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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 *).
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FHE over the integers - Is that paper's scheme known to be insecure against quantum adversar...
According to the answer by Hilder Vitor Lima Pereira in the this question, the main scheme is believed to be quantum secure.