Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA.
(Note: I do realize that in practice this is done through an intermediate symmetric key, but this question assumes we only use asymmetric encryption.)
Say I try to do this: I slice up my data into 2n-byte blocks (
padding with zeros [edit: padding appropriately] if necessary), append the block index to the block (to prevent the same plaintext from turning into the same ciphertext), then use my friend's public key to encrypt each block separately.
Is this a secure scheme, or does the fact that I'm re-using the key make it susceptible to some kind of attack? If so, is it used in practice in any existing algorithms? If not, is there any way to make it safe, aside from using a symmetric key?