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2006 | OriginalPaper | Chapter
Random Subgroups of Braid Groups: An Approach to Cryptanalysis of a Braid Group Based Cryptographic Protocol
Authors : Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov
Published in: Public Key Cryptography - PKC 2006
Publisher: Springer Berlin Heidelberg
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Motivated by cryptographic applications, we study subgroups of braid groups
B
n
generated by a small number of random elements of relatively small lengths compared to
n
. Our experiments show that “most” of these subgroups are equal to the whole
B
n
, and “almost all” of these subgroups are generated by positive braid words. We discuss the impact of these experimental results on the security of the Anshel-Anshel-Goldfeld key exchange protocol [2] with originally suggested parameters as well as with recently updated ones.