Abstract: Since the introduction of algorithms such as RSA and the Diffie-Hellman key exchange in the 1970s, modern cryptography has been dominated by the exploration of computationally difficult problems. The most popular of these subjects - prime factorization, discrete logarithms, and elliptic curves - originate from number theory and thus reside in abelian groups. In the hopes of developing more robust options, several non-abelian cryptosystems have been proposed, with focus on the braid group.

In this talk, we will discuss some existing braid-based algorithms, their weaknesses, and directions for future research. We will not assume any background in either cryptography or braids.