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The Hidden Number Problem in Extension Fields and Its Applications

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LATIN 2002: Theoretical Informatics (LATIN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2286))

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Abstract

We present polynomial time algorithms for certain generalizations of the hidden number problem which has played an important role in gaining understanding of the security of commonly suggested one way functions.

Namely, we consider an analogue of this problem for a certain class of polynomials over an extension of a finite field; recovering a hidden polynomial given the values of its trace at randomly selected points. Also, we give an algorithm for a variant of the problem in free finite dimensional modules. This result can be helpful for studying security of analogues of the RSA and Diffie-Hellman cryptosystems over such modules.

The hidden number problem is also related to the so called black-box field model of computation. We show that simplified versions of the above recovery problems can be used to derive positive results on the computational power of this model.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Oviedo, 33007, Oviedo, Spain

    María Isabel González Vasco

  2. Ericsson Research, 16480, Stockholm, SE, Sweden

    Mats Näslund

  3. Dept. of Computing, Macquarie University, 2109, Sydney, NSW, Australia

    Igor E. Shparlinski

Authors
  1. María Isabel González Vasco
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  2. Mats Näslund
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  3. Igor E. Shparlinski
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Editor information

Editors and Affiliations

  1. Compaq Cambridge Research Laboratory, One Cambridge Center, 02142-1612, Cambridge, MA, USA

    Sergio Rajsbaum

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González Vasco, M.I., Näslund, M., Shparlinski, I.E. (2002). The Hidden Number Problem in Extension Fields and Its Applications. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_14

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  • DOI: https://doi.org/10.1007/3-540-45995-2_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43400-9

  • Online ISBN: 978-3-540-45995-8

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