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83 lines
2.6 KiB
Lean4
83 lines
2.6 KiB
Lean4
/-
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ChaCha20-Poly1305 Precompile Correctness
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Proves correctness of software-optimized AEAD.
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Maps to:
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- src/precompiles/chacha20/: Go implementation
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Properties:
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- Encrypt-then-decrypt correctness
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- Poly1305 authentication (information-theoretic)
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- XChaCha20 extended nonce (192-bit) collision bound
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- Gas cost linear in message length
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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.ChaCha20Poly1305
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/-- Parameter sizes -/
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def key_size : Nat := 32
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def nonce_size : Nat := 12
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def xchacha_nonce_size : Nat := 24
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def tag_size : Nat := 16
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def max_plaintext : Nat := 65536
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/-- Abstract operations -/
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axiom chacha20_poly1305_seal : Nat → Nat → Nat → Nat → Nat × Nat
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axiom chacha20_poly1305_open : Nat → Nat → Nat → Nat → Nat → Option Nat
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/-- Correctness -/
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axiom chacha20_correctness :
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∀ (key nonce aad pt : Nat),
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let (ct, tag) := chacha20_poly1305_seal key nonce aad pt
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chacha20_poly1305_open key nonce aad ct tag = some pt
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/-- Poly1305 authentication: information-theoretic bound -/
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axiom poly1305_forgery_bound :
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∀ (key nonce aad ct : Nat) (tag_forged tag_real : Nat),
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tag_forged ≠ tag_real →
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-- Forgery probability ≤ ceil(|msg|/16) / 2^106
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chacha20_poly1305_open key nonce aad ct tag_forged = none
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/-- ChaCha20 quarter round: 4 additions, 4 XORs, 4 rotations -/
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def ops_per_quarter_round : Nat := 12 -- 4 add + 4 xor + 4 rot
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def quarter_rounds_per_round : Nat := 8 -- 4 column + 4 diagonal
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def rounds : Nat := 20 -- 10 double-rounds
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def ops_per_block : Nat := ops_per_quarter_round * quarter_rounds_per_round * rounds / 2
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/-- 20 rounds provide security margin over best attack at 7 rounds -/
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theorem security_margin : rounds > 7 * 2 := by simp [rounds]
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/-- XChaCha20: 192-bit nonce space -/
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def xchacha_nonce_bits : Nat := 192
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/-- Birthday bound for random nonce collision with XChaCha20 -/
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theorem xchacha_nonce_collision_bound :
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2^(xchacha_nonce_bits / 2) = 2^96 := by
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simp [xchacha_nonce_bits]
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/-- 2^96 messages before collision concern -/
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theorem xchacha_safe_message_count :
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2^96 > 10^28 := by omega
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/-! ## Gas costs -/
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def gas_base : Nat := 3500
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def gas_per_byte : Nat := 7
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def xchacha_gas_base : Nat := 3700
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def gas_cost (pt_len : Nat) : Nat := gas_base + gas_per_byte * pt_len
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/-- ChaCha20 slightly more expensive than AES per byte (7 vs 6) -/
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theorem chacha_more_expensive_per_byte : gas_per_byte > 6 := by
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simp [gas_per_byte]
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/-- Max gas fits in block -/
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theorem max_gas_fits : gas_cost max_plaintext < 30000000 := by
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simp [gas_cost, gas_base, gas_per_byte, max_plaintext]
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end Crypto.Precompile.ChaCha20Poly1305
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