Improved Lower Bound on DHP: Towards the Equivalence of DHP and DLP for Important Elliptic Curves Used for Implementation (1610.01354v3)

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.