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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(2m)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(2m)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。
Elliptic curve because of its own superiority in wireless network security. Two types of elliptic curves that are commonly used in elliptic curve cryptography are the prime curve defined on the finite field GF (P) and the binary curve on the finite field GF (2m). The prime curve calculation is usually applied to software because it does not require a bit-wise bit-blending operation. For hardware applications, it is best to use a binary curve that can be quickly and functionally robust with fewer gates Password system. In the elliptic curve cryptosystem, the NP problem is the core problem that restricts the bottleneck of its application and development. In this paper, we propose an improved elliptic curve dot product algorithm based on wireless network security in GF (2m) domain. In addition, this paper distinguishes the dot product of the elliptic curve from the random point, which has an important realistic meaning.