Implementation and analysis of stream ciphers based on the elliptic curves
In this paper, implementation and analysis of three different versions of pseudorandom bit generators (PRBG) based on elliptic curves over prime and binary fields is presented. Implementations are carried out so that the algorithms could be compared in terms of time complexity and sequences could be compared in terms of periodicity, since the periodicity of all the generated streams are not available in literature. Based on the results of implementation and analysis, the pseudorandom bit generators (PRBG) most suitable for software and hardware realisations of stream cipher are identified. The software implementations of PRBG are carried out using Mathematica and the implementations in VHDL are done using the Altera Quartus IIv6.0 simulation software. The Montgomerys point multiplication method has also been discussed and implemented for comparison with the conventional point multiplication algorithm. Together with this, faster software algorithms for field inversion and point counting are discussed.
elliptic curves pseudorandom bit generator periodicity point multiplication projective coordinates