Fast arithmetic of elliptic curve cryptosystem in mobile communication

Using the elliptic curve discrete logarithm problem, a security solution for mobile communication was built and one digital module of elliptic curve cryptosystem (ECC) was given in this paper. The solution had achieved rapid arithmetic correlated with ECC in finite field GF(p). The security of 160 bit-ECC-key corresponded 1000 bit-key in RSA. Furthermore, the arithmetic efficiency of addition and subtraction put forwards in other field was 20%-40% quicker than common.