… the vector representation of the graph. Section 3 discusses the matrix representation of the
graph. Section 4 includes the binary methods of the elliptic scalar multiplication which are the …

… graph based on an elliptic scalar multiplication operation is defined which is called elliptic
scalar multiplication (ESM) graph. … In this section, a scalar multiplication kR on elliptic curve E …

… that the graph of small prime degree isogenies between ordinary elliptic curves achieves …
properties of these graphs and the security of the elliptic curve discrete logarithm problem. …

… Furthermore representation-theoretic methods occasionally yield results about elliptic
curves that seem inaccessible by classical methods. From my point of view, they are an …

… in this chapter: elliptic curves and modular forros being quite … elliptic curves and modular
forms in a very precise manner, concentrating specifically on results regarding the graph method…

… graphs throughout this paper, however. We show in Section 4.1 that the functional graphs
we create from elliptic curves … Their methods involved computing the number of components, …

… methods to include was based on emphasizing the analogy between operations on the
multiplicative group and operations on the elliptic curve, … directly with the elliptic logarithms. The …

… Perhaps one reason that questions about E(Q) are so difficult is that the adele methods which
are so successful with linear algebraic groups look like a mess in the case of elliptic curves…

… elliptic curves in Section 17.2 in the most efficient version known today. The p-adic methods
for elliptic and hyperelliptic curves … Section 17.3 and the method using complex multiplication …

… an application to factoring, Pollard’s p - 1 method which serves as the model against which
we compare Lenstra’s elliptic curve method of factorization. Chapter 5 begins with a simple …