Authentication codes from e-ASU hash functions with partially secret keys

An authentication code can be constructed with a family of ε-Almost strong universal (ε-ASU) hash functions, with the index of hash functions as the authentication key. This paper considers the performance of authentication codes from ε-ASU, when the authentication key is only partially secret. We show how to apply the result to privacy amplification against active attacks in the scenario of two independent partially secret strings shared between a sender and a receiver.