The supersingular endomorphism ring problem given one endomorphism

ePrint Report: The supersingular endomorphism ring problem given one endomorphism

Arthur Herlédan Le Merdy, Benjamin Wesolowski

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 $\text{disc}(\mathbb{Z}[\alpha])^{1/4}$ , 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 …

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