Constructions of Beyond-Birthday Secure PRFs from Random Permutations, Revisited

In CRYPTO 2019, Chen et al. showed how to construct pseudorandom functions (PRFs) from random permutations (RPs), and they gave one beyond-birthday secure construction from sum of Even-Mansour, namely [Formula: see text] in the single-key setting. In this paper, we improve their work by proving the multi-key security of [Formula: see text] , and further tweaking [Formula: see text] but still preserving beyond birthday bound (BBB) security. Furthermore, we use only one random permutation to construct parallelizable and succinct beyond-birthday secure PRFs in the multi-key setting, and then tweak this new construction. Moreover, with a slight modification of our constructions of tweakable PRFs, two parallelizable nonce based MACs for variable length messages are obtained.