Run m Of Fn query hit
Fischlin.run_mOfFn_query_hit
Plain-language statement
Simulating the verifier's Fin.mOfFn of random-oracle re-queries on a cache that already stores every re-queried record is deterministic: each query is a cache hit returning the stored value, leaving the cache untouched. The result is the pure product of the per-repetition outputs f i (hash i), where hash i is the value cached at record i.
Exact Lean statement
lemma run_mOfFn_query_hit {β : Type} (n : ℕ)
(records : Fin n → (fischlinROSpec Stmt Commit Chal Resp ρ b M).Domain)
(hash : Fin n → Fin (2 ^ b)) (f : Fin n → Fin (2 ^ b) → β)
(cache : (fischlinROSpec Stmt Commit Chal Resp ρ b M).QueryCache)
(hhit : ∀ i, cache (records i) = some (hash i)) :
(simulateQ (fischlinImpl ρ b M)
(Fin.mOfFn n fun i => do
let h ← HasQuery.query (spec := fischlinROSpec Stmt Commit Chal Resp ρ b M) (records i)
pure (f i h))).run cache
= pure ((fun i => f i (hash i)), cache)Formal artifact
Lean source
lemma run_mOfFn_query_hit {β : Type} (n : ℕ) (records : Fin n → (fischlinROSpec Stmt Commit Chal Resp ρ b M).Domain) (hash : Fin n → Fin (2 ^ b)) (f : Fin n → Fin (2 ^ b) → β) (cache : (fischlinROSpec Stmt Commit Chal Resp ρ b M).QueryCache) (hhit : ∀ i, cache (records i) = some (hash i)) : (simulateQ (fischlinImpl ρ b M) (Fin.mOfFn n fun i => do let h ← HasQuery.query (spec := fischlinROSpec Stmt Commit Chal Resp ρ b M) (records i) pure (f i h))).run cache = pure ((fun i => f i (hash i)), cache) := by induction n with | zero => simp only [Fin.mOfFn, simulateQ_pure, StateT.run_pure] congr 1 congr 1 exact Subsingleton.elim _ _ | succ n ih => rw [Fin.mOfFn, simulateQ_bind, StateT.run_bind, simulateQ_bind, roSim.simulateQ_HasQuery_query, StateT.run_bind, QueryImpl.withCaching_run_some (so := uniformSampleImpl) (hhit 0), pure_bind, simulateQ_pure, StateT.run_pure, pure_bind, simulateQ_bind, StateT.run_bind, ih (fun j => records j.succ) (fun j => hash j.succ) (fun j => f j.succ) (fun j => hhit j.succ), pure_bind, simulateQ_pure, StateT.run_pure] congr 1 refine Prod.ext ?_ rfl funext j refine Fin.cases ?_ (fun k => ?_) j · simp [Fin.cons_zero] · simp [Fin.cons_succ]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/Fischlin/Completeness.lean:585-614
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