The supersingular endomorphism ring problem given one endomorphism. (arXiv:2309.11912v2 [cs.CR] UPDATED)

Given a supersingular elliptic curve E and a non-scalar endomorphism $\alpha$
of E, we prove that the endomorphism ring of E can be computed in classical
time about disc(Z[$\alpha$])^1/4 , and in quantum subexponential time, assuming
the generalised Riemann hypothesis. Previous results either had higher
complexities, or relied on heuristic assumptions. Along the way, we prove that
the Primitivisation problem can be solved in polynomial time (a problem
previously believed to be hard), and we prove that the action of …

curve disc elliptic higher non problem prove quantum results ring