Is it possible to sign something, get the hash of that, and upload the hash to a blockchain? The blockchain forms the backbone of a digital notarization servic

Is it possible to sign something, get the hash of that, and upload the hash to a blockchain? The blockchain forms the backbone of a digital notarization service. This guarantees that it was you that sent the message. Then you send the encrypted message to your recipient. The recipient decrypts it with his private key. And then, he can verify on the blockchain that it did indeed come from you. I’m thinking this can be used for verified communications, e-commerce, e-banking, e-contracts, etc. This is just an off the cuff thought. I haven’t really thought through all the scenarios for this idea.