现代密码学协议的安全性多数是建立在数学难题基础之上,比如:大整数因子分解、有限域上的离散对数问题。通常情况下,这些算法不存在多项式时间问题,但随着攻击算法地不断改进,要求使用这些安全协议的算法密钥不断的加大,才得保证其使用的安全性。但密钥的加大增加了算法的复杂性,因此,找到一种能抵抗各种常见攻算法,运算量小,速度快的离散对数密码算法非常重要,椭圆曲线密码算法正好满足这种需要。论文回顾了常用公钥密码体制协议,相对于目前应用的其它密码体制,椭圆曲线密码体制有很大的优势,最后,分析了椭圆曲线密码体制在实际应用中可能受到的各种攻击算法。
The security of the modern cryptography protocols is based on mathematical problems, For example:big integer factor decomposition, finite field of discrete logarithm problem. In the general case, there are no polynomial time algorithms for this problem, constant improvement of the attacking algorithm made these protocols require much larger key size, so that make sure the use of the security. But the larger key size increase the complexity of the algorithms , therefore, it is very important to find a resistant attack algorithm, small burden, the speed the discrete logarithm cryptographic algorithm , elliptic curve cryptography al-gorithms is just to meet this need. In this paper I reviewed the general protocols of the asymmetric cryptography system , and de-scribe the elliptic curve cryptography and its application to may be vulnerable to attack. Finally, I mention other applications that elliptic curves have had upon the analysis of other cryptosystems not involving them.
