Elliptic Curve Cryptosystems
Elliptic Curve Cryptosystems
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DOI：
10.1007/978-1-4757-2226-0_8
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
I. Blake;Xuhong Gao;R. Mullin;S. Vanstone;T. Yaghoobian
中科院分区：
文献类型：
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作者：
I. Blake;Xuhong Gao;R. Mullin;S. Vanstone;T. Yaghoobian
正如我们在6.1节中所看到的，一个有限循环群G的元素可以用来实现几种加密方案，只要在G中找到元素的对数是不可行的。我们可以取eg为一个循环子群ofE(Fq)，即在Fq上定义的椭圆曲线的群offq -有理点；这首先是由N. Koblitz[10]和V. Miller[10]提出的。由于该组中的加法相对简单，而且离散对数问题ingi被认为是难以处理的，因此椭圆曲线密码系统有可能提供与现有公钥方案相当的安全性，但密钥长度更短。短密钥长度在某些应用中是至关重要的因素，例如智能卡系统的设计。
As we have seen in Section 6.1, the elements of a finite cyclic groupGmay be used to implement several cryptographic schemes, provided that finding logarithms of elements in G is infeasible. We may takeGto be a cyclic subgroup ofE(Fq), the group ofFq-rational points of an elliptic curve defined overFq; this was first suggested by N. Koblitz [10] and V. Miller [17]. Since the addition in this group is relatively simple, and moreover the discrete logarithm problem inGis believed to be intractable, elliptic curve cryptosystems have the potential to provide security equivalent to that of existing public key schemes, but with shorter key lengths. Having short key lengths is a factor that can be crucial in some applications, for example the design of smart card systems.