The process to convert plaintext to chippertext is called encription and the reverse is called decription. Private key method provide encription process with only one key, the messages then the messages convert into codes. The codes then decript by same key into first messages, The security of this system is lied on the key. This system is also known as symetric key cryptography. Public key crptography is done by two keys, one private key and one public key, that are related.
Public key is published so that can be used for encription process.
Private key only known by the owner and it is unique. The messages then encripted by public key into codes, the codes then decrited into first messages. The security of this methods is lied on mathematical power that makes no one knows private key by knowing public key. It is also called as asymetric key cryptography. Elliptic Curve Cryptography Logarithm Elliptic curve equation came from Weierstrass equation.