### Abstract

We re-examine the reduction of Maurer and Wolf of the
Discrete Logarithm problem to the Diffie--Hellman
problem.
We give a precise estimate for the number of operations required in
the reduction and use this to estimate the exact security of the
elliptic curve variant of the Diffie--Hellman protocol for various
elliptic curves defined in standards.

Translated title of the contribution | The equivalence between the DHP and DLP for elliptic curves used in practical applications |
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Original language | English |

Pages (from-to) | 50 - 72 |

Number of pages | 22 |

Journal | LMS Journal of Computation and Mathematics |

Volume | 7 |

Publication status | Published - Mar 2004 |

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## Cite this

Smart, NP., Vercauteren, F., & Muzereau, A. (2004). The equivalence between the DHP and DLP for elliptic curves used in practical applications.

*LMS Journal of Computation and Mathematics*,*7*, 50 - 72. http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=2000075