Many papers have demonstrated that the XOR of two random permutations (PRPs) is beyond-birthday-bound (BBB) secure. However, I have not found similar research results for the XOR of two random functions (PRFs). Is it possible to transfer the BBB security results of the XOR of PRPs to the XOR of PRFs using simple methods, such as the PRP/PRF switching lemma? However, I have struggled to find an effective approach, since the gap in the PRP/PRF switching lemma itself is a birthday bound.
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