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On the bit security of the Diffie-Hellman key

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Let p be a finite field of p elements, where p is prime. The bit security of the Diffie-Hellman function over subgroups of * p and of an elliptic curve over p , is considered. It is shown that if the Decision Diffie-Hellman problem is hard in these groups, then the two most significant bits of the Diffie-Hellman function are secure. Under the weaker assumption of the computational (rather than decisional) hardness of the Diffie-Hellman problems, only about (log p)1/2 bits are known to be secure.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, M5S 3G4, Canada

    Ian F. Blake

  2. Department of Mathematics, University of Crete, 71409, Heraklion, Crete, Greece

    Theo Garefalakis

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

    Igor E. Shparlinski

Authors
  1. Ian F. Blake
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  2. Theo Garefalakis
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  3. Igor E. Shparlinski
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Correspondence to Igor E. Shparlinski.

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Blake, I., Garefalakis, T. & Shparlinski, I. On the bit security of the Diffie-Hellman key. AAECC 16, 397–404 (2006). https://doi.org/10.1007/s00200-005-0184-x

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  • DOI: https://doi.org/10.1007/s00200-005-0184-x

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