Multiple sender single receiver Encryption
They do not share their private keys, but they do have to share b^R(i) for each sender i.

What they might do is, the first sender supplies mb^R(1), the second will supply mb^R(1)^R(2) and so on for the numerator round (two rounds). To do this they need to come together (in your paper there is, "Simultaneously, the senders compute for the value of c2 using the formula...").