Abstract:
Elliptic curve cryptosystems are nowadays widely
used in public communication channels for network security.
Their security depends on the complexity of solving the elliptic
curve discrete logarithm problem. But, there are several general
attacks in them. Elliptic curve arithmetic is implemented over
complex fields to improve the security of elliptic curve
cryptosystems. This paper begins the characteristics of elliptic
curve cryptosystems and their security services. Then we
discuss finite field arithmetic and its properties, prime field
arithmetic, binary field arithmetic and complex number
arithmetic, and elliptic curve arithmetic over prime field and
binary field. This paper proposes how to implement complex
number arithmetic under prime field and binary field using java
BigInteger class and we implement elliptic curve arithmetic and
elliptic curve cryptosystems using complex numbers over prime
field and binary field and discuss the experiments that got from
our implementations.
