Question

I’m wondering if I can have multiple public keys for a private key.

Can this be done?
If so, what are the security issues!?

If I generate multiple key pairs based on the same initial values (with no initial vector), shouldn’t the keys be “compatible”?

Answer 1

In all asymmetric crypto-systems I can think off, there is a 1-1 correspondence between the public key and the private key: given the private key you can uniquely determine the public key and given the public key you can uniquely determine the private key (but it should of course be computationally infeasible to determine the private key from the public key).

However given one of the usual asymmetric schemes you can easily create such a scheme: To create a private key with n public keys, just generate n public-private keypairs in the normal scheme and define the “private key” to be the collection of the private keys. When signing just sign with all the private keys, when verifying try to verify one of the signatures. Encryption is the usual operation and decrypting should try to decrypt with all the keys (one of them should work).