Reducing the key size of rainbow using non-commutative rings

Takanori Yasuda, Kouichi Sakurai, Tsuyoshi Takagi

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

10 Citations (Scopus)

Abstract

Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. Rainbow is a digital signature scheme in MPKC, whose encryption and decryption are relatively efficient. However, the security of MPKC depends on the difficulty in solving a system of multivariate polynomials, and the key length of MPKC becomes substantially large compared with that of RSA cryptosystems for the same level of security. The size of the public key in MPKC has been reduced in previous research, but to the best of our knowledge, there are no algorithms to reduce the size of a private key . In this paper, we propose NC-Rainbow, a variation of Rainbow using non-commutative rings and we describe the ability of the proposed scheme to reduce the size of a private key in comparison with the ordinary Rainbow while maintaining the same level of security. In particular, using the proposed NC-Rainbow, the size of a private key is reduced by about 75% at the 80 bit security level. Moreover, the speed of signature generation is accelerated by about 34% at the 80 bit security level.

Original languageEnglish
Title of host publicationTopics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings
Pages68-83
Number of pages16
DOIs
Publication statusPublished - Mar 8 2012
Event12th Cryptographers' Track at the RSA Conference, CT-RSA 2012 - San Francisco, CA, United States
Duration: Feb 27 2012Mar 2 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7178 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th Cryptographers' Track at the RSA Conference, CT-RSA 2012
CountryUnited States
CitySan Francisco, CA
Period2/27/123/2/12

Fingerprint

Non-commutative Rings
Public-key Cryptosystem
Cryptography
RSA Cryptosystem
Quantum Cryptography
Digital Signature
Multivariate Polynomials
Public key
Signature Scheme
Quantum cryptography
Encryption
Electronic document identification systems
Signature
Polynomials

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, T., Sakurai, K., & Takagi, T. (2012). Reducing the key size of rainbow using non-commutative rings. In Topics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings (pp. 68-83). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7178 LNCS). https://doi.org/10.1007/978-3-642-27954-6_5

Reducing the key size of rainbow using non-commutative rings. / Yasuda, Takanori; Sakurai, Kouichi; Takagi, Tsuyoshi.

Topics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings. 2012. p. 68-83 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7178 LNCS).

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

Yasuda, T, Sakurai, K & Takagi, T 2012, Reducing the key size of rainbow using non-commutative rings. in Topics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7178 LNCS, pp. 68-83, 12th Cryptographers' Track at the RSA Conference, CT-RSA 2012, San Francisco, CA, United States, 2/27/12. https://doi.org/10.1007/978-3-642-27954-6_5
Yasuda T, Sakurai K, Takagi T. Reducing the key size of rainbow using non-commutative rings. In Topics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings. 2012. p. 68-83. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-27954-6_5
Yasuda, Takanori ; Sakurai, Kouichi ; Takagi, Tsuyoshi. / Reducing the key size of rainbow using non-commutative rings. Topics in Cryptology, CT-RSA 2012 - The Cryptographers' Track at the RSA Conference 2012, Proceedings. 2012. pp. 68-83 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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