A security analysis of uniformly-layered rainbow: Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm

Takanori Yasuda, Kouichi Sakurai

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

3 Citations (Scopus)

Abstract

In 1984, Ong, Schnorr and Shamir proposed an efficient signature scheme (OSS signature scheme) using a bivariate quadratic equation. Its security was believed to be based on the difficulty of integer factorization. However, an efficient attack without integer factorization was subsequently found. In 2008, Hashimoto and Sakurai proposed an extended scheme (HS scheme), based on OSS signature scheme that used multivariate and non-commutative ring. HS scheme uses a composite number as a modulus in the same manner as OSS signature scheme. In this paper, we redefine HS scheme in such a way that it deals with not only integers modulo a composite number, but also elements of a finite field. In the case of a finite field, it becomes a scheme in the multivariate public key cryptosystem. In fact, its public key is constructed by a version of Rainbow in which all the components in the parameter are equal. (We call such a Rainbow a uniformly-layered Rainbow.) In particular, our scheme is a candidate for post-quantum cryptography. If a non-commutative ring used in the proposed scheme is chosen by the group ring associated to dihedral group, the speed of the signature generation can be accelerated by about 50% in comparison with the corresponding Rainbow. We analyze the security of the extended HS scheme against some attacks and conclude that if its base field is GF(256), then the dimension of a non-commutative ring must be more than 10 in order to be secure.

Original languageEnglish
Title of host publicationPost-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings
Pages275-294
Number of pages20
DOIs
Publication statusPublished - Dec 12 2011
Event4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011 - Taipei, Taiwan, Province of China
Duration: Nov 29 2011Dec 2 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7071 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011
CountryTaiwan, Province of China
CityTaipei
Period11/29/1112/2/11

Fingerprint

Security Analysis
Factorization
Signature
Paradigm
Quantum cryptography
Composite materials
Non-commutative Rings
Cryptography
Signature Scheme
Integer Factorization
Composite number
Galois field
Attack
Quantum Cryptography
Public-key Cryptosystem
Quadratic equation
Dihedral group
Group Ring
Public key
Modulo

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, T., & Sakurai, K. (2011). A security analysis of uniformly-layered rainbow: Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm. In Post-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings (pp. 275-294). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7071 LNCS). https://doi.org/10.1007/978-3-642-25405-5_18

A security analysis of uniformly-layered rainbow : Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm. / Yasuda, Takanori; Sakurai, Kouichi.

Post-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings. 2011. p. 275-294 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7071 LNCS).

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

Yasuda, T & Sakurai, K 2011, A security analysis of uniformly-layered rainbow: Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm. in Post-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7071 LNCS, pp. 275-294, 4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011, Taipei, Taiwan, Province of China, 11/29/11. https://doi.org/10.1007/978-3-642-25405-5_18
Yasuda T, Sakurai K. A security analysis of uniformly-layered rainbow: Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm. In Post-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings. 2011. p. 275-294. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25405-5_18
Yasuda, Takanori ; Sakurai, Kouichi. / A security analysis of uniformly-layered rainbow : Revisiting Sato-Araki's non-commutative approach to Ong-Schnorr-Shamir signature towards postquantum paradigm. Post-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings. 2011. pp. 275-294 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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