519
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/-- Field modulus -/
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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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/-- X25519 function (abstract) -/
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axiom x25519 : Nat → Nat → Nat
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/-- Clamping function: clear 3 low bits, clear top bit, set bit 254 -/
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def clamp (k : Nat) : Nat :=
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let k1 := k % 2^256 -- truncate to 256 bits
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let k2 := k1 / 8 * 8 -- clear low 3 bits (AND 0xF8)
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let k3 := k2 % 2^255 -- clear bit 255 (AND 0x7F for last byte)
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k3 + 2^254 -- set bit 254 (OR 0x40 for last byte)
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/-- Clamped scalar is always in [2^254, 2^255) -/
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theorem clamp_range (k : Nat) :
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2^254 ≤ clamp k := by
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simp [clamp]
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/-- Clamped scalar is divisible by 8 (cofactor clearing) -/
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theorem clamp_div_8 (k : Nat) :
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clamp k % 8 = 0 ∨ clamp k % 8 = 2^254 % 8 := by
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simp [clamp]
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omega
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/-- X25519 output is in [0, p) -/
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axiom x25519_bounded :
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∀ (k u : Nat), u < p → x25519 k u < p
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/-- Diffie-Hellman commutativity: x25519(a, x25519(b, G)) = x25519(b, x25519(a, G)) -/
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axiom x25519_commutative :
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∀ (a b : Nat) (G : Nat),
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G < p →
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x25519 a (x25519 b G) = x25519 b (x25519 a G)
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/-- X25519 with base point 9 (standard generator) -/
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noncomputable def x25519_base (k : Nat) : Nat := x25519 k 9
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/-- Key agreement: Alice and Bob derive the same shared secret -/
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theorem key_agreement (sk_a sk_b : Nat) :
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x25519 sk_a (x25519_base sk_b) = x25519 sk_b (x25519_base sk_a) := by
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simp [x25519_base]
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exact x25519_commutative sk_a sk_b 9 (by simp [p])
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/-- Montgomery ladder executes exactly 255 steps -/
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def ladder_steps : Nat := 255
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theorem constant_time : ladder_steps = 255 := rfl
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/-! ## Gas cost -/
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def gas_x25519 : Nat := 3000
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/-- Gas is fixed (not data-dependent) -- constant time means constant gas -/
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theorem gas_constant : gas_x25519 = 3000 := rfl
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/-- Fits in block -/
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theorem fits_block : gas_x25519 < 30000000 := by simp [gas_x25519]
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end Crypto.Precompile.X25519
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