Public‐Key Cryptosystems

Elliptic‐curve cryptography (ECC) is a high performance alternative approach to RSA for asymmetric algorithms. ECC ensures fast encryption speed with a high complexity of decryption to ensure data confidentiality and authentication. Shorter ECC encryption keys use fewer memory and CPU resources. The elliptic curve cryptography uses elliptic curves over finite fields. This means that the points on the curve are limited to integer coordinates within the field. There are two types of fields to build ECs: prime fields, and extension fields. Breaking an EC cryptosystem is equivalent to solving the computational problem known as elliptic curve discrete logarithm problem. The elliptic curve‐based algorithms used in cryptosystems are categorized as key‐agreement, message signature, and message encryption algorithms. First, the common features are presented, then how ECs is used for each category of algorithms is addressed.