Elliptic Curve Cryptography And Its Implementation In Broadband Wireless IP Networks

Elliptic curve cryptography (ECC) was proposed independently in 1985 by Victor Miller and Neal Koblitz. It is a cryptography with the highest security intensity of each bit up until now. It also has the advantage of small computing amount, short key size and taking up little bandwidth. It is considered to be the most hopeful publie key cryptography in the future.ECC is set up on the basis of solving this mathematics difficult problem of the Elliptic Curve Discrete Logarithm Problem (ECDLP). To set up a perfect elliptic curve cryptography, two respects need considering: choosing the necessary parameters and the concrete algorithms. Round these two respects, how to structure security elliptic curve cryptography and the implementations of ECC is first discussed in this paper. Then we have analysed especially the scalar multiplication on the elliptic curves, and present a new algorithm to quickly implement the fixed point scalar multiplication according to the idea of Interleaving Exponentiation Algorithm and power division. This algorithm is much faster than Fixed-base Windowing Method;and a little faster than Fixed-base Comb Method.Finally, we provide a scheme of ECC that suits the broadband wireless IP environment. The implementation result indicates that the elliptic curves with 192 bit we choosen have stronger security intensity and faster speed than RSA with 1024 bit.