The use of elliptic curves in encryption

The elliptic curve encryption algorithm was proposed as an asymmetric encryption algorithm using the point addition process defined on elliptic curves by Miller and Koblitz independently in 1985, with a method similar to the ElGammal encryption algorithm proposed by Taher ElGammal in 1984. Since the algorithm offers the equivalent security level with a shorter key than RSA, which is the first asymmetric encryption algorithm proposed by Rivest, Shamir and Adleman in 1978, it is widely used today in creating the account addresses of users in crypto money systems. In this study, firstly, elliptic curves and the algebraic basis of the encryption algorithm created on these curves are given, then the elliptic curve encryption algorithm and elliptic curve factorization algorithm are explained.