p2psp team mailing list archive

[Vicente Gonzalez <vicente.gonzalez.ruiz@xxxxxxxxx>]

On Tue, Mar 31, 2015 at 8:29 PM Ilshat Shakirov <im.shakirov@xxxxxxxxx>
wrote:

> Hello!,
>
> Thanks for your feedback =)
>

You're welcome :-)


>
> I couldnt generalize my formula for different values of trusted peers and
> attackers. But I generalized it for different number of trusted peers in
> the team.
> Here it is:
>
> ​where n is size of the team without splitter and T is number of trusted
> peers.
> The main idea is that the attacker will be detected when he will send
> poisoned chunk to trusted peer. The time when he will send poisoned chunk
> to trusted peer depends on position of trusted peer in his peer list.
> So the denominator of fraction is just all the possible combinations of
> trusted peers in peer list.
> And the numerator is all possible combinations of T-1 trusted peers in
> peer list. In more detail:
> The attacker is able to send *#i* poisoned chunks when he has trusted
> peer exactly in* #i* position in his peer list. In [1, #i) he can't have
> trusted peers. So we have T-1 peers and we should place them in remaining
> positions ((#i, n-1)) of peer list.
>

For me your reasonings sound fine. Good job!

Tomorrow I will perform experiments on simulator in order to confirm that
> formula.
>

OK.


> Now I don't know how to generalize the formula to different number of
> attackers, because we expel attacker after we detect him and team size
> become lower. I think I need help with that problem =)
> Thanks in advance for your feedback =)
>

Could be:

\sum_{j=1}^{A} E(n-j)

where E(x) = your formula (where n=x) and A = number of attackers?

(The idea is that the size of the team will be reduced by 1 each time a
attacker has been uncovered. So, the accumulated average number of poisoned
chunks should be the sum the expected number of poisoned chunks, for each
number of attackers).

Hope this helps!


>
> ps Python impl is OK =)
>

OK, thanks.

Best,
Vi.