LibSodium, (https://github.com/jedisct1/libsodium), has a function
crypto_box_detached() which does authenticated encryption using the public key of the recipient and the private key of the sender (using Curve25519). I believe this function is compatible with Daniel J. Berinstein's corresponding function in NaCl (http://nacl.cr.yp.to/), although with a different interface.
If Alice creates a message for Bob using this function and a random nonce, is it possible for Eve to distinguish the ciphertext+MAC from random data?
What about if Eve has the public keys of Alice and Bob, does that make it easier to distinguish it from random data?
If Eve has their public keys, can she in any way deduce that the message came from Alice or that it is destined for Bob?