Knowledge Soundness
Fischlin.knowledgeSoundness
Plain-language statement
Knowledge soundness of the Fischlin transform via online (straight-line) extraction (Fischlin 2005, Theorem 2). If the Σ-protocol is specially sound with unique responses, then for any cheating prover making at most Q hash queries, the probability that the verifier accepts but the online extractor fails to recover a valid witness is at most `(Q + 1) · (...
Exact Lean statement
theorem knowledgeSoundness
(hss : σ.SpeciallySound) (hur : σ.UniqueResponses)
(adv : KnowledgeSoundnessAdv ρ b M)
(Q : ℕ) (hρ : 0 < ρ)
(hQ : ∀ x msg, ROQueryBound ρ b M (adv.run x msg) Q)
(x : Stmt) (msg : M) :
Pr[= true | knowledgeSoundnessExp σ hr ρ b S M adv.run x msg]
≤ knowledgeSoundnessError Q ρ b SFormal artifact
Lean source
theorem knowledgeSoundness (hss : σ.SpeciallySound) (hur : σ.UniqueResponses) (adv : KnowledgeSoundnessAdv ρ b M) (Q : ℕ) (hρ : 0 < ρ) (hQ : ∀ x msg, ROQueryBound ρ b M (adv.run x msg) Q) (x : Stmt) (msg : M) : Pr[= true | knowledgeSoundnessExp σ hr ρ b S M adv.run x msg] ≤ knowledgeSoundnessError Q ρ b S := by refine le_trans (knowledgeSoundness_badEvent_le σ hr ρ b S M hss hur adv Q hρ hQ x msg) ?_ rw [knowledgeSoundnessError] -- Monotonicity: replace the small-sum count by its stars-and-bars upper bound. gcongr exact_mod_cast smallSumCount_le ρ b S- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/Fischlin/KnowledgeSoundness.lean:2522-2534
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