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arXiv · 1610.01354

Improved Lower Bound on DHP: Towards the Equivalence of DHP and DLP for Important Elliptic Curves Used for Implementation

Prabhat Kushwaha
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Abstract

In 2004, Muzereau et al. showed how to use a reduction algorithm of the discrete logarithm problem to Diffie-Hellman problem in order to estimate lower bound on Diffie-Hellman problem on elliptic curves. They presented their estimates for various elliptic curves that are used in practical applications. In this paper, we show that a much tighter lower bound for Diffie-Hellman problem on those curves can be achieved, if one uses the multiplicative group of a finite field as an auxiliary group. Moreover, improved lower bound estimates on Diffie-Hellman problem for various recommended curves are also given which are the tightest; thus, leading us towards the equivalence of Diffie-Hellman problem and the discrete logarithm problem for these recommended elliptic curves.

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Prabhat Kushwaha. 2016-10-05. Improved Lower Bound on DHP: Towards the Equivalence of DHP and DLP for Important Elliptic Curves Used for Implementation. https://doi.org/10.1515/jmc-2017-0053

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