Computing the trace of an endomorphism of a supersingular elliptic curve

We provide an explicit algorithm for computing the trace of an endomorphism of an elliptic curve which is given by a chain of small-degree isogenies. We analyze its complexity, determining that if the length of the chain, the degree of the isogenies, and the log of the field-size are all O(n), the trace of the endomorphism can be computed in O(n⁶) bit operations. This makes explicit a theorem of Kohel which states that such a polynomial time algorithm exists. The given procedure is based on Schoof's point-counting algorithm.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2021

Author dc:creator

• Wills, Michael Thomas

Chairs dc:contributor.committeechair

• Matthews, Gretchen L.
• Morrison, Travis William

Committee members dc:contributor.committeemember

• Shimozono, Mark M.
• Orr, Daniel D.

• elliptic curves
• endomorphism rings
• arithmetic geometry
• supersingular elliptic curves

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:31073

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/103821