What are the fundamentals to accomplish data encryption with exactly two keys (which could be password-based), but needing only one (either one) of the two keys to decrypt the data?
For example, data is encrypted with a user’s password and his company’s password, and then he or his company can decrypt the data. Neither of them know the other password. Only one copy of the encrypted data is stored.
I don’t mean public/private key. Probably via symmetric key cryptography and maybe it involves something like XORing the keys together to use them for encrypting.
Update: I would also like to find a solution that does not involve storing the keys at all.
The way this is customarily done is to generate a single symmetric key to encrypt the data. Then you encrypt the symmetric key with each recipient’s key or password to that they can decrypt it on their own. S/MIME (actually the Cryptographic Message Syntax on which S/MIME is based) uses this technique.
This way, you only have to store one copy of the encrypted message, but multiple copies of its key.