# Multiple sender single receiver Encryption

I had this article given to me by my teacher, and I would like to enhance it. It's titled Modified El Gamal Algorithm for Multiple Senders and Single Receiver Encryption. I planned on having the algorithm accommodate multiple senders and receivers.

But I got really confused, and I would like to ask for some help in the encryption part of this modified algorithm.

[Key Generation]

receiver generates {P,g,a}, and sends {P,g,b} to public(?) for the senders to get.
P = prime
g = generator
a = private key of receiver
b = g^a


[Encryption]

Sender 1
generate R1 (private key)
computes c11 = g^R1

Sender 2
generate R2 (private key)
computes c12 = g^R2

Sender 3
generate R3 (private key)
computes c13 = g^R3

Message(m) is encrypted using this formula:

c2 = m*b^R2 / b^R1*b^R3

The cipher keys {c11,c12,c13,c2} are then sent to the receiver.



[Decryption]

m = c2*c11*c13 / c12


I would like to ask: how did the other senders get hold of the private keys of the other senders? I think I'm missing something.