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What is the security of multiple encryption using Even–Mansour scheme (XEX)?

This is better known as iterated Even-mansour or key-alternating cipher. From Theorem 1 of Hoang-Tessaro we have $$ \mathrm{Adv}^{\pm\mathrm{prp}}_{\mathrm{KAC}[\pi,t]} \le \frac{4^tqp_1\cdots p_t}{2^{...
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