In recent years, isogeny-based cryptosystems have captured the attention of the math/crypto community for their potential resistance to quantum attacks. In this context, the most promising protocols have as central objects supersingular elliptic curves defined over a finite field, and their security is therefore based on the mathematical problem of calculating an isogeny between two supersingular elliptic curves $E$ and $E'.$ It has been shown that this problem can be reduced to the calculation of the endomorphism rings of $E$ and $E'.$ In this seminar, after reviewing the mathematical and cryptographic context, we will then present an improved algorithm for computing the endomorphism ring of a supersingular elliptic curve over a finite field.
Computing the endomorphism ring of a supersingular elliptic curve*
Annamaria Iezzi, Università degli Studi di Napoli Federico IIAuthors: Jenny G. Fuselier, Annamaria Iezzi, Mark Kozek, Travis Morrison, Changningphaabi Namoijam.
2022 AWM Research Symposium
Rethinking Number Theory