Computation Hardness Assumptions?

I am thinking about using this implementation to implement an encryption scheme. Is the Bilinear Diffie-Hellman assumption believed to hold for this pairing? What about stronger assumptions (e.g., Strong Diffie-Hellman, Bilinear Diffie-Hellman Exponent, etc.)?

If you additionally know any papers/other sources discussing this, that would be very useful.

