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Multivariate Signature Scheme Using Quadratic Forms

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Book cover Post-Quantum Cryptography (PQCrypto 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7932))

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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.

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Author information

Authors and Affiliations

  1. Institute of Systems, Information Technologies and Nanotechnologies, Kyushu University, Japan

    Takanori Yasuda & Kouichi Sakurai

  2. Institute of Mathematics for Industry, Kyushu University, Japan

    Tsuyoshi Takagi

  3. Department of Informatics, Kyushu University, Japan

    Kouichi Sakurai

Authors
  1. Takanori Yasuda
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  2. Tsuyoshi Takagi
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  3. Kouichi Sakurai
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Editor information

Editors and Affiliations

  1. XLIM Laboratory, Department DMI, Université de Limoges, 123, Avenue Albert Thomas, 87000, Limoges, France

    Philippe Gaborit

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Yasuda, T., Takagi, T., Sakurai, K. (2013). Multivariate Signature Scheme Using Quadratic Forms. In: Gaborit, P. (eds) Post-Quantum Cryptography. PQCrypto 2013. Lecture Notes in Computer Science, vol 7932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38616-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-38616-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38615-2

  • Online ISBN: 978-3-642-38616-9

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