# Identify the value of the plaintext from a noised expression

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.

• hint: See Wikipedia Paillier cryptosystem#Homomorphic properties – kelalaka Aug 30 '20 at 21:31
• 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 – sof Aug 30 '20 at 21:51
• Now, can you assume that $A=g^x$ for some $x$? – kelalaka Aug 30 '20 at 23:03