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.
Exact Lean statement
theorem IND_CPA_LR_hybridGame_q_evalDist_eq_left_of_MakesAtMostQueries [Finite C] [Inhabited C]
(adversary : encAlg'.IND_CPA_adversary) (q : โ)
(hq : adversary.MakesAtMostQueries q) :
๐[encAlg'.IND_CPA_LR_hybridGame adversary q] =
๐[encAlg'.IND_CPA_LR_experiment adversary true]Formal artifact
Lean source
theorem IND_CPA_LR_hybridGame_q_evalDist_eq_left_of_MakesAtMostQueries [Finite C] [Inhabited C] (adversary : encAlg'.IND_CPA_adversary) (q : โ) (hq : adversary.MakesAtMostQueries q) : ๐[encAlg'.IND_CPA_LR_hybridGame adversary q] = ๐[encAlg'.IND_CPA_LR_experiment adversary true] := by simp only [IND_CPA_LR_hybridGame, IND_CPA_LR_experiment, evalDist_bind] congr 1 funext โจpk, _skโฉ exact IND_CPA_run'_evalDist_eq_queryImpl'_of_bounded_eq (encAlg' := encAlg') (implCounted := fun pk b realUntil => if b then encAlg'.IND_CPA_queryImpl_hybridLR_counted pk realUntil else encAlg'.IND_CPA_queryImpl_hybridLR_counted pk 0) (hsame := by intro pk b realUntil t st hcond cases t with | inl _ => cases b <;> simp [IND_CPA_queryImpl'_counted, IND_CPA_queryImpl_hybridLR_counted, IND_CPA_queryImplFromChallenge] | inr mm => have hcond' : st.2 < realUntil := by simpa using hcond cases b <;> simp only [IND_CPA_queryImpl'_counted, IND_CPA_challengeOracle'_counted, IND_CPA_queryImpl_hybridLR_counted, IND_CPA_hybridChallengeOracleLR_counted, IND_CPA_queryImplFromChallenge, QueryImpl.add_apply_inr, Bool.false_eq_true, ite_true, ite_false] <;> exact IND_CPA_countedChallengeOracle_run_eq_of_select_eq pk _ _ mm st (by simp [hcond'])) pk true q (adversary pk) q (hq pk) โ
0 (by omega)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/AsymmEncAlg/INDCPA/Oracle.lean:447-476
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