Covert ECDH over secp256k1
If ECDH is used to establish a shared session secret for an encrypted connection, two elliptic curve points need to be transmitted (one in each direction) before encryption starts. In order to avoid being identifiable as a (specific) ECDH negotiation, ideally those two points are sent in a way that is indistinguishable from random.
This problem is easily addressed by using curves that support Elligator-style encodings: functions that encode a (subset of) elliptic curve points as sequences of bytes with no observable bias: (almost) every byte sequence corresponds to exactly one point, and the others correspond to none.
Unfortunately, no Elligator-style encoding is known for secp256k1.