Conquering Bad Norms in RstOE: Pure-Database Substitution and Early-Defense

The Recording Standard Oracle with Errors (RstOE) technique is an important tool for quantum security proofs in symmetric-key cryptography. However, against adaptive quantum chosen-plaintext adversaries, traditional RstOE-based proofs may suffer from the ``trivialization of norm” problem. This issue arises from three main causes: the delayed evaluation of bad events, the presence of unrecorded external variables, and the unconstrained independence of intermediate variables. To address this obsta