Braid groups has drawn the attention of cryptographers for a few years, as a promising platform for post-quantum cryptographic protocols. The security of the proposed schemes mostly relied on conjugacy problems, and attacks against this problem were discovered, and cryptographers lost interest in those braid groups. But as far as I know, those attacks don't completely break the security of braid groups. For example, conjugacy problems can be solved by computing the USS (Ultra Summit Set) of a braid, but this set can have exponential size in the length of the braid (for some classes of braids).
I don't know much about other attacks on braid groups, but do they definitely put an end to any applications of braids to cryptography? If we could highlight properties of braids comparable to bilinear pairings for elliptic curves, allowing some of the related advanced protocols in a post-quantum world, would they become more interesting or are they definitely too weak for cryptography?
Note that my question didn't mean to say "is anyone still interested in braids", but rather "do we know attacks (that I am not aware of) on conjugacy related problems for braids that definitely label them as 'not suitable for cryptography'". I am certainly not looking for (or expecting) as an answer any opinion about how interesting they are.