Experiments on Implementation of Elliptic Curve Arithmetic over Complex Fields Using java BigInteger Class
Ni Ni Hla, Tun Myat Aung · Journal of Communications · 2019
Elliptic curve cryptosystems are nowadays widelyused in public communication channels for network security.Their security depends on the complexity of solving the ellipticcurve discrete logarithm problem. But, there are several generalattacks in them. Elliptic curve arithmetic is implemented overcomplex fields to improve the security of elliptic curvecryptosystems. This paper begins the characteristics of ellipticcurve cryptosystems and their security services. Then wediscuss finite field arithmetic and its properties, prime fieldarithmetic, binary field arithmetic and complex numberarithmetic, and elliptic curve arithmetic over prime field andbinary field. This paper proposes how to implement complexnumber arithmetic under prime field and binary field using javaBigInteger class and we implement elliptic curve arithmetic andelliptic curve cryptosystems using complex numbers over primefield and binary field and discuss the experiments that got fromour implementations.