Two step encryption

Question

Consider the following user case:

1. I have some sensitive data (eg: credit card number)
2. I encrypt this data and store it in the database

3. Now I want to send this data to a user X, but I don't want to:

   1. Decrypt this data before sending
   2. Give user X my key used for decrypting stored data

I would like to give to user X his own private key and use one more round of encryption on the encrypted data before I send it to him.

Is there encryption algorithm which changes the decryption key with each each subsequent encryption round? Something that looks like this:

Ct = Encrypt(KeyA, Pt)   # I store Ct in the database

CtB = Encrypt(KeyB, Ct)  # I now encrypt it with different key and 
                         # send CtB along with a private key KeyC to the user
                         # KeyC is derived from KeyB

Pt = Decrypt(KeyC, CtB)  # the user can now use this KeyC to get the original data

With this, I can create different ciphertexts for each user, stopping them from sharing keys. This also means data would never be in plaintext form on the server.

Use case is only theoretical and I know there are different solutions appropriate for such situation.

Answer 1

It sounds like what you are asking about is probably mathematically possible, but it would likely be hard (and maybe impossible) to find a way to do it such that it is both mathematically true and hard to guess. I suspect you are unlikely to find an existing system that meets your exact specifications as I can not think of any use case that couldn't be more effectively handled using much simpler applications of common cryptographic algorithms.

If you have a particular case that you can think of that you think this would handle that couldn't otherwise be handled, then perhaps posting that use case scenario (even if theoretical) would help better answer your question. It also might be worth bringing up the idea over on Cryptography or even Math since they tend to deal more with the theoretical math side of things if that is where your interests lie.

Answer 2

@AJ Henderson includes a reasonable answer; I'm going to try to explain more clearly.

1) Your question mixes what you want done (secure storage and transmission) with how you want to do it (two step encryption).

2) If you want to store the information securely, encrypt it with a symmetric key (choose a new symmetric key for every "thing" you want to store). Now encrypt the symmetric key with a public key and store that.

3) if you want to share the information: 3a) Decrypt the symmetric key, and encrypt it with the recipients public key. 3b) Send the encrypted data along with the symmetric key encrypted by the recipients public key.

The recipient (and only the recipient) can use their private key to decrypt the information. At no time is data transmitted in the clear.

I think that answers what you want done, although the how is different.

Answer 3

First, you should never store data encrypted with a public/private key system. Public/Private key cryptography is significantly more expensive to use and in general provides far less security for the key-length being used and are far more processor intensive. Your best bet is to encrypt a data storage key using a public/private key system and use the symmetric data storage key for your encrypted storage. It is then possible to do what you are looking for.

Encryption, server generates a new data storage key and encrypts the CC number. Data storage key is encrypted with the public key of the server and stored. When you want to send the data to user X, you use the server's private key to decrypt the data storage key and re-encrypt the data storage key with user X's public key. User X can now access the symmetric data storage key in an encrypted state and can then decrypt it locally to be able to decrypt the symmetrically encrypted data.