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

Xoring two permutations is a very simple way to construct pseudorandom functions from pseudorandom permutations. In [14], it is proved that we have security against CPA-2 attacks when m O(2), 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 “Hσ technique”. It will be interesting to compare the two techniques, their similarities and the differences between the proofs and the results.