Prf implies uf cma
PRFScheme.prf_implies_uf_cma
Plain-language statement
Boneh-Shoup Theorem 6.2. PRF security implies UF-CMA security for the derived MAC: for any forger A, the constructed distinguisher macToPRFReduction prf A satisfies UF_CMA_Advantage(A) ≤ prfAdvantage(prf, B) + 1/|R|.
Exact Lean statement
theorem prf_implies_uf_cma [Nonempty R] [SampleableType R] [Fintype R]
(prf : PRFScheme K D R) (adversary : (prf.toMacAlg).UF_CMA_Adversary) :
(MacAlg.UF_CMA_Advantage ProbCompRuntime.probComp adversary).toReal ≤
prf.prfAdvantage (macToPRFReduction prf adversary) +
(Fintype.card R : ℝ)⁻¹Formal artifact
Lean source
theorem prf_implies_uf_cma [Nonempty R] [SampleableType R] [Fintype R] (prf : PRFScheme K D R) (adversary : (prf.toMacAlg).UF_CMA_Adversary) : (MacAlg.UF_CMA_Advantage ProbCompRuntime.probComp adversary).toReal ≤ prf.prfAdvantage (macToPRFReduction prf adversary) + (Fintype.card R : ℝ)⁻¹ := by rw [← prfRealExp_macToPRFReduction_eq_UF_CMA_Exp prf adversary] unfold prfAdvantage set a := (Pr[= true | prf.prfRealExp (macToPRFReduction prf adversary)]).toReal set b := (Pr[= true | prfIdealExp (macToPRFReduction prf adversary)]).toReal linarith [le_abs_self (a - b), prfIdealExp_macToPRFReduction_le prf adversary]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/MacFromPRF.lean:400-409
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