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 the 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.