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For an easy to grasp explanation, you can have a look at the talk Obfuscation I at the Cryptography Bootcamp by Amit Sahai. Here's a link to youtube. In this context he also explains matrix branching programs, which are also used in the construction of indistuingishability obfuscation. He starts explaining them at the minute 40. In short: You're given $2k$ ...


A toy example would be this simple map with $\mathbb{G} = \mathbb{Z}/5$ to $\mathbb{G}_T = \mathbb{Z}^*/11$, as follows: $$e(x,y) = 3^{xy} \bmod 11$$ It's easy to verify that both equations hold (except that $e(0,0) = 1$; that's actually a necessary consequence of the first equation, and so I'll consider that an acceptable exception). Of course, even if ...

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