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Chapter and Conference Paper
Isogeny Volcanoes of Elliptic Curves and Sylow Subgroups
Given an ordinary elliptic curve over a finite field located in the floor of its volcano of \( \ell \) -isogenies, we ...
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Chapter and Conference Paper
Isogeny Volcanoes and the SEA Algorithm
Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete description of the struct...
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Chapter and Conference Paper
Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy
The use of elliptic curves in cryptography relies on the ability to count the number of points on a given curve. Before 1999, the SEA algorithm was the only efficient method known for random curves. Then Satoh...