Sign Attempt expected Query Cost eq output Expectation
FiatShamirWithAbort.signAttempt_expectedQueryCost_eq_outputExpectation
Plain-language statement
The expected weighted query cost of one signing attempt is the expectation of the queried commitment cost over the attempt output distribution.
Exact Lean statement
theorem signAttempt_expectedQueryCost_eq_outputExpectation
{ω : Type} [AddMonoid ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF]
[MonadLiftT m SetM] [LawfulMonadLiftT m SetM] [EvalDistCompatible m]
(runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
(costFn : M × Commit → ω) (val : ω → ENNReal) :
ExpectedQueryCost[
fsAbortSignAttempt ids M pk sk msg in runtime by costFn via val
] =
∑' attempt : Commit × Option Resp,
Pr[= attempt | HasQuery.Program.eval
(fun [HasQuery (M × Commit →ₒ Chal) m] =>
fsAbortSignAttempt (m := m) ids M pk sk msg)
runtime] * val (costFn (msg, attempt.1))Formal artifact
Lean source
theorem signAttempt_expectedQueryCost_eq_outputExpectation {ω : Type} [AddMonoid ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF] [MonadLiftT m SetM] [LawfulMonadLiftT m SetM] [EvalDistCompatible m] (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M) (costFn : M × Commit → ω) (val : ω → ENNReal) : ExpectedQueryCost[ fsAbortSignAttempt ids M pk sk msg in runtime by costFn via val ] = ∑' attempt : Commit × Option Resp, Pr[= attempt | HasQuery.Program.eval (fun [HasQuery (M × Commit →ₒ Chal) m] => fsAbortSignAttempt (m := m) ids M pk sk msg) runtime] * val (costFn (msg, attempt.1)) := by calc ExpectedQueryCost[ fsAbortSignAttempt ids M pk sk msg in runtime by costFn via val ] = ∑' attempt : Commit × Option Resp, Pr[= attempt | AddWriterT.outputs (HasQuery.Program.withAddCost (fun [HasQuery (M × Commit →ₒ Chal) (AddWriterT ω m)] => fsAbortSignAttempt (m := AddWriterT ω m) ids M pk sk msg) runtime costFn)] * val (costFn (msg, attempt.1)) := HasQuery.expectedQueryCost_eq_tsum_outputs_of_usesCostAs (signAttempt_usesCostAsQueryCost ids M runtime pk sk msg costFn) _ = ∑' attempt : Commit × Option Resp, Pr[= attempt | HasQuery.Program.eval (fun [HasQuery (M × Commit →ₒ Chal) m] => fsAbortSignAttempt (m := m) ids M pk sk msg) runtime] * val (costFn (msg, attempt.1)) := by rw [signAttempt_outputs_withAddCost_eq_eval]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean:141-171
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