[Cryptography] Is storing a hash of a private key a security risk?

[Peter Gutmann]

For private keys stored in a secure enclave in an embedded environment,
there's some concern that over long periods of time the key components may be
subject to bit rot/corruption.  One possible solution is to store a truncated
hash of the private key components outside the enclave and use that to verify
that nothing has changed, by asking the enclave whether the stored key
corresponds to the given hash value.  Without going into a huge amount of
detail on the specific application, it has to be a hash, it can't be a MAC or
something similar, and the hash can't be stored inside the enclave because it
only stores key components (it's a hardware constraint).

This is something that, on the one hand, seems to be not a good idea, but on
the other hand I can't see any obvious problem that it would cause (you can
use it to find out whether a given key is stored inside the enclave, but you
can do that anyway without the hash because you need to identify the key to
query the enclave whether the hash matches).

Can anyone see any problems with this?  Or suggest an alternative approach
that doesn't violate the constraints imposed by the hardware?

Peter.