Any language in IP has a divertible ZKIP

Toshiya Itoh, Kouichi Sakurai, Hiroki Shizuya

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

A notion of “divertible” zero-knowledge interactive proof systems was introduced by Okamoto and Ohta, and they showed that for any commutative random self-reducible relation, there exists a divertible (perfect) zero-knowledge interactive proof system of possession of information. In addition, Burmester and Desmedt proved that for any language L ∈ NP, there exists a divertible zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist. In this paper, we classify the notion of divertible into three types, i.e., perfectly divertible, almost perfectly divertible, and computationally divertible, and investigate which complexity class of languages has a perfectly (almost perfectly) (computationally) divertible zero-knowledge interactive proof system. The main results in this paper are: (1) there exists a perfectly divertible perfect zero-knowledge interactive proof system for graph non-isomorphism (GNI) without any unproven assumption; and (2) for any language L having an interactive proof system, there exists a computationally divertible computational zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist.

Original languageEnglish
Title of host publicationAdvances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings
EditorsHideki Imai, Tsutomu Matsumoto, Ronald L. Rivest
PublisherSpringer Verlag
Pages382-396
Number of pages15
ISBN (Print)9783540573326
Publication statusPublished - Jan 1 1993
Event1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991 - Fujiyoshida, Japan
Duration: Nov 11 1991Nov 14 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume739 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991
CountryJapan
CityFujiyoshida
Period11/11/9111/14/91

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Interactive Proof Systems
Zero-knowledge Proof
Cryptography
Homomorphisms
Encryption
Complexity Classes
Language
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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Itoh, T., Sakurai, K., & Shizuya, H. (1993). Any language in IP has a divertible ZKIP. In H. Imai, T. Matsumoto, & R. L. Rivest (Eds.), Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings (pp. 382-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 739 LNCS). Springer Verlag.

Any language in IP has a divertible ZKIP. / Itoh, Toshiya; Sakurai, Kouichi; Shizuya, Hiroki.

Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings. ed. / Hideki Imai; Tsutomu Matsumoto; Ronald L. Rivest. Springer Verlag, 1993. p. 382-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 739 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Itoh, T, Sakurai, K & Shizuya, H 1993, Any language in IP has a divertible ZKIP. in H Imai, T Matsumoto & RL Rivest (eds), Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 739 LNCS, Springer Verlag, pp. 382-396, 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991, Fujiyoshida, Japan, 11/11/91.
Itoh T, Sakurai K, Shizuya H. Any language in IP has a divertible ZKIP. In Imai H, Matsumoto T, Rivest RL, editors, Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings. Springer Verlag. 1993. p. 382-396. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Itoh, Toshiya ; Sakurai, Kouichi ; Shizuya, Hiroki. / Any language in IP has a divertible ZKIP. Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings. editor / Hideki Imai ; Tsutomu Matsumoto ; Ronald L. Rivest. Springer Verlag, 1993. pp. 382-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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