Efficient solutions to the braid isotopy problem

We describe the most efficient solutions to the word problem of Artin's braid group known so far, i.e., in other words, the most efficient solutions to the braid isotopy problem, including the Dynnikov method, which could be especially suitable for cryptographical applications. Most results appear in literature; however, some results about the greedy normal form and the symmetric normal form and their connection with grid diagrams may have never been stated explicitly. Because they are both not too simple and not too complicated, Artin's braid groups Bn have been and remain one of the most natural and promising platform groups for non-commutative group-based cryptography [2, 22, 13]. More precisely, braid groups are not too simple in that they lead to problems with presumably difficult instances, typically the conjugacy problem and the related conjugacy and multiple conjugacy search problems, and they are not too complicated in that there exist efficient solutions to the word...

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Patrick Dehornoy
• Keywords: Braid Groups, DAM 2008, Normal Form, Word Problem