基于无线网络安全的ECC点积算法研究

椭圆曲线因其自身的优越性应用于无线网络安全中。椭圆曲线密码应用中常使用的两类椭圆曲线为定义在有限域GF（P）上的素曲线和在有限域GF（2^m）上的二元曲线。素曲线计算因不需二元曲线所需要的位混淆运算，常应用于软件：而对硬件应用而言，则最好使用二元曲线，它可用很少的门电路来得到快速且功能强大的密码体制．在椭圆曲线加密体制中，NP问题是制约其应用和发展的瓶颈的核心问题。文中提出了基于无线网络安全的GF（2^m）域上的椭圆曲线点积算法的改进。且本文将椭圆曲线的基点和随机点的点积算法区别开来，具有重要的现实实现意义。

Research on Key Algorithms of Point Multiplication on the Elliptic Curve Cryptosystem Based on Wireless Network Security

The elliptic curve cryptosystem is widely used in the wireless network security for its own superiority.There are two kinds of elliptic curve cryptosystem,one is based on the GF(P),the other is based on the GF(2m).The bit disturbing algorithm is not needed in the first cryptosystem,so is often used in the software;for hardware application,the later system is the better choice for its few circuit,high speed and strong function.The NP problem is a critical problem in the elliptic curve cryptosystem.This essay gives the better algorithms of point multiplication on the elliptic curve cryptosystem over GF(2m) based on wireless network security.This paper gives different algorithms on the base point and the random point,which is of great significance in real implementation.