How to store private data in blockchain and smart contract
If I've understood correctly, I don't think you need block-chain technology to achieve what you want. This is exactly what asymmetric public key encryption is designed for. 

A simply encrypts some information using A's private key and B's public key... thereby ensuring:


Only B can decrypt the information 
B can verify the information was
encrypted by A (using A's public key)


There's no way for A to prove to B that their copy of the information has been destroyed or forgotten by A, but at least secure transmission is ensured.