The Trivium encryption algorithm has two inputs, key and IV, both of which are 80 bits long. Let's call it Trivium(key, IV) → keystream. My question is whether doing Trivium(key, input) and taking the first 80 bit of keystream would result in a secure PRF.
I have found another way to create a PRF from a stream cipher, but that seems to be for stream ciphers that do not have an IV input, so such a complex construction might not be needed for one that does. Based on reading the Trivium algorithm description paper and the Trivium design paper I feel like my construction should be secure but I have no idea how to go around proving it.
This question was spurred by wondering whether I could implement authenticated encryption using only Trivium as a primitive. If I could turn it into a PRF, as far as I understand I could construct something similar to CBC-MAC from it. (Of course this doesn't make much sense to because rekeying the cipher, which you'd need to do for every 8 bytes, is quite slow.)