Question

A “reducibility criterion” proven by Ernst Kani shows that for a “diamond configuration” of these things, there is a unique reducible anti-isometry. By finding the horizontal, ascending, and descending kinds of these things, one can show that a graph of these things has a “volcano” structure, with levels of vertices below a “crater” at the top. Velu’s formulas are used to compute one of these things for a given kernel. A recent cryptosystem called CSIDH (“seaside”) relies on the difficulty of finding these things. Another system that involves walking on a graph of these things was unexpectedly broken in 2022 after making it to round 4 of NIST’s post-quantum cryptography competition. The S stands for “supersingular” and the I (15[1])stands for this word in the name of that cryptosystem, SIKE. For 15 points, name these maps that are roughly (-5[1])homomorphisms between elliptic curves. (15[1])■END■ (0[2])

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