New answers tagged discrete-logarithm
2
The question is referring to Nigel P. Smart's The Discrete Logarithm Problem on Elliptic Curves of Trace One, in Journal of Cryptology (1999) (earlier version). Quoting the intro:
(…) we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice, the method ...
8
Let's call the problem Square Diffie-Hellman (SDH).
SDH is at least as hard as CDH in groups of known order and the reduction goes as follows.$^*$ Given an adversary $\mathsf{A}$ that breaks SDH, our goal is to construct an adversary $\mathsf{A}'$ that breaks CDH. Given the CDH challenge $(g,g^x,g^y)$, $\mathsf{A}'$ runs $\mathsf{A}$ thrice -- first on $(g,g^...
6
This problem is equivalent to the CDH problem:
Here is how to solve CDH given an Oracle that solves this problem:
Given $g, g^x$, we can compute $g^{x^{-1}}$ (which is equivalent to the CDH problem) by doing the following:
Call the Oracle with $g, g^x$; the Oracle gives us a pair $g^{y}, xy$
We compute $(g^{y})^{(xy)^{-1}} = g^{x^{-1}}$, hence showing one ...
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