I am searching for an asymmetric encryption algorithm with a simple PHP implementation which is not generating different public/private keys each time I run it (but always the same for the same password).
The reason is simple: My customers often forget/reset their password, but once they remember it, they should be able to recover old encrypted files sent to them using the old public key. With RSA, every time they reset their password (and by that, their public key), a new random public key gets generated, even for the same password.
Thanks in advance!
Just encrypt the private key using password based encryption. That is first derive a secret key from a password (using PBKDF2 or bcrypt for instance) and then encrypt the private exponent or the whole key. This is the way e.g. PGP works. Of course this requires storing the encrypted private key.