Verify expected Query Cost eq
FiatShamirWithAbort.verify_expectedQueryCost_eq
Plain-language statement
Verification has expected weighted query cost equal to the cost of the single verification query when a signature is present, and 0 when the signature is none.
Exact Lean statement
theorem verify_expectedQueryCost_eq
{ω : Type} [AddMonoid ω] [Preorder ω]
(runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (msg : M)
(sig : Option (Commit × Resp))
(costFn : M × Commit → ω) (val : ω → ENNReal) (hval : Monotone val) (maxAttempts : ℕ) :
ExpectedQueryCost[
(FiatShamirWithAbort ids hr M maxAttempts).verify pk msg sig in runtime by costFn via val
] =
match sig with
| none => val 0
| some (w', _) => val (costFn (msg, w'))Formal artifact
Lean source
theorem verify_expectedQueryCost_eq {ω : Type} [AddMonoid ω] [Preorder ω] (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (msg : M) (sig : Option (Commit × Resp)) (costFn : M × Commit → ω) (val : ω → ENNReal) (hval : Monotone val) (maxAttempts : ℕ) : ExpectedQueryCost[ (FiatShamirWithAbort ids hr M maxAttempts).verify pk msg sig in runtime by costFn via val ] = match sig with | none => val 0 | some (w', _) => val (costFn (msg, w')) := by rcases sig with _ | ⟨w', z⟩ · letI : DecidableEq ω := Classical.decEq ω simp [FiatShamirWithAbort, HasQuery.expectedQueryCost, AddWriterT.expectedCost, HasQuery.Program.withAddCost] · refine HasQuery.expectedQueryCost_eq_of_usesCostExactly ?_ hval change Cost[ HasQuery.Program.withAddCost (fun [HasQuery (M × Commit →ₒ Chal) (AddWriterT ω m)] => (FiatShamirWithAbort (m := AddWriterT ω m) ids hr M maxAttempts).verify pk msg (some (w', z))) runtime costFn ] = costFn (msg, w') rw [AddWriterT.hasCost_iff] simp [FiatShamirWithAbort, HasQuery.Program.withAddCost, QueryImpl.withAddCost_apply, AddWriterT.outputs, AddWriterT.costs, AddWriterT.addTell]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/FiatShamir/WithAbort/ExpectedCost.lean:463-488
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