An oriented supersingular elliptic curve is a curve which is enhanced with the information of
an endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve is …

Given a supersingular elliptic curve E and a non-scalar endomorphism $\alpha $ of E, we
prove that the endomorphism ring of E can be computed in classical time about disc (Z …

In supersingular isogeny-based cryptography, the path-finding problem reduces to the
endomorphism ring problem. Can path-finding be reduced to knowing just one …

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 …

We consider finite graphs whose vertexes are supersingular elliptic curves, possibly with
level structure, and edges are isogenies. They can be applied to the study of modular forms …

Finding problems that allow for superpolynomial quantum speedup is one of the most
important tasks in quantum computation. A key challenge is identifying problem structures …

Given x, y on an unweighted undirected graph G, the goal of the pathfinding problem is to
find an x–y path. In this work, we first construct a graph G based on welded trees and define …

Let $ p> 3$ be a prime and $ E $ be a supersingular elliptic curve defined over $\mathbb {F}
_ {p^ 2} $. Let $ c $ be a prime with $ c< 3p/16$ and $ G $ be a subgroup of $ E [c] $ of order …

Let p> 3 be a prime and E be a supersingular elliptic curve defined over F p 2. Let c be a
prime with c< 3 p/16 and G be a subgroup of E [c] of order c. The pair (E, G) is called a …

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