XPX: Generalized Tweakable Even-Mansour with Improved Security Guarantees

We present XPX, a tweakable blockcipher based on a single permutation P . On input of a tweak (t11, t12, t21, t22) ∈ T and a message m, it outputs ciphertext c = P (m⊕∆1)⊕∆2, where ∆1 = t11k⊕t12P (k) and ∆2 = t21k⊕t22P (k). Here, the tweak space T is required to satisfy a certain set of trivial conditions (such as (0, 0, 0, 0) 6∈ T ). We prove that XPX with any such tweak space is a strong tweakable pseudorandom permutation. Next, we consider the security of XPX under related-key attacks, where the adversary can freely select a key-deriving function upon every evaluation. We prove that XPX achieves various levels of related-key security, depending on the set of key-deriving functions and the properties of T . For instance, if t12, t22 6= 0 and (t21, t22) 6= (0, 1) for all tweaks, XPX is XOR-related-key secure. XPX generalizes Even-Mansour (EM), but also Rogaway’s XEX based on EM, and tweakable EM used in Minalpher. As such, XPX finds a wide range of applications. We show how our results on XPX directly imply related-key security of the authenticated encryption schemes Prøst-COPA and Minalpher, and how a straightforward adjustment to the MAC function Chaskey and to keyed Sponges makes them provably related-key secure.