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Do PHE schemes in general also suffer from noise overflow problem?

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If by PHE you mean systems such as Paillier, then the answer is no. They don't have noise as in FHE and SWHE.

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  • $\begingroup$ May i ask why is that PHE schemes do not suffer from noise overflow? $\endgroup$ – fallere456 Aug 20 at 10:49
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    $\begingroup$ Very imprecisely, in FHE, the noise and the plaintext are in the same space. When evaluating a function $f$ homomorphically, you are actually computing $ f(plaintext + noise)$. The noise can be eliminated from the result only if it does not exceed a certain modulus, e.g. see here crypto.stackexchange.com/questions/35150/…. In PHE, the problem does not exist. The plaintext is always being evaluated in its own space. Although PHE also uses random numbers in encryption, the random numbers don't interfere with the plaintext in the homomorphic computation. $\endgroup$ – Changyu Dong Aug 20 at 12:38
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    $\begingroup$ The above comment could be added to the answer.. $\endgroup$ – fgrieu Aug 20 at 15:08

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