A qualitative study of families of Edwards Curves and their applications in cryptography / Nurul Azwa Kamaruddin and Nurul Ain Mustakim

Cryptography is the science of hiding information and its applications include ATM cards, computer passwords and electronic commerce in this modern world. There are many types of scheme used in encrypting a message so that it can be sent to a particular receiver from a particular sender without the third party knowing the content of the message known as cryptosystem. For example, RSA, DES (Data Encryption Standard), Symmetric Key Cryptography. Among those cryptosystems, there are three types of public key cryptographic systems that are currently considered both secure and efficient, classified according to the mathematical problems upon which they are based: the Integer Factorization Systems (of which the RSA algorithm is the most well known example), the Discrete logarithm Systems (such as the US Government’s Digital Signature Algorithm) and the Elliptic Curve Cryptosystem (ECC). Many previous researches focused on elliptic curve and its applications in mobile communication. The purpose of the qualitative study is to explore and develop basic understanding of the properties of the families of Edwards curves, one of the special forms of elliptic curves, and their applications in cryptography, using grounded theory approach, in which the data are hand-analyzed, coded and grouped into themes under study. It is important to distinguish the properties of each member in the families of Edward curves as to encourage further studies and may be useful in wireless and mobile communication.