Hardness assumptions on composite order bilinear groups I am not at all knowledgeable in elliptic curve cryptography. So, here lies a couple of questions that I failed to find answers for to my satisfaction.


Is there any known Type-III bilinear pairing defined over composite order groups?
Do DLIN/SXDH assumptions hold in composite order 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.