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3

The problem can be simplified to the following problem, since the standard argument doesn't really take into account that you can't generate all the polynomials of the given maximum degree : Assume that we have sampled a random point $\vec{x}\in \mathbb{F}_p^n$. We let an adversary adaptively choose polynomials of degree at most $d$ and after each choice ...

0

Layering your encryption mechanisms like that would not display collusion-resistance between the two schemes. For example, someone with an Org-A key could decrypt the outer encryption over a record designated for Org-A administrators and then pass the inner ciphertext to someone with an Administrator key. Of course, you could use a different key for each ...

3

The BSW07 CP-ABE scheme is a pairing based construction. Denoting the pairing as $e:G\times G\rightarrow G_T$ (symmetric notation for simplicity), the message space of this scheme is the prime order $q$ group $G_T$, which in practice is a prime order $q$ subgroup of the multiplicative group of some finite field. Consequently, if you have a message $m$ and ...

4

In real world applications Attribute-based Encryption (ABE) is used in conjunction with a symmetric cipher, because you can only encrypt group elements with ABE. In this case it is the multiplicative group $G_T$. The number of bits is limited when you try to represent text messages (bit strings) with a group element, because the size of the group is derived ...

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