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It is known that the security evaluation can be done by smoothing of Renyi entropy of order 2 in the classical ans quantum settings when, the authors apply universal2 hash functions. This fact can be extended to the case when, they apply almost dual universal2 hash functions. They approximately demonstrate the smoothing of Renyi entropy of order 2, and derived security bounds for universal composability and mutual information criterion under the condition in the classical and quantum setting. Further, they apply this analysis to the secret key generation with error correction.
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