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computation time. If all workers function at the same speed and execute a job in a unit time,
then T is given by dN/We unit times and error rate is given as N × f × s/N = f × s .
It might be readily apparent that is proportional to the number of saboteurs and sabotage
rate s .
The sabotage model are classified into the following two major classes depending on
the values of incorrect results from saboteurs.
Random attack model [23]
Random attack model is the simplest sabotage model. In this mode, each saboteur
returns a random incorrect result with probability s . The values of those incorrect
results are determined at random and never match each other.
Collusion attack model
A potential threat of collusion attack comes up in recent VC systems as Zhao et al.
[26] acknowledge. In fact, actual developments such as collaborative data distribution
[30] or P2P systems [31] are enabling connection of workers. These solutions violate
the workers independence assumption, as they enable workers to communicate and
collude, thus empowering sabotage.
In this chapter, we define a collusion attack model as an extension of the random
attack model to treat colluding of saboteurs. The saboteurs in the collusion attack
model can communicate with each other, and return incorrect results which have the
same value to increase the probability that the master accepts their incorrect results.
The collusion attack model are classified into the following three categories depend-
ing on the colluding method, e.g. how to determine the values of incorrect results.
- Predefined colluding method
Predefined colluding is the simplest colluding method. In this method, the val-
ues of incorrect results are predefined for each job. Hence, when saboteurs
collude, all incorrect results of job j x have the same incorrect value x . In pre-
defined colluding method, a saboteur colludes with probability c , i.e. colluding
rate for each job allocation.
The values of incorrect results in predefined colluding method are summarized
as follows. When job j x is allocated to a saboteur, the value of incorrect result
is set to specified value x with probability s × c and set to a random value with
probability s × (1 − c) .
- Direct colluding method
Direct colluding method allows a saboteur to communicate with other saboteur
directly and determine the incorrect value for every sabotaging. Thus, the values
of incorrect results are dynamically determined by saboteurs who communicate
with each other (colluding group). In this method, the number of saboteurs in
each colluding group tends to be small since all saboteurs in a colluding group
must know informations of all saboteurs in the gruop for direct communications.
- Indirect colluding method
Indirect colluding method extends direct colluding to enable building an exten-
sive colluding group of saboteurs. Instead of the direct communication among
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