Paper 2020/262

A Note on the Ending Elliptic Curve in SIDH

Christopher Leonardi

Abstract

It has been suspected that in supersingular isogeny-based cryptosystems the two ending elliptic curves computed by the participants are exactly equal. Resolving this open problem has not been pressing because the elliptic curves are known to be isomorphic, and therefore share a $j$-invariant which can be used as a shared secret. However, this is still an interesting independent problem as other values of the elliptic curves may be valuable as shared information as well. This note answers this open problem in the affirmative.