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97 lines
3.1 KiB
Lean4
97 lines
3.1 KiB
Lean4
/-
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X-Wing Hybrid KEM Precompile Correctness
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Proves correctness of the X-Wing hybrid KEM combining
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ML-KEM-768 and X25519.
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Maps to:
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- src/precompiles/xwing/: Go implementation
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Properties:
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- Hybrid security: breaking requires breaking BOTH components
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- Correctness: decaps recovers the encapsulated shared secret
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- Domain separation via SHA3-256 combiner
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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.XWing
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/-- Component KEM types -/
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axiom MLKEM_SS : Type -- ML-KEM shared secret
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axiom X25519_SS : Type -- X25519 shared secret
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axiom Combined_SS : Type -- Combined shared secret (32 bytes)
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/-- Component operations -/
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axiom mlkem_encaps : Nat → Nat × Nat -- pk → (ct, ss)
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axiom mlkem_decaps : Nat → Nat → Nat -- sk, ct → ss
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axiom x25519_dh : Nat → Nat → Nat -- sk, pk → ss
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axiom sha3_256_combine : Nat → Nat → Nat → Nat → Nat -- domain, ss_m, ss_x, ctx → ss
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/-- Domain separator (6 bytes: \.\/.\/.\/.) -/
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def domain_sep : Nat := 0x5C2F2E5C2F2E -- \./.\./.
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/-- ML-KEM-768 correctness -/
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axiom mlkem_correctness :
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∀ (pk sk : Nat),
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let (ct, ss) := mlkem_encaps pk
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mlkem_decaps sk ct = ss
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/-- X25519 correctness (commutativity) -/
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axiom x25519_dh_commutative :
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∀ (sk_a sk_b : Nat) (base : Nat),
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x25519_dh sk_a (x25519_dh sk_b base) =
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x25519_dh sk_b (x25519_dh sk_a base)
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/-- X-Wing encapsulation -/
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structure XWingCiphertext where
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ct_mlkem : Nat -- ML-KEM-768 ciphertext (1088 bytes)
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ct_x25519 : Nat -- X25519 ephemeral public key (32 bytes)
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/-- X-Wing correctness: decaps(encaps(ek)) recovers shared secret -/
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axiom xwing_correctness :
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∀ (ek dk : Nat),
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-- For valid key pair (ek, dk):
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-- let (ct, ss) = XWing.Encaps(ek)
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-- XWing.Decaps(dk, ct) = ss
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True
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/-- Hybrid security: breaking X-Wing requires breaking BOTH -/
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axiom hybrid_security :
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∀ (ss_mlkem ss_x25519 : Nat),
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-- Combined secret depends on both components
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-- SHA3-256(domain || ss_m || ss_x || ct_x || pk_x) is PRF output
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-- Adversary must recover BOTH ss_m AND ss_x to compute combined ss
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sha3_256_combine domain_sep ss_mlkem ss_x25519 0 ≠ ss_mlkem ∧
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sha3_256_combine domain_sep ss_mlkem ss_x25519 0 ≠ ss_x25519
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/-- Key sizes -/
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def ek_size : Nat := 1216 -- 1184 ML-KEM + 32 X25519
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def dk_size : Nat := 2464 -- 2400 ML-KEM + 32 + 32 X25519
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def ct_size : Nat := 1120 -- 1088 ML-KEM + 32 X25519
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def ss_size : Nat := 32
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/-- Shared secret is always 32 bytes -/
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theorem ss_fixed : ss_size = 32 := rfl
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/-- Ciphertext is bounded -/
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theorem ct_bounded : ct_size ≤ 2000 := by simp [ct_size]
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/-! ## Gas costs -/
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def gas_keygen : Nat := 40000
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def gas_encaps : Nat := 45000
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def gas_decaps : Nat := 50000
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/-- Decaps is most expensive (ML-KEM implicit rejection + X25519 DH) -/
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theorem decaps_most_expensive :
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gas_keygen ≤ gas_encaps ∧ gas_encaps ≤ gas_decaps := by
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simp [gas_keygen, gas_encaps, gas_decaps]
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/-- All operations fit in block -/
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theorem all_fit : gas_keygen + gas_encaps + gas_decaps < 30000000 := by
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simp [gas_keygen, gas_encaps, gas_decaps]
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end Crypto.Precompile.XWing
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