Is there a way to store and share a private key through blockchain? This is more a blockchain than a bitcoin question:

I would like to use a blockchain (potentially a permissioned one) to manage ownership of a device. But linked to the device there is a private key. 

Is there a way for the owner of a device to access to this private key, ideally only using blockchain?
A blockchain, in whatever form, is ultimately a shared transaction log that multiple nodes eventually agree on.

All information in the chain is public (to all participants of the system, not necessarily the whole world). Sharing secret information using a public log makes no sense: everyone would see the key.