Project-declaredLean 4.32.0 · mathlib@81a5d257

Nma run Prob shift Left signed Fresh Adv le fork

FiatShamir.Stateful.nma_runProb_shiftLeft_signedFreshAdv_le_fork

program verification separation logic cryptography chain

Plain-language statement

H5 boundary in shifted-NMA form. This is the fork-side statement after the native H4 normalization has moved cmaSim to nma ∘ cmaToNma. The bound is in terms of the verify-wrapped adversary nmaAdvFromCmaWithFinalQuery at fork slot parameter qH (the framework's Fin (qH + 1) indexing accommodates the wrapper's verifier-point query).

Exact Lean statement

theorem nma_runProb_shiftLeft_signedFreshAdv_le_fork
    [Finite Chal] [Finite Commit] [Finite Resp] [Inhabited Commit] [Inhabited Resp]
    (adv : SourceAdv (σ := σ) (hr := hr) (M := M))
    (simT : Stmt → ProbComp (Commit × Chal × Resp))
    (qS qH : ℕ)
    (hQ : ∀ pk, signHashQueryBound (M := M) (Commit := Commit)
      (Chal := Chal) (S' := Commit × Resp) (oa := adv.main pk) qS qH) :
    Pr[= true |
        (nma (Stmt := Stmt) (Wit := Wit) M Commit Chal hr).runProb
          (nmaInit M Commit Chal Stmt Wit)
          ((cmaToNma M Commit Chal simT).shiftLeft ([] : List M)
            (signedFreshAdv σ hr M adv))]
      ≤ Fork.advantage σ hr M (nmaAdvFromCmaWithFinalQuery σ hr M adv simT)
          qH

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem nma_runProb_shiftLeft_signedFreshAdv_le_fork    [Finite Chal] [Finite Commit] [Finite Resp] [Inhabited Commit] [Inhabited Resp]    (adv : SourceAdv (σ := σ) (hr := hr) (M := M))    (simT : Stmt → ProbComp (Commit × Chal × Resp))    (qS qH : ℕ)    (hQ : ∀ pk, signHashQueryBound (M := M) (Commit := Commit)      (Chal := Chal) (S' := Commit × Resp) (oa := adv.main pk) qS qH) :    Pr[= true |        (nma (Stmt := Stmt) (Wit := Wit) M Commit Chal hr).runProb          (nmaInit M Commit Chal Stmt Wit)          ((cmaToNma M Commit Chal simT).shiftLeft ([] : List M)            (signedFreshAdv σ hr M adv))]      ≤ Fork.advantage σ hr M (nmaAdvFromCmaWithFinalQuery σ hr M adv simT)          qH := by  letI : Fintype Chal := Fintype.ofFinite Chal  have hbridge :      Pr[= true |          (nma (Stmt := Stmt) (Wit := Wit) M Commit Chal hr).runProb            (nmaInit M Commit Chal Stmt Wit)            ((cmaToNma M Commit Chal simT).shiftLeft ([] : List M)              (signedFreshAdv σ hr M adv))]        =      Pr[= true |          forkH5Body (M := M) (Commit := Commit) (Chal := Chal)            (Resp := Resp) σ hr adv simT] := by    rw [nma_runProb_shiftLeft_signedFreshAdv_eq_forkH5Body (σ := σ) (hr := hr)      (M := M) (Commit := Commit) (Chal := Chal) (Resp := Resp) adv simT]    exact probOutput_simulateQ_forkWrappedUniformImpl      (Chal := Chal)      (oa := forkH5Body (M := M) (Commit := Commit) (Chal := Chal)        (Resp := Resp) σ hr adv simT) true  have hbody := forkH5Body_prob_true_le_fork_advantage (σ := σ) (hr := hr)    (M := M) (Commit := Commit) (Chal := Chal) (Resp := Resp)    adv simT hQ  exact hbridge.trans_le hbody

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/FiatShamir/Sigma/Stateful/Chain.lean:1840-1874

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Plain-language statement

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