Completeness
InductiveMerkleTree.completeness
Project documentation
Completeness theorem for Merkle trees. The proof proceeds by reducing to the functional completeness theorem by a theorem about the OracleComp monad, and then applying the functional version of the completeness theorem.
Exact Lean statement
@[simp]
theorem completeness [DecidableEq α] [Inhabited α] [SampleableType α] {s}
(leaf_data_tree : LeafData α s) (idx : BinaryTree.SkeletonLeafIndex s)
(preexisting_cache : (spec α).QueryCache) :
Pr[fun v => v.1 = true | (simulateQ (spec α).randomOracle (do
let cache ← buildMerkleTree leaf_data_tree
let proof := generateProof cache idx
let verified ← (verifyProof (m := OracleComp (spec α)) idx (leaf_data_tree.get idx)
(cache.getRootValue) proof)
return verified)).run preexisting_cache] = 1Formal artifact
Lean source
@[simp]theorem completeness [DecidableEq α] [Inhabited α] [SampleableType α] {s} (leaf_data_tree : LeafData α s) (idx : BinaryTree.SkeletonLeafIndex s) (preexisting_cache : (spec α).QueryCache) : Pr[fun v => v.1 = true | (simulateQ (spec α).randomOracle (do let cache ← buildMerkleTree leaf_data_tree let proof := generateProof cache idx let verified ← (verifyProof (m := OracleComp (spec α)) idx (leaf_data_tree.get idx) (cache.getRootValue) proof) return verified)).run preexisting_cache] = 1 := by refine (probEvent_eq_one_simulateQ_randomOracle_run_iff (spec := spec α) (p := fun b : Bool => b = true) _ _).mpr ?_ intro f _hf simp only [evalWithAnswerFn, verifyProof, simulateQ_bind, simulateQ_pure, simulateQ_buildMerkleTree, simulateQ_getPutativeRoot] change ((_ : α) == _) = true rw [beq_iff_eq] exact functional_completeness idx leaf_data_tree fun left right => f (left, right)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/MerkleTree/Inductive/Completeness.lean:57-74
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