Public key encryption algorithm for short messages
Using RSA with short keys is a bad idea since it would make the encryption less secure. 

The standard way to use asymmetric encryption is to only use the asymmetric encryption algorithm to encrypt a symmetric encryption key and then use that key to do the actual communication. In this case you only get the message overhead of the asymmetric encryption scheme once which can then be amortized over many small messages.

Is there any reason you can not use this approach in your application?