We have an application that requires cleartext passwords for user authentication because of the authentication mechanism in use (RADIUS/CHAP), which unfortunately we cannot change. Since we don't want to store cleartext passwords, an idea is to use asymmetric encryption to secure them as good as possible. After creating/chaning a password, it will be encrypted with the public key and replicated through more or less unsecured channels to the authentication systems. When a user tries to authenticate, the encrypted password will be decrypted with the private key (which has to be available on the authentication servers, obviously).
So we would have a database with lots of encrypted passwords, but all encrypted with the same key. After some research I see that this not the way asymmetric encryption is commonly used. Usually the payload is encrypted with a block cipher and the symmetric key is encrypted with an asymmetric key. But since passwords are quite short I wonder if this additional encryption layer can safely be avoided or if this would be simplification would be a serious risk.
Related to this: What algorithm would you recommend? I kind of narrowed it down to RSA and Elgamal, mostly because these two seem to be most widely used and are available through well-known libraries (OpenSSL, gcrypt). RSA seems to require longer keys to provide the same security, so Elgamal seem to be the better option there's no other argument against it.