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Short Exponent Diffie-Hellman Problems

  • Takeshi Koshiba
  • Kaoru Kurosawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2947)

Abstract

In this paper, we study short exponent Diffie-Hellman problems, where significantly many lower bits are zeros in the exponent. We first prove that the decisional version of this problem is as hard as two well known hard problems, the standard decisional Diffie-Hellman problem (DDH) and the short exponent discrete logarithm problem. It implies that we can improve the efficiency of ElGamal scheme and Cramer-Shoup scheme under the two widely accepted assumptions. We next derive a similar result for the computational version of this problem.

Keywords

Discrete Logarithm Modular Exponentiation Probabilistic Polynomial Time Choose Ciphertext Attack Choose Plaintext Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Takeshi Koshiba
    • 1
    • 2
  • Kaoru Kurosawa
    • 3
  1. 1.Secure Computing Lab.Fujitsu Laboratories Ltd. 
  2. 2.ERATO Quantum Computation and Information ProjectJapan Science and Technology AgencyKyotoJapan
  3. 3.Department of Computer and Information SciencesIbaraki UniversityHitachi, IbarakiJapan

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