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Cryptography Based on Quadratic Forms: Complexity Considerations

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Research in Cryptology (WEWoRC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4945))

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Abstract

We study the computational problem Trafo of finding an integral equivalence transform between two given quadratic forms. This is motivated by a recent identification scheme based on this problem [10]. We prove that for indefinite forms over ℤ, its hardness is concentrated in dimensions 3 and 4. Moreover, over the field of rational numbers the complexity of Trafo is closely related to that of factoring. However, for definite forms over ℤ, as well as for forms over finite fields, the transformation problem is solvable in polynomial time.

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Author information

Authors and Affiliations

  1. Johann Wolfgang Goethe Universität Frankfurt a. M., Postfach 11 19 32; Fach 238, 60054, Frankfurt a. M., Germany

    Rupert J. Hartung

Authors
  1. Rupert J. Hartung
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Editor information

Editors and Affiliations

  1. Fakultät Medien, Bauhaus-Universität Weimar, Bauhausstr. 11, 99423, Weimar, Germany

    Stefan Lucks

  2. Horst Görtz Institute for IT Security, Ruhr-University of Bochum, Germany

    Ahmad-Reza Sadeghi

  3. Horst Görtz Institute for IT-Security, Ruhr-University Bochum, Germany

    Christopher Wolf

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Hartung, R.J. (2008). Cryptography Based on Quadratic Forms: Complexity Considerations. In: Lucks, S., Sadeghi, AR., Wolf, C. (eds) Research in Cryptology. WEWoRC 2007. Lecture Notes in Computer Science, vol 4945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88353-1_5

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  • DOI: https://doi.org/10.1007/978-3-540-88353-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88352-4

  • Online ISBN: 978-3-540-88353-1

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