I implemented Multi authority Attribute based Chameleon Hash function MAP-ABCH.

I implemented Multi authority Attribute based Chameleon Hash function MAP-ABCH. I need to analyze the security and the math behind this algorithm based on Bilinear Diffie Hellman or Elliptic curve. Please read the attached reports to understand the algorithm and to prove how the function is Indistinguishable , Private collision resistance and public collision resistance based on Decisional Diffie Hellman Problem .
The paper in the material is a previous work that explains how they prove similar function I need something similar to MAP-ABCH