Random subgroups and analysis of the length-based and quotient attacks

@article{Myasnikov2008RandomSA,
  title={Random subgroups and analysis of the length-based and quotient attacks},
  author={Alexei G. Myasnikov and Alexander Ushakov},
  journal={J. Mathematical Cryptology},
  year={2008},
  volume={2},
  pages={29-61}
}
In this paper we discuss generic properties of ”random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they ”sit” inside G in a very particular way. This gives a strong mathematical foundation for cryptanalysis of several group-based cryptosystems and indicates on how to chose ”strong keys”. To illustrate our technique we analyze the Anshel-Anshel-Goldfeld (AAG) cryptosystem and give a… CONTINUE READING
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