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

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルPost-Quantum Cryptography - 4th International Workshop, PQCrypto 2011, Proceedings
ページ275-294
ページ数20
DOI
出版ステータス出版済み - 12 12 2011
イベント4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011 - Taipei, 台湾省、中華民国
継続期間: 11 29 201112 2 2011

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7071 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011
国/地域台湾省、中華民国
CityTaipei
Period11/29/1112/2/11

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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