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Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms

  • Ueli M. Maurer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 839)

Abstract

Let G be an arbitrary cyclic group with generator g and order |G| with known factorization. G could be the subgroup generated by g within a larger group H. Based on an assumption about the existence of smooth numbers in short intervals, we prove that breaking the Diffie-Hellman protocol for G and base g is equivalent to computing discrete logarithms in G to the base g when a certain side information string S of length 2 log |G| is given, where S depends only on |G| but not on the definition of G and appears to be of no help for computing discrete logarithms in G. If every prime factor p of |G| is such that one of a list of expressions in p, including p − 1 and p + 1, is smooth for an appropriate smoothness bound, then S can efficiently be constructed and therefore breaking the Diffie-Hellman protocol is equivalent to computing discrete logarithms.

Keywords

Elliptic Curve Elliptic Curf Prime Divisor Discrete Logarithm Hyperelliptic Curve 
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 1994

Authors and Affiliations

  • Ueli M. Maurer
    • 1
  1. 1.Institute for Theoretical Computer ScienceETH ZürichZürichSwitzerland

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