# Collusion Attack CP-ABE

Suppose that there are Alice with attributes $A$ and $C$ and Bob with attributes $B$ and $D$. I have a ciphertext with this policy: $A\ \operatorname{AND}\ B$.

Why don't users collude ? If Alice sends the attribute $A$ to Bob, he could regenerate private key and decrypt the document. Why is this not possible ? I don't understand this concept (I'm reading Security intuition in Ciphertext-Policy Attribute-Based Encryption).

Collusions are not possible here since each user's private keys are randomized. As you can see in the Key Generation function, for each user a random value $r$ is generated and embedded into all his private keys. Therefore, if you try to use private keys from different users, you will not be using the same random $r$ during the decryption process, so it will fail.
• Private keys are usually created by an Attribute Authority, who is in possession of a master key $MK$. Users cannot create private keys since they don't now $MK$. – cygnusv Mar 1 '16 at 11:38