Hardness assumptions on composite order bilinear groups
The BGN (Boneh Goh Nissam) cryptosystem uses a Type-III bilinear pairing defined over composite order groups to have 1 homomorphic multiplication along with unlimited homomorphic additions.
You may want to have a look at their paper: Evaluating 2-DNF Formulas on Ciphertexts, or any lecture on this cryptosystem.

I hope this will help you.