Security of pairing-based cryptography over binary fields regarding new attacks
Antoine Joux announced the computation of discrete logarithm over $\mathbb{F}_{2^{257 \times 24}}$, which is now pretty close to what was being used in pairing-based cryptography.

According to Joux, "a direct consequence of this record is that supersingular curves (of
genus 1 or 2) defined over GF(2^257) cannot be used securely for
pairing-based cryptography."

It seems now that pairing-based cryptography over binary fields is dead.