Smart Contracts Encryption – Can Smart Contracts Compute on Encrypted Data?

Since the smart contract is replicated on all the nodes across the network, will every one be able to see all the contents of the smart contract?

Short answer: yes.

If the contract does the decryption, it needs to store the private key. If the private key is stored in the contract, it is replicated to every node, and yes, as a result every node will do the decryption.

There is probably some cryptographically complex way to do what you want, but I'd guess it's one of those things that you want reviewed by lots of people who know crypto and blockchains, and if you get even a bit of it wrong, your data would be vulnerable.

Depending on your use case, you might have data sent (encrypted with the contract's public key) to the contract and stored, but only decrypted by a node/app you control that has the private key secured.

You can't make an Ethereum contract start with plaintext and meaningfully encrypt a message, because all contract execution has to be verifiable by all the nodes in the network, so as you say everybody would also have to be able to see your plaintext.

If you want to send a message from one user of a contract to another user of the contract, the obvious thing to do is for the contract to manage an identifier for the user who wants to receive the message - say a PGP fingerprint - and the sender to use that to look up their PGP public key on a regular key server and use that to encrypt the message for them.

You probably don't want the encrypted message to actually transit the blockchain unless it's very small as it will cost gas, but you might want to use the blockchain to let the receiver know where to find the encrypted message - for example, store the encrypted message in IPFS, and have the sender update the contract to let the receiver know the hash of the document they've put on IPFS.