Project-declaredLean 4.32.0 · mathlib@81a5d257

IND CPA Game eq IND CCA Game to IND CCA

KEMScheme.IND_CPA_Game_eq_IND_CCA_Game_toIND_CCA

program verification separation logic cryptography key encap mech

Plain-language statement

The one-stage IND-CPA game is exactly the IND-CCA game instantiated with the trivial CPA-to-CCA embedding (toIND_CCA) that never uses the decryption oracle.

Exact Lean statement

theorem IND_CPA_Game_eq_IND_CCA_Game_toIND_CCA
    {kem : KEMScheme (OracleComp spec) K PK SK C}
    (runtime : ProbCompRuntime (OracleComp spec))
    (adversary : kem.IND_CPA_Adversary) :
    kem.IND_CPA_Game runtime adversary = kem.IND_CCA_Game runtime adversary.toIND_CCA

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem IND_CPA_Game_eq_IND_CCA_Game_toIND_CCA    {kem : KEMScheme (OracleComp spec) K PK SK C}    (runtime : ProbCompRuntime (OracleComp spec))    (adversary : kem.IND_CPA_Adversary) :    kem.IND_CPA_Game runtime adversary = kem.IND_CCA_Game runtime adversary.toIND_CCA := by  have h : ∀ (impl₂ : QueryImpl (C →ₒ Option K) (OracleComp spec))      {α : Type} (oa : OracleComp spec α),      simulateQ ((HasQuery.toQueryImpl (spec := spec) (m := OracleComp spec)) + impl₂)        (simulateQ (HasQuery.toQueryImpl (spec := spec)          (m := OracleComp (spec + (C →ₒ Option K)))) oa) = oa := by    intro impl₂ α oa    rw [← QueryImpl.simulateQ_compose]    have : (HasQuery.toQueryImpl (spec := spec) (m := OracleComp spec) + impl₂) ∘ₛ        HasQuery.toQueryImpl (spec := spec) (m := OracleComp (spec + (C →ₒ Option K))) =        QueryImpl.id' spec := by      ext t      simp only [QueryImpl.compose, QueryImpl.id']      change simulateQ (QueryImpl.id' spec + impl₂)        (liftM (liftM (spec.query t) :          OracleQuery (spec + (C →ₒ Option K)) _)) = _      simp [simulateQ_query]    rw [this, simulateQ_id']  simp only [IND_CPA_Game, IND_CCA_Game, IND_CPA_Adversary.toIND_CCA,    IND_CCA_preChallengeImpl, IND_CCA_postChallengeImpl, IND_CCA_oracleSpec, h]

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/KeyEncapMech.lean:169-192

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