Project-declaredLean 4.32.0 · mathlib@81a5d257

Perfectly Correct compose With DEM

KEMScheme.perfectlyCorrect_composeWithDEM

program verification separation logic cryptography kemdem

Plain-language statement

If a KEM and externally keyed DEM are both perfectly correct in the concrete probabilistic semantics of m, then their composition is also perfectly correct.

Exact Lean statement

theorem perfectlyCorrect_composeWithDEM
    [LawfulMonad m]
    (kem : KEMScheme m K PK SK CKEM) (dem : DEMScheme m K M CDEM)
    (hkem : Pr[= true | kem.CorrectExp] = 1)
    (hdem : ∀ k : K, ∀ msg : M, Pr[= true | dem.CorrectExp k msg] = 1) :
    ∀ msg, Pr[= true | (kem.composeWithDEM dem).CorrectExp msg] = 1

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem perfectlyCorrect_composeWithDEM    [LawfulMonad m]    (kem : KEMScheme m K PK SK CKEM) (dem : DEMScheme m K M CDEM)    (hkem : Pr[= true | kem.CorrectExp] = 1)    (hdem : ∀ k : K, ∀ msg : M, Pr[= true | dem.CorrectExp k msg] = 1) :    ∀ msg, Pr[= true | (kem.composeWithDEM dem).CorrectExp msg] = 1 := by  intro msg  rw [← hkem]  simp only [AsymmEncAlg.CorrectExp, composeWithDEM, KEMScheme.CorrectExp, monad_norm]  refine probOutput_bind_congr fun ⟨pk, sk⟩ hks => ?_  refine probOutput_bind_congr fun ⟨kc, k⟩ hck => ?_  rw [probOutput_bind_bind_swap (mx := dem.encrypt k msg) (my := kem.decaps sk kc)]  refine probOutput_bind_congr fun kOpt hkOpt => ?_  obtain rfl := kem_decaps_mem_support hkem hks hck hkOpt  simpa [DEMScheme.CorrectExp, probOutput_pure, monad_norm] using hdem k msg

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/KEMDEM.lean:65-79

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