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Cryptosystems which support computation on encrypted data. They might be partially homomorphic (support for one operation such as + or *) or they might be fully homomorphic (any sequence of + and *).
4
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Is there a way of encryption that allows to check what encrypted values are close to their m...
If I understand what you're looking for correctly, that would completely destroy the security.
First off, if an attacker can compute the difference between her value and the mean, it is trivial to fi …