A New Variant of 3GPP-MAC With Provable Security and Higher Efficiency *

3GPP-MAC, also called f 9, is an integrity scheme adopted by Universal Mobile Telecommunication System as a standard for the 3rd generation wireless communications. In this paper, we investigate the feasibility of improving its efficiency, with the precondition that its security would not be compromised. As we show, the newly proposed f 9 − enjoys provable security under the solo PRP assumption; more importantly, f 9 − removes the last block-cipher invocation of f 9, which means it needs less time and resources to compute MACs than f 9, offering higher efficiency in practice. Furthermore, f 9 − keeps the main structure of f 9 almost unchanged, making it easy to update f 9 to f 9 − in reality