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

us flag

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?

kelalaka avatar
in flag
See [this](https://crypto.stackexchange.com/q/76470/18298), if still, something is not clear, please indicate.
Manglemix avatar
us flag
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?
kelalaka avatar
in flag
What about the $\bmod n^2$. What is the ciphertext space? That is the crucial part of your missing point.
Manglemix avatar
us flag
yes i am missing the point, could you help point it out
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