Project-declaredLean 4.32.0 · mathlib@81a5d257

Simulated Nma Adv hash Query Bound

FiatShamir.simulatedNmaAdv_hashQueryBound

program verification separation logic cryptography cma to nma

Plain-language statement

Hash-query bound for simulatedNmaAdv: if the CMA adversary makes at most qS signing-oracle queries and qH random-oracle queries, the NMA reduction makes at most qH live hash queries. The qS signing queries are absorbed into the managed cache rather than issued live.

Exact Lean statement

theorem simulatedNmaAdv_hashQueryBound
    [DecidableEq M] [DecidableEq Commit] [Finite Commit]
    [Finite Chal] [Inhabited Chal] [SampleableType Chal]
    [Finite Resp]
    (simTranscript : Stmt → ProbComp (Commit × Chal × Resp))
    (adv : SignatureAlg.unforgeableAdv
      (FiatShamir (m := OracleComp (unifSpec + (M × Commit →ₒ Chal))) σ hr M))
    (qS qH : ℕ)
    (hQ : ∀ pk, signHashQueryBound (M := M) (Commit := Commit) (Chal := Chal)
      (S' := Commit × Resp) (oa := adv.main pk) qS qH) :
    ∀ pk, nmaHashQueryBound (M := M) (Commit := Commit) (Chal := Chal)
      (oa := (simulatedNmaAdv (σ := σ) (hr := hr) (M := M)
        (simTranscript := simTranscript) (adv := adv)).main pk) qH

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem simulatedNmaAdv_hashQueryBound    [DecidableEq M] [DecidableEq Commit] [Finite Commit]    [Finite Chal] [Inhabited Chal] [SampleableType Chal]    [Finite Resp]    (simTranscript : Stmt → ProbComp (Commit × Chal × Resp))    (adv : SignatureAlg.unforgeableAdv      (FiatShamir (m := OracleComp (unifSpec + (M × Commit →ₒ Chal))) σ hr M))    (qS qH : ℕ)    (hQ : ∀ pk, signHashQueryBound (M := M) (Commit := Commit) (Chal := Chal)      (S' := Commit × Resp) (oa := adv.main pk) qS qH) :    ∀ pk, nmaHashQueryBound (M := M) (Commit := Commit) (Chal := Chal)      (oa := (simulatedNmaAdv (σ := σ) (hr := hr) (M := M)        (simTranscript := simTranscript) (adv := adv)).main pk) qH := by  have : Fintype Chal := Fintype.ofFinite Chal  have : Fintype Resp := Fintype.ofFinite Resp  have : Fintype Commit := Fintype.ofFinite Commit  let : IsUniformSpec ((M × Commit →ₒ Chal) : OracleSpec _) :=    IsUniformSpec.ofFintypeInhabited _  intro pk  change nmaHashQueryBound (M := M) (Commit := Commit) (Chal := Chal)    (oa := (simulateQ (simulatedNmaImpl (M := M) (Commit := Commit) (Chal := Chal)      (Resp := Resp) simTranscript pk) (adv.main pk)).run ∅) qH  unfold nmaHashQueryBound simulatedNmaImpl  refine OracleComp.IsQueryBoundP.simulateQ_run_add_inl_of_step    (fun _ => Bool.false_ne_true) (hQ pk).2 ?_ ?_ ?_ ∅  · rintro (_ | mc) hp s'    · simp at hp    · exact simulatedNmaRoSim_run_hashQueryBound (M := M) mc s'  · rintro (n | _) hnp s'    · exact simulatedNmaFwd_run_hashQueryBound (M := M) (.inl n) s'    · simp at hnp  · intro msg s'    exact simulatedNmaSigSim_run_hashQueryBound (M := M) (Resp := Resp) simTranscript pk msg s'

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/FiatShamir/Sigma/CmaToNma.lean:210-242

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