A tight parallel repetition theorem for partially simulatable interactive arguments via smooth kl-divergence

Itay Berman, Iftach Haitner, Eliad Tsfadia

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

ملخص

Hardness amplification is a central problem in the study of interactive protocols. While “natural” parallel repetition transformation is known to reduce the soundness error of some special cases of interactive arguments: three-message protocols (Bellare, Impagliazzo, and Naor [FOCS ’97]) and public-coin protocols (Håstad, Pass, Wikström, and Pietrzak [TCC ’10], Chung and Liu [TCC ’10] and Chung and Pass [TCC ’15]), it fails to do so in the general case (the above Bellare et al.; also Pietrzak and Wikström [TCC ’07]). The only known round-preserving approach that applies to all interactive arguments is Haitner’s random-terminating transformation [SICOMP ’13], who showed that the parallel repetition of the transformed protocol reduces the soundness error at a weak exponential rate: if the original m-round protocol has soundness error 1-ε, then the n-parallel repetition of its random-terminating variant has soundness error (1-ε)ε n/m4 (omitting constant factors). Håstad et al. have generalized this result to partially simulatable interactive arguments, showing that the n-fold repetition of an m-round δ-simulatable argument of soundness error 1-ε has soundness error (1-ε)ε δ2 n/m2 . When applied to random-terminating arguments, the Håstad et al. bound matches that of Haitner. In this work we prove that parallel repetition of random-terminating arguments reduces the soundness error at a much stronger exponential rate: the soundness error of the n parallel repetition is (1-ε)n/m, only an m factor from the optimal rate of (1-ε)n achievable in public-coin and three-message arguments. The result generalizes to δ-simulatable arguments, for which we prove a bound of (1-ε)δ n/m. This is achieved by presenting a tight bound on a relaxed variant of the KL-divergence between the distribution induced by our reduction and its ideal variant, a result whose scope extends beyond parallel repetition proofs. We prove the tightness of the above bound for random-terminating arguments, by presenting a matching protocol.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيفAdvances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings
المحررونDaniele Micciancio, Thomas Ristenpart
الصفحات544-573
عدد الصفحات30
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2020
الحدث40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, الولايات المتّحدة
المدة: ١٧ أغسطس ٢٠٢٠٢١ أغسطس ٢٠٢٠

سلسلة المنشورات

الاسمLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
مستوى الصوت12172 LNCS

!!Conference

!!Conference40th Annual International Cryptology Conference, CRYPTO 2020
الدولة/الإقليمالولايات المتّحدة
المدينةSanta Barbara
المدة١٧/٠٨/٢٠٢١/٠٨/٢٠

All Science Journal Classification (ASJC) codes

  • !!Theoretical Computer Science
  • !!General Computer Science

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