Encryption and decryption using elliptic curves for public key cryptosystems

Cryptography is the art of science and is a centuries old technique used to convert an intelligible message into non-intelligible message so that when it is transmitted from source to destination in any form, it can't be understood by the unintended persons. Hence, the message is secured from eavesdropping, hacking and deliberate modifications done by the unauthorized persons. The researchers have developed a number of techniques over the decades for protecting the message during transmission over the public networks but, because of the rapid technological growth, the increase of processors' computing power, availability of inexpensive large memory and advancements in VLSI chips, today, these cryptographic methods are not able to sustain. To protect the messages with the existing cryptographic techniques, there is a need to use large number of bits in the keys resulting in slower encryption and decryption speeds and increase in the amount of memory required for computations. In this paper, we discuss a new approach for encryption and decryption using elliptic curves that results in faster encryption and decryption speeds and minimizing the amount of memory required for computations at the same time offering the equal level of security as that of provided by popular public key cryptographic methods.