How reasonable would it be to speak TLS over the secp256k1 curve? My initial experiments show that OpenSSL supports it (albeit with special flags, see below): Running an OpenSSL client against an OpenSSL server (or some random node.js server that I found) negotiates the suite ECDHE-ECDSA-AES128-GCM-SHA256 and establishes a regular TLS 1.2 session.
On the other hand, neither curl nor browsers appear to like that particular curve. (Although that is not necessary for my use case.)
The reason I'm using secp256k1 is because there is a nice algorithm to derive new keys from an existing key (BIP 32). Those keys cannot be correlated with each other, which is a big plus in peer-to-peer scenarios.
Now my question is: Is it reasonable to use an uncommon curve like secp256k1 for TLS? Or alternatively, is there a secure mechanism to derive a private key for another (more common?) curve from a secp256k1 private key?
The flags I mentioned above:
Edit: My question is less about theoretical weaknesses of secp256k1, but rather what kinds of practical problems to expect.