In this paper, we add the information of level structure to supersingular elliptic curves and
study these objects with the motivation of isogeny-based cryptography. Supersingular elliptic …

In this paper, we study several related computational problems for supersingular elliptic
curves, their isogeny graphs, and their endomorphism rings. We prove reductions between …

We advance previous studies on decomposed Richelot isogenies (Katsura--Takashima
(ANTS 2020) and Katsura (ArXiv 2021)) which are useful for analysing superspecial …

We investigate the isogeny graphs of supersingular elliptic curves over $\mathbb {F} _ {p^ 2}
$ equipped with a $ d $-isogeny to their Galois conjugate. These curves are interesting …

Isogenies are widely used in elliptic curves. Since Moody and Shumow [20] proposed
isogenies on Edwards and Huff curves analogues of Vélu's formulas, they have pointed out …

Computing endomorphism rings of supersingular elliptic curves is an important problem in
computational number theory, and it is also closely connected to the security of some of the …

Loops and cycles play an important role in computing endomorphism rings of supersingular
elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽 …

In this short note, we briefly describe cryptosystems that are believed to be quantum-
resistant and focus on isogeny-based cryptosystems. Recent SIDH (Supersingular Isogeny …

Constructing a supersingular elliptic curve whose endomorphism ring is isomorphic to a
given quaternion maximal order (one direction of the Deuring correspondence) is known to …

Isogenies between elliptic curves play a very important role in elliptic curve related
cryptosystems and cryptanalysis. It is widely known that different models of elliptic curves …