A simple client/server authentication protocol
If Eve knows $C, \space N, \space K_{CA}(N)$ then she is able to impersonate $C$ just by following the protocol you described above.

If she just knows $K_{CA}(N)$ for a single $N$ then the effectiveness of the attack depends on the set wherein $N$ is picked.

But as you are supposing that the communication channel is not secure, an attacker could spy several authentication session to get a sufficient number of pairs $(N, K_{CA}(N))$ to successfully attack with high probability.