I'm making an application in PHP and there is a requirement that it must be possible to decrypt the passwords in order to avoid problems in the future with switching user database to different system. Consider that it's not possible to modify this future system's password method and I need plain text passwords in order to have the passwords generated.
The plan is to encrypt the user's password with a public key that is stored on the server. Authentication is done by encrypting the input and comparing the results. There is NO decryption done. The private key capable of the decryption is stored off-site for later usage.
What encryption/decryption algorithm would you suggest? Are the encrypted passwords still as safe as hashing (MD5/SHA1) when you consider the private key is not available to the attacker?