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In Paillier, as you note, multiplication in the ciphertext domain translates to addition in the plaintext domain. Thanks to the algebraic structure behind Paillier what you can do to get subtraction is use the multiplicative. This works fine when the result is positive. When the result is negative, however, you would like to return that value, but what ...


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Based on the additional details in the comments, it seems like your question is: given $c_1=a\oplus d$ and $c_2=b\oplus d$, can we get $(a+b)\oplus d$. Where $a,b,d\in\mathbb{Z}_p$, $+$ is addition modulo $p$, and $\oplus$ is a bitwise XOR of the values, then taken modulo $p$. Or put another way, is there an operation $\boxplus$, such that $(a\oplus ...


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η is the bit-length of the secret key (which is the hidden approximate-gcd of all the public-key integers), SO u can calculate given functions and P should be the key that will be used and it should be between [2^η−1,2^η) Hope this answers your question


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It's actually straight-forward; we'll assume that all the inputs are either encrypted versions of 0, or encrypted version of 1; then: We can replace an AND gate with just an FHE multiplication of the two inputs: $$AND(x,y) = x*y$$ Where $*$ is our Homeomorpic multiplcation operation. This obviously evaluates to an encrypted 1 if both of the inputs are ...



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