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This question is related. Note that this question does say that security is analyzed by comparison with AES/SHA3, as you suspect. Perhaps the most informative way to learn more about this is to go "hands on" though, and read the security analysis sections of various NIST PQC round 3 candidates. These should be close to the community consensus of ...


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There's really very little that can be done in this sort of situation. The noise is only parameterised by $\Delta f/\epsilon$ where $\Delta f$ precisely represents how much the function changes when such an outlier is added or removed from a queried set and $\epsilon$ precisely quantifies how hard it is for an adversary to detect a change. Your options are ...


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If both secure schemes are UC-secure, combining them to design a new secure scheme is also secure in terms of the security properties defined in the original secure schemes. It has been proved in the UC framework.


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