TY - GEN
T1 - Random subgroups of braid groups
T2 - 9th International Conference on Theory and Practice in Public-Key Cryptography, PKC 2006
AU - Myasnikov, Alexei
AU - Shpilrain, Vladimir
AU - Ushakov, Alexander
PY - 2006
Y1 - 2006
N2 - Motivated by cryptographic applications, we study subgroups of braid groups Bn 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 Bn, 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.
AB - Motivated by cryptographic applications, we study subgroups of braid groups Bn 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 Bn, 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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U2 - 10.1007/11745853_20
DO - 10.1007/11745853_20
M3 - Conference contribution
AN - SCOPUS:33745819514
SN - 3540338519
SN - 9783540338512
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 302
EP - 314
BT - Public Key Cryptography - PKC 2006 - 9th International Conference on Theory and Practice in Public-Key Cryptography, Proceedings
Y2 - 24 April 2006 through 26 April 2006
ER -