Unforgeable Adv advantage le unforgeable Exp No Fresh
SignatureAlg.unforgeableAdv.advantage_le_unforgeableExpNoFresh
Plain-language statement
Phase B (freshness-drop) bound. The CMA advantage is bounded above by the success probability of the same experiment with the freshness check dropped. Both unforgeableExp and unforgeableExpNoFresh factor as runtime.evalDist (joint >>= ...) sharing the same prefix joint. The hypothesis h_pull packages the runtime-specific factoring step that...
Exact Lean statement
lemma unforgeableAdv.advantage_le_unforgeableExpNoFresh
{sigAlg : SignatureAlg (OracleComp spec) M PK SK S}
(runtime : ProbCompRuntime (OracleComp spec))
(h_pull : ∀ {α β : Type} (f : α → β) (mx : OracleComp spec α),
runtime.evalDist (mx >>= fun x => pure (f x)) = f <$> runtime.evalDist mx)
(adv : unforgeableAdv sigAlg) :
adv.advantage runtime ≤ Pr[= true | unforgeableExpNoFresh runtime adv]Formal artifact
Lean source
lemma unforgeableAdv.advantage_le_unforgeableExpNoFresh {sigAlg : SignatureAlg (OracleComp spec) M PK SK S} (runtime : ProbCompRuntime (OracleComp spec)) (h_pull : ∀ {α β : Type} (f : α → β) (mx : OracleComp spec α), runtime.evalDist (mx >>= fun x => pure (f x)) = f <$> runtime.evalDist mx) (adv : unforgeableAdv sigAlg) : adv.advantage runtime ≤ Pr[= true | unforgeableExpNoFresh runtime adv] := by letI : DecidableEq M := Classical.decEq M letI : DecidableEq S := Classical.decEq S unfold unforgeableAdv.advantage unforgeableExp unforgeableExpNoFresh set joint : OracleComp spec (M × QueryLog (M →ₒ S) × Bool) := do let (pk, sk) ← sigAlg.keygen let impl : QueryImpl (spec + (M →ₒ S)) (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) := (HasQuery.toQueryImpl (spec := spec) (m := OracleComp spec)).liftTarget (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) + sigAlg.signingOracle pk sk let sim_adv : WriterT (QueryLog (M →ₒ S)) (OracleComp spec) (M × S) := simulateQ impl (adv.main pk) let ((msg, σ), log) ← sim_adv.run let verified ← sigAlg.verify pk msg σ pure (msg, log, verified) with hjoint_def have hExp : (runtime.evalDist do let (pk, sk) ← sigAlg.keygen let impl : QueryImpl (spec + (M →ₒ S)) (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) := (HasQuery.toQueryImpl (spec := spec) (m := OracleComp spec)).liftTarget (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) + sigAlg.signingOracle pk sk let sim_adv : WriterT (QueryLog (M →ₒ S)) (OracleComp spec) (M × S) := simulateQ impl (adv.main pk) let ((msg, σ), log) ← sim_adv.run let verified ← sigAlg.verify pk msg σ pure (!log.wasQueried msg && verified)) = (fun t : M × QueryLog (M →ₒ S) × Bool => !t.2.1.wasQueried t.1 && t.2.2) <$> runtime.evalDist joint := by rw [← h_pull] congr 1 simp only [hjoint_def, monad_norm] have hNoFresh : (runtime.evalDist do let (pk, sk) ← sigAlg.keygen let impl : QueryImpl (spec + (M →ₒ S)) (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) := (HasQuery.toQueryImpl (spec := spec) (m := OracleComp spec)).liftTarget (WriterT (QueryLog (M →ₒ S)) (OracleComp spec)) + sigAlg.signingOracle pk sk let sim_adv : WriterT (QueryLog (M →ₒ S)) (OracleComp spec) (M × S) := simulateQ impl (adv.main pk) let ((msg, σ), _) ← sim_adv.run sigAlg.verify pk msg σ) = (fun t : M × QueryLog (M →ₒ S) × Bool => t.2.2) <$> runtime.evalDist joint := by rw [← h_pull] congr 1 simp only [hjoint_def, monad_norm] rw [hExp, hNoFresh, ← probEvent_eq_eq_probOutput, ← probEvent_eq_eq_probOutput, probEvent_map, probEvent_map] exact probEvent_mono fun _ _ => Bool.and_elim_right- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/SignatureAlg.lean:221-277
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