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**2013/368**

**Title:**

Security in O(2^n) for the Xor of Two Random Permutations\ – Proof with the standard H technique–

**Authors:**
Jacques Patarin

**Abstract:**

Xoring two permutations is a very simple way to construct pseudorandom functions from pseudorandom permutations. In~\cite{P08a}, it is proved that we have security against CPA-2 attacks when m \ll O(2^n), where m is the number of queries and n is the number of bits of the inputs and outputs of the bijections. In this paper, we will obtain similar (but slightly different) results by using the `standard H technique'' instead of the `

H_{\sigma} technique’'. It will be interesting to compare the two techniques, their similarities and the differences between the proofs and the results.

**ePrint:**
https://eprint.iacr.org/2013/368

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