A Comprehensive Security Analysis of the TUAK Algorithm Set

The authentication and key generation functions play a significant role to guarantee security and privacy in cellular mobile communications. MILENAGE is a set of authentication and key generation functions proposed by the 3 Generation Partnership Project (3GPP). Most recently, the 3GPP Task Force proposed a new set of authentication and key generation functions, called TUAK, as an alternative for the 4G LTE cellular mobile communications. The design of the TUAK functions makes use of the Keccak permutation, which is a core function in the SHA-3 hash function. One may expect that the TUAK functions may inherit attack resistance properties from that of the Keccak permutation. However, TUAK functions are obtained by assigning keys, different constants and padding bits at different input positions of the Keccak permutation. Therefore, a security analysis for the construction of the TUAK functions is needed. In this paper, for the first time, we present a comprehensive security analysis of the TUAK function set. Our main contribution is to provide a security analysis of TUAK’s authentication and key derivation functions under various relevant cryptanalytic attacks. We consider powerful cryptanalytic attacks including differential attack, linear attack, distinguishing attack, boomerang attack and key-recovery attacks such as algebraic attacks and cube attacks. We conduct an experiment to find collisions on f2 and f5 functions and our experiment finds collisions on f2 function and near-collision on f5 function, due to the small output sizes. Our security analysis shows that the TUAK functions are resistant to the cryptanalytic attacks.