Security Proof in Fuzzy Identity Based Encryption?

Been having a great deal of difficulty understanding the use of simulators to prove security of ABE schemes so I though I would start from the first ABE paper (Fuzzy Identity Based Encryption) to try and understand it better.

From my understanding of the use of simulators, the idea is to show that a simulator can be created which is acting in the ideal world but through the view of the Adversary who is acting in the real world and showing that they both learn the same amount of information and have the same advantage (Correct me here if I am wrong!)

My other question is basically an explanation of what the author has done in Phase 1 (Most confusing part is the highlighted section). Are there any predetermined guidelines that the author has followed that I need to familiarize myself with? or is it at the discretion of the author to have used the procedures he used in that phase?

Also how did the author get the final advantage of the simulator?

• Are you familiar with simulation-based proofs in general? If not, the recent tutorial of Lindell may be of interest. – fkraiem Jun 20 '16 at 17:18
• @fkraiem I have looked at the tutorial and from it I understand the underlying approach and reasoning behind the process. I still cant seem to connect it with the security proofs of the ABE schemes I have been studying. – chisky Jun 20 '16 at 18:27
• Actually, that is a standard game based proof, no simulation based one. What the authors denote as simulator here is actually the reduction that simulates the challenger in the fuzzy selective ID game for the adversary. – DrLecter Jun 21 '16 at 2:59
• @DrLecter this means I may have been approaching it all wrong then. Could you provide me with additional details or point me towards the right resources? Also is there a guideline they follow in their selection of values for the the different variables? – chisky Jun 21 '16 at 13:46
• @chisky If you are entirely new to such types of game based proofs, starting with fuzzy ibe may not be the best strategy. I would recommend to study IND-CPA proofs of classical simple encryption schemes such as ElGamal and then maybe ibe schemes (such as Boneh Franklin - which builds upon the ideas behind ElGamal, but in a bilinear setting) and then come back to fuzzy ibe or abe. – DrLecter Jun 21 '16 at 14:13