Project-declaredLean 4.32.0 · mathlib@81a5d257

Tv Dist simulate Q with Caching with Programming le prob Event bad

OracleComp.ProgramLogic.Relational.tvDist_simulateQ_withCaching_withProgramming_le_probEvent_bad'

program verification separation logic cryptography programming oracle

Plain-language statement

Heterogeneous identical-until-bad bridge (output marginal). The TV-distance between the output marginal of so.withCaching and the output marginal of so.withProgramming policy is bounded by the probability that the bad flag of withProgramming policy fires during the run, for any base implementation so valued in OracleComp spec' with spec' u...

Exact Lean statement

theorem tvDist_simulateQ_withCaching_withProgramming_le_probEvent_bad'
    (so : QueryImpl spec (OracleComp spec')) (policy : ProgrammingPolicy spec)
    (oa : OracleComp spec α) (cache : spec.QueryCache) :
    tvDist
        ((simulateQ so.withCaching oa).run' cache)
        ((simulateQ (so.withProgramming policy) oa).run' (cache, false))
      ≤ Pr[fun z : α × spec.QueryCache × Bool => z.2.2 = true |
          (simulateQ (so.withProgramming policy) oa).run (cache, false)].toReal

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem tvDist_simulateQ_withCaching_withProgramming_le_probEvent_bad'    (so : QueryImpl spec (OracleComp spec')) (policy : ProgrammingPolicy spec)    (oa : OracleComp spec α) (cache : spec.QueryCache) :    tvDist        ((simulateQ so.withCaching oa).run' cache)        ((simulateQ (so.withProgramming policy) oa).run' (cache, false))      ≤ Pr[fun z : α × spec.QueryCache × Bool => z.2.2 = true |          (simulateQ (so.withProgramming policy) oa).run (cache, false)].toReal := by  classical  set sim₁ := (simulateQ (so.withProgramming policy) oa).run (cache, false) with hs1  set sim₂ := (simulateQ (so.withCachingTrackingPolicy policy) oa).run (cache, false) with hs2  have h_joint :      tvDist sim₁ sim₂ ≤        Pr[fun z : α × spec.QueryCache × Bool => z.2.2 = true | sim₁].toReal :=    tvDist_withProgramming_withCachingTrackingPolicy_run_le_probEvent_bad' so policy oa cache  have h_map :      tvDist ((simulateQ (so.withProgramming policy) oa).run' (cache, false))          ((simulateQ (so.withCachingTrackingPolicy policy) oa).run' (cache, false))        ≤ tvDist sim₁ sim₂ := by    rw [StateT.run']    exact tvDist_map_le (m := OracleComp spec') (α := α × spec.QueryCache × Bool) (β := α)      Prod.fst sim₁ sim₂  have h_proj :      (simulateQ (so.withCachingTrackingPolicy policy) oa).run' (cache, false) =        (simulateQ so.withCaching oa).run' cache :=    withCachingTrackingPolicy_run'_eq' so policy oa cache false  rw [tvDist_comm, ← h_proj]  exact le_trans h_map h_joint

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/ProgramLogic/Relational/ProgrammingOracle.lean:316-343

Reuse this declaration

Bring the exact result into your workflow

The import identifies the source module. Your project still needs the pinned package dependency shown on this page.

What this badge means

This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.

Continue in this project

Related declarations

Project-declaredLean 4.32.0

Expected Cost Nat eq sum tail probs of pathwise Cost At Most

AddWriterT.expectedCostNat_eq_sum_tail_probs_of_pathwiseCostAtMost

Plain-language statement

Finite tail-sum formula for natural-valued writer cost under a pathwise upper bound. If every execution path of oa incurs cost at most n, then the tail probabilities vanish above n, so the infinite tail sum truncates to Finset.range n.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record

Project-declaredLean 4.32.0

IND CPA advantage to Real le sum step signed Advantage Real abs

AsymmEncAlg.IND_CPA_advantage_toReal_le_sum_step_signedAdvantageReal_abs

Plain-language statement

Planned generic one-time-to-many-time lift: bounded multi-query IND-CPA advantage is at most the sum of the extracted one-time signed advantages over the first q fresh LR queries.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record

Project-declaredLean 4.32.0

IND CPA LR hybrid Game q eval Dist eq left of Makes At Most Queries

AsymmEncAlg.IND_CPA_LR_hybridGame_q_evalDist_eq_left_of_MakesAtMostQueries

Plain-language statement

If an adversary makes at most q fresh LR queries, then the leftUntil = q LR-hybrid is the all-left endpoint game.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record