How about using ECC point multiplication and AES:

1. Get recipient's public key R (R = r*G, r is private key)
2. For each message, generate unique keypair S,s: S = s*G.
3. Create a shared secret: K = R*s
4. Compute 256-bit encryption key out of that shared secret: key = SHA256(SHA256(K))
5. Encrypt the message with that key and send the message together with unique pubkey S.
6. Recipient gets the message and computes key using his private key r and S: key = SHA256(SHA256(r*S))
7. Recipient's key turns out to be the same because r*S = R*s = r*s*G.

I like this scheme more because it allows to efficiently encrypt messages of arbitrary sizes.