Dear Cypherpunks community,

   I came across a post on the Whonix forum recently. Since I am also
   interested in this question I copied it here:

   [1]https://forums.whonix.org/t/math-behind-honest-tor-nodes/12464

   [2]http://forums.dds6qkxpwdeubwucdiaord2xgbbeyds25rbsgr73tbfpqpt4a6vjws
   yd.onion/t/math-behind-honest-tor-nodes/12464

   The question (edited):

   How can I calculate how much impact X honest Tor relays have?

   Is it better to calculate with bandwidth consumed (250Gbps), despite
   the number of relays (~7000)?

   Basically, I want to get the mathematical equation to this statement:

   I run X Tor relays at Y Mb/s each and by doing so I secure Z % of the
   Tor network!

   Starting thoughts:

   - Each “normal” route has three nodes involved: Guard, Middle, Exit

   - I am aware of guard pinning and vanguard protection for middle relay
   pinning

   - Maybe it is easier to assume an infinite usage time of the network to
   eliminate guard and vanguard pinning

   - I guess the best is to assume a scenario with 1%, 5%, 10%, etc.
   dishonest relays

   My take on this:

   Tor has approximately 7000 relays.
   If I consider a number of 5% malicious relays, this would be: 350

   My calculation:

   (1/(7000/350))*(1/(7000/349))*(1/(7000/348))

   = 0.000123931

   = 0.0123931%
   1) Is my approach correct?
   2) Not every relay has the same bandwidth. How could I change the
   calculation to make it more realistic?
   3) How can I add the effect of guard fixation?
   4) How can I include the effect of mid-node fixation by the vanguard?

   I would love to hear your thoughts about it and a concrete math
   equation would be amazing.

References

   1. https://forums.whonix.org/t/math-behind-honest-tor-nodes/12464
   2. http://forums.dds6qkxpwdeubwucdiaord2xgbbeyds25rbsgr73tbfpqpt4a6vjwsyd.onion/t/math-behind-honest-tor-nodes/12464