On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves. (arXiv:2210.01160v1 [math.NT])

We show how the Weil pairing can be used to evaluate the assigned characters
of an imaginary quadratic order $\mathcal{O}$ in an unknown ideal class
$[\mathfrak{a}] \in \mathrm{Cl}(\mathcal{O})$ that connects two given
$\mathcal{O}$-oriented elliptic curves $(E, \iota)$ and $(E', \iota') =
[\mathfrak{a}](E, \iota)$. When specialized to ordinary elliptic curves over
finite fields, our method is conceptually simpler and often somewhat faster
than a recent approach due to Castryck, Sot\'akov\'a and Vercauteren, who rely
on the Tate pairing instead. The main …

actions class diffie elliptic hellman math problem