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:

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.