有限域GF（2^m）上椭圆曲线密码体制的运算分析及NTL实现

Arithmetic Analysis and Implementation with NTL on Elliptic Curve Cryptosystem Over Finite Field GF(2m)

椭圆曲线密码体制主要是基于有限域GF(p)和GF(2m)上建立的,建立在GF(2m)的椭圆曲线密码体制的运算可以用比特流来实现,因而其效率更高。本文详细分析了有限域GF(2m)和椭圆曲线群上的两层运算;讨论了由美国纽约大学的VictorShoup(国际标准ISO18033-2的编写人)开发并维护的C++开放源代码的数论算法库NTL,并用NTL实现了其中的关键运算,编程测试结果良好。

Elliptic curve cryptosystem is built up base on finite field GF(p) and GF(2m).Arithmetics of Elliptic curve cryptosystem over GF(2m) can be implemented using bit string,therefore it’s efficiency of implementation is more higher.This paper analyses two layer arithmetic of finite field GF(2m) and elliptic curve group in detail,and discuss NTL(Numbery Theory Library) with open C++ source which is written and maintained by Victor Shoup,New York University,writer of ISO 18033-2.Here we use NTL library to implement the key arithmetics.Program testing shows the results are good.