Multivariate Signature Scheme Using Quadratic Forms

  • Takanori Yasuda
  • Tsuyoshi Takagi
  • Kouichi Sakurai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7932)


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.


Multivariate Public Key Cryptosystem Digital signature Rainbow Post-quantum cryptography 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Takanori Yasuda
    • 1
  • Tsuyoshi Takagi
    • 2
  • Kouichi Sakurai
    • 1
    • 3
  1. 1.Institute of Systems, Information Technologies and NanotechnologiesKyushu UniversityJapan
  2. 2.Institute of Mathematics for IndustryKyushu UniversityJapan
  3. 3.Department of InformaticsKyushu UniversityJapan

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