# Do we need to consider overflow in paillier encryption?

Homomorphic multiplication of plaintexts in Paillier cryptosystem can be constructed as follow: Dsk(E(x1)^x2 mod N^2) = x1x2 mod N. So after the decryption, we get the result of multiplication x1x2. My question is, is it necessary for us to think about the situation : x1*x2>N which leads to an overflow? Or because the parameter N is quite large(usually 1024 bits or even 2048 bits) so in most usage scenarios we don't have to consider this problem by default?