Dishonest Tor relay math question - tor-talk is to lazy

[grarpamp]

> 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?

Generically, assuming you're only running the
exit use case, not the HS onion case.

You'll probably want to consider some adjustments...

- There's not 7k exits, only ~1k, but it's a ratio term
so then it only matters if you're expecting different
densities of bad/good across each of the guard/mid/exit roles.
- There's not 7k guards, only ... .
- tor only uses family, /nn cidr blocks, etc once in a circuit...
effect is not 7k nodes, but G groups made up of 1-N nodes.
Read torspec, scrape consensus, determine the resultant
number G that tor actually gives itself to choose from.
- Some nodes are down, sleeping, busy, filtered, etc.
- Not all exits serve the clearnet ports you want.
- Circuits expire, nodes rotate, etc.

> 2) Not every relay has the same bandwidth. How could I change the
> calculation to make it more realistic?

Read torspec, scrape consensus, determine how tor is
allocating clients across its bandwidth gravity well, etc.
See also...
https://metrics.torproject.org/

> 3) How can I add the effect of guard fixation?
> 4) How can I include the effect of mid-node fixation by the vanguard?

You didn't really define exactly what attack ("dishonesty")
you're trying to model, so these settings could render you
anywhere from safe, to having no effect and thus still being
subject to the exploit.

See also...
https://anonbib.freehaven.net/
https://git.torproject.org/torspec/