# In paillier homomorphism, how is the randomness r changed during addition?

Two add the plaintexts encrypted in a ciphertext, you would just multiply the ciphertext and modulo it. However, how does the randomness value of the new ciphertext change? Assuming you the encryptor knew the randomness values in both ciphertexts, could you calculate the new randomness value?

• See this, if still, something is not clear, please indicate. Nov 27 '21 at 11:41
• Yes I see that r1 and r2 are now multiplied, but shouldn't that be highly likely to make the new r greater than n? Nov 27 '21 at 11:54
• What about the $\bmod n^2$. What is the ciphertext space? That is the crucial part of your missing point. Nov 27 '21 at 11:56
• yes i am missing the point, could you help point it out Nov 27 '21 at 23:29