Post-Quantum Security of Keyed Sum of Permutations and Its Siblings

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The rapid advancement of quantum computing poses significant challenges to the security of existing cryptographic constructions. Several constructions that are provably secure in the classical setting, e.g., the $3$-round Luby–Rackoff, Even–Mansour, Keyed Sum of Permutations, become vulnerable when the adversary is granted quantum oracle access (the Q2 model). In contrast, when the adversary is restricted to classical oracle queries while retaining the ability to perform quantum computations loc