Problems when using PBKDF2 to create an ECDSA private key from a password? System based on, e.g.:
PBKDF2, ECDSA and authenticator's random challenges.

Key derived from a password would be ECDSA's private key used to sign random challenges.

Is password brute force the only thing I should worry about or is there another threat involved with using such key as a ECDSA seed?
How are you going to trust the resulting public key that is required to verify anything signed by the private key?

How are you going to maintain security after you've authenticated?

ECDSA may be vulnerable against analysis using quantum computing.



You've only partly described one part of a cryptographic system. This means you've got plenty to worry about.