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Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equations

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Information Security and Cryptology (Inscrypt 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7763))

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Abstract

Let X = (x 1,..,x n ) and Y = (y 1,...,y m ) be a pair of corresponding plaintext and ciphertext for a cryptosystem. We define an embedded surface of this cryptosystem as any polynomial equation:

$$ E(X, Y) = E(x_1,..,x_n,y_1,...,y_m)=0, $$

which is satisfied by all such pairs. In this paper, we present a new attack on the multivariate public key cryptosystems from Diophantine equations developed by Gao and Heindl by using the embedded surfaces associated to this family of multivariate cryptosystems.

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Author information

Authors and Affiliations

  1. Chongqing University, China

    Jintai Ding

  2. University of Cincinnati, USA

    Jintai Ding & Ai Ren

  3. South China University of Technology, China

    Chengdong Tao

Authors
  1. Jintai Ding
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  2. Ai Ren
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  3. Chengdong Tao
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Editor information

Editors and Affiliations

  1. Department of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski

  2. Computer Science Department, Columbia University and Google Inc., Amsterdam Avenue 1214, 10027, New York, NY, USA

    Moti Yung

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Ding, J., Ren, A., Tao, C. (2013). Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equations. In: Kutyłowski, M., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2012. Lecture Notes in Computer Science, vol 7763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38519-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-38519-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38518-6

  • Online ISBN: 978-3-642-38519-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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