CAKE requires programming - On the provable post-quantum security of (O)CAKE

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We revisit the post-quantum security of Password-Authenticated Key Ex- change (PAKE) from Key Encapsulation Mechanisms (KEM), focusing on (O)CAKE. Despite extensive study, these protocols still lack a security proof against quantum adversaries. We pinpoint exactly why by identifying the precise remaining obstacle. Most game-hopping arguments extend to the quantum setting via standard QROM techniques. The difficulty lies with ideal ciphers: adaptive programming and query recording are well und