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Having the following instructions:

  1. Using Paillier encryption to encrypt $m$. So, we get $Enc(m)$
  2. Multiply $Enc(m)$ and $A$ to Get $C$. So, $C = Enc(m).A $
  3. Decrypt $C$ using Paillier Decryption algorithm ($Dec(Enc(m).A)$

Knowing the value of $A$, is there a possibility to have $Dec(C) = A.Dec(m)$ ?

How can we get the value of $Dec(m)$ in this case.

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  • $\begingroup$ hint: See Wikipedia Paillier cryptosystem#Homomorphic properties $\endgroup$ – kelalaka Aug 30 '20 at 21:31
  • $\begingroup$ But in my case, I do not have a multiplication of two ciphertext or addition of two ciphertext. I have a multpilication of a ciphertext with a plaintext as C $\endgroup$ – sof Aug 30 '20 at 21:51
  • $\begingroup$ Now, can you assume that $A=g^x$ for some $x$? $\endgroup$ – kelalaka Aug 30 '20 at 23:03

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