# KP-ABE Key Generation

In Key Policy Attribute-based encryption if we need a targeted broadcast where the set of attributes are the same for a group of users. It means they all share the same secret key right? Or is it that every user needs to have at least 1 attribute value different from all other users.

Example: If I need to encrypt a message to everyone who is a researcher in CS then attribute= researcher dept=CS. Then in this case all share the same secret key.

• I don't know the exact setting of targeted broadcast encryption, but in the case of ABE itself, I think if the KeyGen (or Extract) algorithm be a randomized algorithm then the secret key of different users, even with same credits, will be different. Just encoded access structure part in their secret keys will be equal. Apr 29 at 8:32

I read your previous post also. In KP-ABE, the key space $$K$$ the set of all poly-sized boolean formulas $$φ(\vec z)=φ(z_1, z_2, ..., z_n)$$, so $$φ$$ is essentially a boolean function that is encoded into each user's key.
In a CS department for example, each person's key may have the following boolean formula format encoded into its key $$φ(\text{name, surname, rank, department}) = name \lor surname \lor rank \lor CS$$.
In KP-ABE each message can be decrypted iff the predicate $$P_{n} = 1$$, where $$P_{n}$$ is defined on $$K$$ x $$I$$ as
$$P_{n}(\phi \in K \backslash\{\epsilon\}, \text { ind }=\vec{z} \in I):= \begin{cases}1 & \text { if } \phi(\vec{z})=1, \text { and } \\ 0 & \text { otherwise }\end{cases}$$
and each plaintext is a pair $$(ind = \vec z, m)$$