Welcome to the resource topic for
**2019/554**

**Title:**

How to Build Pseudorandom Functions From Public Random Permutations

**Authors:**
Yu Long Chen, Eran Lambooij, Bart Mennink

**Abstract:**

Pseudorandom functions are traditionally built upon block ciphers, but with the trend of permutation based cryptography, it is a natural question to investigate the design of pseudorandom functions from random permutations. We present a generic study of how to build beyond birthday bound secure pseudorandom functions from public random permutations. We first show that a pseudorandom function based on a single permutation call cannot be secure beyond the 2^{n/2} birthday bound, where n is the state size of the function. We next consider the Sum of Even-Mansour (SoEM) construction, that instantiates the sum of permutations with the Even-Mansour construction. We prove that SoEM achieves tight 2n/3-bit security if it is constructed from two independent permutations and two randomly drawn keys. We also demonstrate a birthday bound attack if either the permutations or the keys are identical. Finally, we present the Sum of Key Alternating Ciphers (SoKAC) construction, a translation of Encrypted Davies-Meyer Dual to a public permutation based setting, and show that SoKAC achieves tight 2n/3-bit security even when a single key is used.

**ePrint:**
https://eprint.iacr.org/2019/554

**Talk: **https://www.youtube.com/watch?v=fMRlqmbO2W8

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