Computing Orientations from the Endomorphism Ring of Supersingular Curves and Applications

ePrint Report: Computing Orientations from the Endomorphism Ring of Supersingular Curves and Applications

Jonathan Komada Eriksen, Antonin Leroux

This work introduces several algorithms related to the computation of orientations in endomorphism rings of supersingular elliptic curves. This problem boils down to representing integers by ternary quadratic forms, and it is at the heart of several results regarding the security of oriented-curves in isogeny-based cryptography.
Our main contribution is to show that there exists efficient algorithms that can solve this problem …

algorithms applications computation computing down elliptic eprint report forms problem report ring rings work