Abstract
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.
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Myasnikov, A., Shpilrain, V., Ushakov, A. (2006). Random Subgroups of Braid Groups: An Approach to Cryptanalysis of a Braid Group Based Cryptographic Protocol. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds) Public Key Cryptography - PKC 2006. PKC 2006. Lecture Notes in Computer Science, vol 3958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11745853_20
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