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["L.G.Casado" <leo@xxxxxx>]

Dear Ilshat,
El mar, 11-08-2015 a las 12:46 +0600, Ilshat Shakirov escribió:
> Hello!,
> 
> Sorry for the some delay.
> 
> Regarding math predictions about buffer correctness and avg. number
> of rounds to expel all the malicious peers:
> a) Buffer correctness
> I don't know how to evaluate the buffer correctness in team with
> trusted peers, but without them it's an easy task:
> BC = 1 - M / (N - 1 + 1) = 1 - M / N, where M - number of malicious
> peers and N - team size. I've confirmed this model with some
> experiments (using my script, I've run the team without trusted
> peers).
According to your definition BC= correct chuncks/ correct+bad, in
[0,1]. Let's see the extreme cases:
M=0, N=10 -> BC=1/10, which should be 1.
M=N=10 -> BC=-9/10, which should be 0.
Instead it can be BC=N-M/N.
M=0, N=10 -> BC=10/10=1
M=N=10 -> BC=0/0=0
Trursted peers, means that M<N. 
> b) Average Number of rounds> I've made some assumptions>  in this problem:1. The trusted peer checks every X-th chunk (in current implementation X is a random value)> 2. The probability to check chunk from malicious peer is P = M / (N - 1) where M is number of malicious peer and N is a teamsize (for one trusted peer).
N-1, is set because there is one Trusted peer, does it?
How is set X, random check yes/no? 
Best,
Leo
> > Let's calculate probability to check chunk from malicious peer for T (>1) trusted peers. It will be:

> 
> > P(A) = T * (\frac{M}{N - 1} * (1 - \frac{M}{N - 1})^{T - 1})> > Now we can use this formula:> This formula calculates probability to get one success from n experiments.> So, q = 1 - P(A), and we can assign P smth like 0.95 and calculate n - required number of checks to discover malicious peer with prob. 0.95> Then, the required number of rounds to expel one malicious peer equals R = n * X / N, where N is teamsize.> 
> Now, I am performing tests with STrPe and STrPe-DS mechanisms, I will provide some results asap.> 
> Thanks!> 

> 2015-08-05 1:41 GMT+06:00 Juan Álvaro Muñoz Naranjo > <juanalvaro83@xxxxxxxxx>> :
> > 

> > 

> > > One remarkable result here is the fact that having a second trusted
> > >  peer does not have a real impact on malicious peer expulsion. I realize
> > >  now that this is due to how the Str technique is designed. Not for 
> > > GSoC, but maybe we should think of a evolution of the protocol that 
> > > reflected the aggregation of trusted peers. Cristóbal, that might be 
> > > intersting if it has not been researched yet.> > > > But adding second trusted peer accelerates the expulsion of attackers, you can see it in the last graphs (-m 50 -t 1 and -m 50 -t 2) : in the case of one trusted there not all attackers were expelled from the team for given time, and in the second case - all attackers were expelled by ~100 round.> > 
> > Ok let me rephrase like this: the addition of a second trusted peer has little impact. The speed at which expulsions are done is comparable, and for the 1 trusted peer case the remaining malicious peers are 1 or 2 at most. But you're right, having 2 peers eliminates all malicious peers in all cases, which is already a remarkable result ;)> > 

> > Can't wait to see what happens with 4 and 8!> > 

> > Juan
> > 


>