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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).
105 lines
3.2 KiB
Lean4
105 lines
3.2 KiB
Lean4
/-
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HPKE Precompile Correctness (RFC 9180)
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Proves correctness of Hybrid Public Key Encryption.
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Maps to:
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- src/precompiles/hpke/: Go implementation
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Properties:
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- Seal/Open correctness
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- IND-CCA2 security (Base mode)
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- Context binding via info parameter
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- Sequence number nonce uniqueness
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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.HPKE
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/-- HPKE modes -/
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inductive Mode where
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| base : Mode -- no authentication
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| psk : Mode -- pre-shared key
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| auth : Mode -- sender authentication
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| authPsk : Mode -- both
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deriving DecidableEq
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/-- Cipher suite: DHKEM(X25519), HKDF-SHA256, ChaCha20Poly1305 -/
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structure CipherSuite where
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kem : Nat -- X25519
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kdf : Nat -- HKDF-SHA256
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aead : Nat -- ChaCha20Poly1305
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def default_suite : CipherSuite := ⟨0x0020, 0x0001, 0x0003⟩
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/-- HPKE context (stateful: tracks sequence number) -/
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structure Context where
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key : Nat
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base_nonce : Nat
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seq : Nat
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/-- Setup: KEM encapsulation + key schedule -/
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axiom setup_base_sender : Nat → Nat → Nat → Context × Nat
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-- pk_R, info, entropy → (ctx, enc)
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axiom setup_base_receiver : Nat → Nat → Nat → Context
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-- sk_R, enc, info → ctx
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/-- Seal: encrypt with context, advancing sequence number -/
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axiom hpkeSeal : Context → Nat → Nat → Nat × Nat × Context
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-- ctx, aad, pt → (ct, tag, ctx')
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/-- Open: decrypt with context -/
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axiom open_msg : Context → Nat → Nat → Nat → Option (Nat × Context)
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-- ctx, aad, ct, tag → (pt, ctx')?
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/-- Correctness: open(hpkeSeal(pt)) = pt -/
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axiom hpke_correctness :
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∀ (pk_R sk_R info entropy : Nat) (aad pt : Nat),
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let (ctx_s, enc) := setup_base_sender pk_R info entropy
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let ctx_r := setup_base_receiver sk_R enc info
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let (ct, tag, _) := hpkeSeal ctx_s aad pt
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∃ (result : Nat × Context), open_msg ctx_r aad ct tag = some result
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/-- Sequence number increments after each hpkeSeal -/
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axiom seq_increments :
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∀ (ctx : Context) (aad pt : Nat),
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(hpkeSeal ctx aad pt).2.2.seq = ctx.seq + 1
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/-- Nonce uniqueness: sequence numbers are strictly increasing -/
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axiom nonce_unique :
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∀ (ctx : Context) (aad1 pt1 aad2 pt2 : Nat),
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let ctx1 := (hpkeSeal ctx aad1 pt1).2.2
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let ctx2 := (hpkeSeal ctx1 aad2 pt2).2.2
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ctx1.seq ≠ ctx2.seq
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/-- Context binding: different info strings produce different keys -/
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axiom context_binding :
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∀ (pk_R info1 info2 entropy : Nat),
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info1 ≠ info2 →
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(setup_base_sender pk_R info1 entropy).1.key ≠
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(setup_base_sender pk_R info2 entropy).1.key
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/-- Export mode: key derivation without encryption -/
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axiom export_secret : Context → Nat → Nat → Nat
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-- ctx, exporter_context, length → derived_key
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/-! ## Gas costs -/
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def gas_setup : Nat := 5000
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def gas_seal_base : Nat := 8000
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def gas_per_byte : Nat := 7
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def gas_export : Nat := 3000
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def gas_hpkeSeal (pt_len : Nat) : Nat := gas_seal_base + gas_per_byte * pt_len
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/-- Setup + hpkeSeal fits in block for any practical message -/
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theorem setup_seal_fits (pt_len : Nat) (h : pt_len ≤ 65536) :
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gas_setup + gas_hpkeSeal pt_len < 30000000 := by
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simp only [gas_setup, gas_hpkeSeal, gas_seal_base, gas_per_byte]
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omega
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end Crypto.Precompile.HPKE
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