Stream Ciphers Based on the Elliptic Curves

In the recent years the popularity of stream ciphers is increased many fold. Since elliptic curve is replacing RSA in most of the cryptosystems for applications such as key exchange, an encryption system based on elliptic curves has great significance. The heart of a stream cipher is a pseudorandom bit generator (PRBG). In this paper, comparison of three different versions of PRBGs based on elliptic curves defined over prime fields is presented. Comparison of the three algorithms in terms of periodicity and time complexity is done and the versions most suitable for software and hardware implementations are identified. The software implementations of PRBG are carried out using the Mathematica software.