RIBE Scheme Implementation - How to encrypt message This question is regarding "A Fully Secure Revocable ID-Based Encryption
in the Standard Model" - Tung-Tso TSAI, Yuh-Min TSENG, Tsu-Yang WU

The encryption method specifies part of the encryption process to be $\hat e(g_1, g_2)^r \cdot M$ where $g_1$ and $g_2$ are public parameters in cyclic group $G_1$, $\hat e$ is the pairing function and $M$ is the actual message.

My question is what this $\cdot$ operator actually implies for an implementation - is it taking chunks of the $M$ equal to the bit length of the result of $\hat e(g_1, g_2)^r$ and then adding* them together?

*My understanding, perhaps wrongly, is that the multiply operation for elliptic curve groups is  addition based on this
Given that the authors (as any sane person should¹) use multiplicative notation for all of the involved groups, "$\cdot$" simply represents the group operation in the target group $G_2$.

It does not seem to be explicitly specified as far as I can tell from skimming the paper, but this implies that the message space of the encryption scheme is exactly $G_2$, meaning that we always have $M\in G_2$. So there are no "chunks" involved.

If you want to encrypt a message directly with the scheme, this means that you will need to encode it as a $G_2$ element. If your message is too long for that, you will need to use one of the standard domain extension techniques, such as using the RIBE as a KEM in a hybrid encryption scheme.



¹This is a hill I'm willing to die on.