Presented by Luca de Feo at the [[The Isogeny Club]]:
(See recent paper, "Dlog is Practically as Hard (or Easy) as DH – Solving Dlogs via DH Oracles on EC Standards", May/Schneider, https://eprint.iacr.org/2023/539.pdf )
Let SCDH oracle: $h \longrightarrow h^z$
Compare to CDH oracle (which is stronger): $g, g^a, g^b \longrightarrow g^{ab}$
GAIP = Group Action Inverse Problem (?)
If you can solve GAIP then you can solve CSIDH-CDH.
In the other direction, if you can solve CSIDH-CDH, then you can solve GAIP *using a quantum computer*. ([[Shors algoritme]] is an essential part of the reduction.)
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