Project-declaredLean 4.32.0 · mathlib@81a5d257

Sign Attempt run with Unit Cost eq

FiatShamirWithAbort.signAttempt_run_withUnitCost_eq

program verification separation logic cryptography cost

Plain-language statement

Unit-cost specialization of the run formula: each signing attempt run tags its output with a single unit of cost (cf. signAttempt_run_withAddCost_eq).

Exact Lean statement

lemma signAttempt_run_withUnitCost_eq
    (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M) :
    WriterT.run
        (HasQuery.Program.withUnitCost
          (fun [HasQuery (M × Commit →ₒ Chal) (AddWriterT ℕ m)] =>
            fsAbortSignAttempt (m := AddWriterT ℕ m) ids M pk sk msg)
          runtime) =
      (fun attempt : Commit × Option Resp => (attempt, Multiplicative.ofAdd 1)) <$>
        HasQuery.Program.eval
          (fun [HasQuery (M × Commit →ₒ Chal) m] =>
            fsAbortSignAttempt (m := m) ids M pk sk msg)
          runtime

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma signAttempt_run_withUnitCost_eq    (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M) :    WriterT.run        (HasQuery.Program.withUnitCost          (fun [HasQuery (M × Commit →ₒ Chal) (AddWriterT ℕ m)] =>            fsAbortSignAttempt (m := AddWriterT ℕ m) ids M pk sk msg)          runtime) =      (fun attempt : Commit × Option Resp => (attempt, Multiplicative.ofAdd 1)) <$>        HasQuery.Program.eval          (fun [HasQuery (M × Commit →ₒ Chal) m] =>            fsAbortSignAttempt (m := m) ids M pk sk msg)          runtime := by  change WriterT.run      (HasQuery.Program.withAddCost        (fun [HasQuery (M × Commit →ₒ Chal) (AddWriterT ℕ m)] =>          fsAbortSignAttempt (m := AddWriterT ℕ m) ids M pk sk msg)        runtime (fun _ ↦ 1)) = _  exact signAttempt_run_withAddCost_eq      (ids := ids) (M := M) (runtime := runtime) (pk := pk) (sk := sk) (msg := msg)      (costFn := fun _ ↦ (1 : ℕ))

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean:103-122

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