Combiner. In many cases, certain cryptographic construction is believed to be secure, but later got broken. In order to build more robust systems. A combiner is one of such methods. Given two construc- tions (?1,?2) of a cryptographic primitive, a combiner will make calls to each construction and compile them into a third construction ?3. The third new construction will be secure as long as one of (?1,?2) is secure. Specifically, consider the following:

Given two constructions of symmetric encryption ?1 = (KeyGen1, Enc1, Dec1), ?2 = (KeyGen2, Enc2, Dec2), where the IND-CPA security of ?1 is based on Assumption-I, e.g, PRF, the IND-CPA security of ?2 is based on Assumption II, e.g., some mathematical assumption.

Construct a secure encryption scheme ?3 = (KeyGen3, Enc3, Dec3), which will be IND-CPA secure as long as one of Assumption-I or Assumption-II holds, and briefly explain why.