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arXiv cs/0306032cs.CR
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一类基于组的加密重写系统的长度攻击

Length-Based Attacks for Certain Group Based Encryption Rewriting Systems

James Hughes, Allen Tannenbaum

摘要:

在这篇笔记中,我们描述了一个概率攻击的公钥密码系统的基础上的字/共轭问题,最近提出的类型的Anshel,Anshel和Goldfeld。在这样一个方案中,人们利用了这样的性质,即在给定的组中,字问题具有多项式时间解,而共轭问题没有已知的多项式解。一个例子是来自拓扑学的辫子群,其中字问题在多项式时间内是可解的,而共轭问题的唯一已知解是指数的。本文中的攻击是基于具有每个字符串的规范表示,相对于该规范表示,可以计算长度函数。这就是长期攻击。已知辫群存在这样的典型代表。

英文摘要:

In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of the property that in the given group the word problem has a polynomial time solution, while the conjugacy problem has no known polynomial solution. An example is the braid group from topology in which the word problem is solvable in polynomial time while the only known solutions to the conjugacy problem are exponential. The attack in this paper is based on having a canonical representative of each string relative to which a length function may be computed. Hence the term length attack. Such canonical representatives are known to exist for the braid group.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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