Quantum Oracle Distribution Switching and Applications to Falcon and Ring Signatures

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Motivated by digital signature algorithms ranging from Falcon to fully-anonymous ring signatures used in Signal-style key exchange, such as Gandalf, we revisit a fundamental problem in post-quantum security proofs: distinguishing oracle functions whose outputs are sampled independently from distributions $P$ and $Q$ that are close. In the context of signatures, closeness is often measured via Rényi divergences, which yield multiplicative bounds in the classical setting. A counterexample shows th