On the round security of symmetric-key cryptographic primitives

We put forward a new model for understanding the security of symmetric-key primitives, such as block ciphers. The model captures the fact that many such primitives often consist of iterating simpler constructs for a number of rounds, and may provide insight into the security of such designs. We completely characterize the security of four-round Luby-Rackoff ciphers in our model, and show that the ciphers remain secure even if the adversary is given black-box access to the middle two round functions. A similar result can be obtained for message authentication codes based on universal hash functions.