Multivariate signature scheme using quadratic forms

Takanori Yasuda, Tsuyoshi Takagi, Kouichi Sakurai

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

9 Citations (Scopus)

Abstract

Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. MPKC has an advantage in that its encryption and decryption are relatively efficient. In this paper, we propose a multivariate signature scheme using quadratic forms. For a finite dimensional vector space V, it is known that there are exactly two equivalence classes of non-degenerate quadratic forms over V. We utilize the method to transform any non-degenerate quadratic form into the normal form of either of the two equivalence classes in order to construct a new signature scheme in MPKC. The signature generation of our scheme is between eight and nine times more efficient more than the multivariate signature scheme Rainbow at the level of 88-bit security. We show that the public keys of our scheme can not be represented by the public keys of other MPKC signature schemes and this means our scheme is immune to many attacks that depend on the form of the central map used by these schemes.

Original languageEnglish
Title of host publicationPost-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings
Pages243-258
Number of pages16
DOIs
Publication statusPublished - Sep 26 2013
Event5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013 - Limoges, France
Duration: Jun 4 2013Jun 7 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7932 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013
CountryFrance
CityLimoges
Period6/4/136/7/13

Fingerprint

Signature Scheme
Quadratic form
Cryptography
Public-key Cryptosystem
Equivalence classes
Public key
Equivalence class
Quantum cryptography
Quantum Cryptography
Vector spaces
Normal Form
Encryption
Vector space
Signature
Attack
Transform

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, T., Takagi, T., & Sakurai, K. (2013). Multivariate signature scheme using quadratic forms. In Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings (pp. 243-258). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7932 LNCS). https://doi.org/10.1007/978-3-642-38616-9_17

Multivariate signature scheme using quadratic forms. / Yasuda, Takanori; Takagi, Tsuyoshi; Sakurai, Kouichi.

Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings. 2013. p. 243-258 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7932 LNCS).

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

Yasuda, T, Takagi, T & Sakurai, K 2013, Multivariate signature scheme using quadratic forms. in Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7932 LNCS, pp. 243-258, 5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013, Limoges, France, 6/4/13. https://doi.org/10.1007/978-3-642-38616-9_17
Yasuda T, Takagi T, Sakurai K. Multivariate signature scheme using quadratic forms. In Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings. 2013. p. 243-258. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-38616-9_17
Yasuda, Takanori ; Takagi, Tsuyoshi ; Sakurai, Kouichi. / Multivariate signature scheme using quadratic forms. Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings. 2013. pp. 243-258 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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