Project-declaredLean 4.32.0 · mathlib@81a5d257

Decaps uses Weighted Query Cost At Most

UTransform.decaps_usesWeightedQueryCostAtMost

program verification separation logic cryptography utransform

Plain-language statement

Under per-family upper bounds on the two U-transform oracle families, decapsulation incurs weighted query cost at most the sum of those bounds.

Exact Lean statement

theorem decaps_usesWeightedQueryCostAtMost {ω : Type}
    [AddCommMonoid ω] [PartialOrder ω] [IsOrderedAddMonoid ω] [CanonicallyOrderedAdd ω]
    [MonadLiftT m SetM] [LawfulMonadLiftT m SetM]
    (runtime : QueryImpl (UTransform.hashOracleSpec M R KD K) m)
    (pke : AsymmEncAlg.ExplicitCoins ProbComp M PK SK R C)
    (kdInput : M → C → KD)
    (policy : FujisakiOkamoto.RejectionPolicy K C)
    (pk : PK) (sk : SK) (fb : policy.FallbackState) (c : C)
    (costFn : (UTransform.hashOracleSpec M R KD K).Domain → ω)
    (wCoins wKey : ω)
    (hCoins : ∀ msg, costFn (Sum.inl msg) ≤ wCoins)
    (hKeys : ∀ kd, costFn (Sum.inr kd) ≤ wKey) :
    QueryCost[
      (UTransform pke kdInput policy).decaps ((pk, sk), fb) c in runtime by costFn
    ] ≤ wCoins + wKey

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem decaps_usesWeightedQueryCostAtMost {ω : Type}    [AddCommMonoid ω] [PartialOrder ω] [IsOrderedAddMonoid ω] [CanonicallyOrderedAdd ω]    [MonadLiftT m SetM] [LawfulMonadLiftT m SetM]    (runtime : QueryImpl (UTransform.hashOracleSpec M R KD K) m)    (pke : AsymmEncAlg.ExplicitCoins ProbComp M PK SK R C)    (kdInput : M → C → KD)    (policy : FujisakiOkamoto.RejectionPolicy K C)    (pk : PK) (sk : SK) (fb : policy.FallbackState) (c : C)    (costFn : (UTransform.hashOracleSpec M R KD K).Domain → ω)    (wCoins wKey : ω)    (hCoins : ∀ msg, costFn (Sum.inl msg) ≤ wCoins)    (hKeys : ∀ kd, costFn (Sum.inr kd) ≤ wKey) :    QueryCost[      (UTransform pke kdInput policy).decaps ((pk, sk), fb) c in runtime by costFn    ] ≤ wCoins + wKey := by  rw [HasQuery.UsesCostAtMost]  cases hdec : pke.decrypt sk c with  | none =>    exact HasQuery.usesCostAtMost_of_usesCostExactly      (decaps_usesZeroQueryCost_of_decrypt_eq_none        (runtime := runtime) (pke := pke) (kdInput := kdInput) (policy := policy)        (pk := pk) (sk := sk) (fb := fb) (c := c) (costFn := costFn) hdec)      zero_le  | some msg =>    letI := (runtime.withAddCost costFn).toHasQuery    simp only [HasQuery.Program.withAddCost, UTransform, FujisakiOkamoto.scheme, hdec]    refine AddWriterT.pathwiseCostAtMost_bind (w₁ := wCoins) (w₂ := wKey) ?_ ?_    · exact HasQuery.usesCostAtMost_query_of_le        (runtime := runtime) (costFn := costFn) (t := Sum.inl msg) (b := wCoins) (hCoins msg)    · intro r      split      · rw [bind_pure_comp]        exact AddWriterT.pathwiseCostAtMost_map some          (HasQuery.usesCostAtMost_query_of_le            (runtime := runtime) (costFn := costFn)            (t := Sum.inr (kdInput msg c)) (b := wKey) (hKeys (kdInput msg c)))      · exact AddWriterT.pathwiseCostAtMost_mono          (AddWriterT.pathwiseCostAtMost_pure (m := m) (policy.onReject fb c : Option K)) zero_le

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/CryptoFoundations/FujisakiOkamoto/UTransform.lean:342-379

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