# Use of the master key in Delerablée's Identity-based Broadcast Encryption

I'm reading “Identity-Based Broadcast Encryption with Constant Size Ciphertexts and Private Keys” by Cécile Delerablée.

On page 207, the encryption process needs $\gamma$ which is part of the master key. This does not make sense to me.

I want to know whether I read this thesis wrongly or not. Can anybody give me a opinion?

That value can be computed with the data you have in the public key. You just need to use the fact: $$h^{\gamma} \times h^{H(ID)} = h^{\gamma + H(ID)}.$$
Note that in the public key you have all the $h^{\gamma^i}$ you need for the computation.
If you want to compute the correct value you could compute the product: $$\pi = \prod_{i=1}^s (\gamma + H(ID_i))$$ considering $\gamma$ as unknown and later compute $h^\pi$ making the needed substitutions.