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Lecture Notes in Computer Science
In this paper, we study several related computational problems for supersingular elliptic curves, their isogeny graphs, and their endomorphism rings. We prove reductions between the problem of path finding in the -isogeny graph, computing maximal orders isomorphic to the endomorphism ring of a supersingular elliptic curve, and computing the endomorphism ring itself. We also give constructive versions of Deuring's correspondence, which associates to a maximal order in a certain quaterniondoi:10.1007/978-3-319-78372-7_11 fatcat:wvs4ee46hbak3plxmpmmlnqsmm