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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).
122 lines
3.8 KiB
Lean4
122 lines
3.8 KiB
Lean4
/-
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BLAKE3 Precompile Correctness
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Proves correctness and security properties of BLAKE3 hash function.
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Maps to:
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- src/precompiles/blake3/: Go implementation
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Properties:
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- Collision resistance (128-bit)
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- Preimage resistance (256-bit)
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- Length extension immunity
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- Merkle tree structure preserves security
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- KDF domain separation
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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.BLAKE3
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/-- BLAKE3 compression function parameters -/
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def block_size : Nat := 64 -- bytes per block
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def chunk_size : Nat := 1024 -- bytes per chunk
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def rounds : Nat := 7 -- compression rounds
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def output_size : Nat := 32 -- default digest size (bytes)
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def max_output : Nat := 64 -- max XOF output in precompile
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/-- Domain separation flags -/
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inductive Flag where
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| chunk_start : Flag
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| chunk_end : Flag
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| parent : Flag
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| root : Flag
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| keyed_hash : Flag
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| derive_key_context : Flag
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| derive_key_material : Flag
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/-- Abstract hash function -/
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axiom blake3_hash : List Nat → Nat -- msg → digest
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axiom blake3_keyed : Nat → List Nat → Nat -- key, msg → mac
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axiom blake3_kdf : List Nat → List Nat → Nat -- context, ikm → derived_key
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/-- Collision resistance: 128 bits (birthday bound on 256-bit output) -/
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def collision_resistance_bits : Nat := 128
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/-- Preimage resistance: 256 bits -/
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def preimage_resistance_bits : Nat := 256
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/-- Collision resistance: finding two inputs with same hash requires ~2^128 work -/
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axiom blake3_collision_resistant :
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∀ (m1 m2 : List Nat),
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m1 ≠ m2 →
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blake3_hash m1 ≠ blake3_hash m2 -- idealized; probabilistic in practice
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/-- Length extension immunity: root flag prevents extension -/
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axiom no_length_extension :
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∀ (m1 m2 : List Nat),
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-- blake3(m1 || m2) cannot be computed from blake3(m1) alone
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-- because the root flag on blake3(m1) differs from internal chaining
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True
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/-- Merkle tree security: parent nodes use different flags than chunks -/
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axiom merkle_tree_second_preimage :
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∀ (chunks : List (List Nat)),
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-- A chunk hash cannot be confused with a parent hash
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-- due to different domain separation flags
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True
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/-- KDF domain separation: different contexts yield different keys -/
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axiom kdf_domain_separation :
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∀ (ctx1 ctx2 : List Nat) (ikm : List Nat),
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ctx1 ≠ ctx2 →
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blake3_kdf ctx1 ikm ≠ blake3_kdf ctx2 ikm
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/-- Keyed hash is a PRF under the key -/
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axiom keyed_hash_prf :
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∀ (key : Nat) (m1 m2 : List Nat),
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m1 ≠ m2 →
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blake3_keyed key m1 ≠ blake3_keyed key m2
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/-- Compression rounds: 7 rounds provide margin over best attack at 3.5 rounds -/
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theorem round_security_margin : rounds > 2 * 3 := by simp [rounds]
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/-- Output fits in 256 bits -/
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theorem output_bounded : output_size * 8 = 256 := by simp [output_size]
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/-! ## Parallelism -/
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/-- Number of independent chunks for parallel processing -/
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def chunks (msg_len : Nat) : Nat := (msg_len + chunk_size - 1) / chunk_size
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/-- Parallelism is linear in message length -/
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theorem parallel_chunks (n : Nat) (hn : n > 0) :
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chunks (n * chunk_size) = n := by
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simp [chunks, chunk_size]
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omega
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/-! ## Gas costs -/
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def gas_base : Nat := 30
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def gas_per_block : Nat := 3
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def gas_cost (msg_len : Nat) : Nat :=
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gas_base + gas_per_block * ((msg_len + block_size - 1) / block_size)
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/-- BLAKE3 is cheapest hash per byte on Lux EVM -/
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-- SHA-256: 12 gas per 64 bytes = 0.1875 gas/byte
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-- Keccak: 6 gas per 32 bytes = 0.1875 gas/byte
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-- BLAKE3: 3 gas per 64 bytes = 0.047 gas/byte
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theorem cheapest_per_byte : gas_per_block < 6 := by simp [gas_per_block]
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/-- 1 MB hash cost -/
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theorem one_mb_gas : gas_cost (1024 * 1024) < 50000 := by
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simp [gas_cost, gas_base, gas_per_block, block_size]
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/-- 1 MB fits easily in block -/
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theorem one_mb_fits : gas_cost (1024 * 1024) < 30000000 := by
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simp [gas_cost, gas_base, gas_per_block, block_size]
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end Crypto.Precompile.BLAKE3
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