The maximum order of an element of a finite symmetric group
American Mathematical Monthly
Polynomial time algorithms for modules over finite dimensional algebras
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Word Processing in Groups
New Key Agreement Protocols in Braid Group Cryptography
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
New Public-Key Cryptosystem Using Braid Groups
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Pseudorandomness from Braid Groups
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
An Efficient Implementation of Braid Groups
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Practical Attack on Some Braid Group Based Cryptographic Primitives
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A Weak Key Test for Braid Based Cryptography
Designs, Codes and Cryptography
One-more matching conjugate problem and security of braid-based signatures
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Towards generating secure keys for braid cryptography
Designs, Codes and Cryptography
Journal of Systems Architecture: the EUROMICRO Journal
Length based attack and braid groups: cryptanalysis of Anshel-Anshel-Goldfeld key exchange protocol
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Cryptanalysis of the public-key encryption based on braid groups
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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The braid group with its conjugacy problem is one of the recent hot issues in cryptography. At CT-RSA 2001, Anshel, Anshel, Fisher, and Goldfeld proposed a commutator key agreement protocol (KAP) based on the braid groups and their colored Burau representation. Its security is based on the multiple simultaneous conjugacy problem (MSCP) plus a newly adopted key extractor. This article shows how to reduce finding the shared key of this KAP to the list-MSCPs in a permutation group and in a matrix group over a finite field. We also develop a mathematical algorithm for the MSCP in braid groups. The former implies that the usage of colored Burau representation in the key extractor causes a new weakness, and the latter can be used as a tool to investigate the security level of their KAP.