Elliptic-Curve Cryptography

Abstract

Elliptic-curve cryptography (ECC) represents a public-key cryptography approach. It is based on the algebraic structure of elliptic curves over finite fields. ECC can be used in cryptography applications and primitives, such as key agreement, digital signature, and pseudo-random generators. It can also be used for operations such as encryption through a combination between key agreements with a symmetric encryption scheme. Some other interesting usages can be seen in several types of integer factorization algorithms that are based on elliptic curves (EC), with applications in cryptography, such as Lenstra Elliptic-Curve Factorization (L-ECC) [1]. Elliptic curves appeared for the first time in Diophantus’ works [3], a subject that has remained close to Diophantine geometry [2].