Use R-CTR (randomized counter mode) to compute MAC I've read that in conjunction with CBC-MAC, R-CTR (randomized counter mode) can be used to compute a MAC, but why wouldn't you just use a block cipher in R-CTR on its own to compute a MAC?
I'll assume that R-CTR is CTR with a random IV or nonce.



Counter mode cannot be used to compute a MAC for the simple reason that the ciphertext of any part of the plaintext does not depend on any other part of the plaintext.

With CBC the ciphertext over the previous block is used as input (vector) for the next block encryption; it is XOR-ed with the next block of plaintext before it is encrypted. This means that the last block of ciphertext depends on all previous blocks. This makes it possible to create MACs such as CBC-MAC and the more secure CMAC out of CBC mode encryption. 

Counter mode first creates a key stream which is then directly XOR'ed with the plaintext to produce the ciphertext. This means that each and every bit of plaintext is encrypted completely independently of any other bit of plaintext. So in the end you're just as far as you were before.



I cannot explain how you could combine CBC-MAC and R-CTR to create a MAC without seeing the definition of this scheme. In principle you'd just need CBC-MAC or course, even if that requires that the length can be determined in advance.