Security Assessment of TUAK Algorithm Set

The 3rd Generation Partnership Project (3GPP) aims at the development of the specifications for the next generation cellular system. The TUAK algorithm set, which contains authentication and key generation algorithms, is proposed as an alternative to MILENAGE for the 3GPP. The design of algorithms in TUAK is based upon the winner of the SHA-3 competition, Keccak’s permutation Keccak-f [1600]. It contains eight different algorithms, namely TOPC , f1, f ∗ 1 , f2, f3, f4, f5, f ∗ 5 . The f1 (and f ∗ 1 that is used as re-synchronisation message authentication) algorithm ensures the authenticity of messages, f2 is used for generating responses and f3 to f5 (f ∗ 5 ) are used as key derivation functions. In this report, we provide a comprehensive security appraisement of the TUAK algorithm set. In summary, our security assessment on TUAK consists of three phases. First, we analyze the security of TUAK algorithms by performing various relevant cryptanalytic attacks on authentication and key derivation functions. We show the attack resistant properties of the TUAK algorithm set by providing the complexity of the attacks. Second, we present the security proofs on the soundness of the algorithms in TUAK when they are used as message authentication codes and key derivation algorithms. Finally, to further explore the security properties of TUAK, we develop a new cryptanalytic method, called multi-output filtering model, and apply it on TUAK. We study the algorithm f1 in more detail since it is the MAC generating function and more suitable for our attacking scenario. To better measure the performance of TUAK algorithms under this new attack, we also apply this technique on AES,KASUMI and PRESENT. Our study shows that f1 has very good randomness properties and performs similarly to AES under the same model.