(Diffie-Hellman)

1) extend Diffei Hellman protocol to four people (P_0...P3) so that P₀ can send messages only to P₁,..., P₃ can send messages only to P₀ - and explain why it is safe against a passive adversary that can only listen to messages, but it is not safe agaisnt an active adversary that can change messages that are being transmitted between participants.

2) improve the protocol you've written so it will be safe against an active adversary that can change messages in only one communication line(for instance it can only change messages between P₂ to P₃). Hint for 2: to do so, now each participant can change messages to two participants whose index is bigger/small by 1. for instance: P₃ can send messages to either P_{2 or} P₀ explain well what you did and show the algorithm you changed. thank you very much for helping me!