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Constructions of Beyond-Birthday Secure PRFs from Random Permutations, Revisited
Jiehui Nan1, Ping Zhang2, Honggang Hu1
1Key Laboratory of Electromagnetic Space Information, Chinese Academy of Sciences, School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China.
Abstract:
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 SoEM22 in the single-key setting. In this paper, we improve their work by proving the multi-key security of SoEM22, and further tweaking SoEM22 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.
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