Secure and Efficient LCMQ Entity Authentication Protocol

The simple, computationally efficient HB-like entity authentication protocols based on the learning parity with noise (LPN) problem have attracted a great deal of attention in the past few years due to the broad application prospect in low-cost RFID tags. However, all previous protocols are vulnerable to a man-in-the-middle attack discovered by Ouafi, Overbeck, and Vaudenay. In this paper, we propose a lightweight authentication protocol named LCMQ and prove it secure in a general man-in-the-middle model. The technical core in our proposal is a special type of circulant matrix, for which we prove the linear independence of matrix vectors, present efficient algorithms on matrix operations, and describe a secure encryption against ciphertext-only attack. By combining all of those with LPN and related to the multivariate quadratic problem, the LCMQ protocol not only is provably secure against all probabilistic polynomial-time adversaries, but also transcends HB-like protocols in terms of tag's computation overhead, storage expense, and communication cost.