When homomorphic encryption goes wrong? Consider I have two ciphertext $c_1$ and $c_2$ encrypted using RSA encryption. By definition if I multiply them I'd get $c_1.c_2 \ modN$. My question is what would happen if $c_1.c_2 &gt;N$. Can we still decrypt it and obtain the product of two plaintext?
Yes; as long as the product of the two plaintexts $p_1 \cdot p_2 &lt; N$, you'll get their product; it doesn't matter what the ciphertext values actually are.

The relevant question is: what happens if the plaintexts overflow; that is, what if $p_1 \cdot p_2 \ge N$?  In that case, when you decrypt, you'll get the result $p_1 \cdot p_2 \bmod N$