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Is there a higher probability, if an attacker is using one OR of bandwidth 5 MB/s than 5 ORs with each 1 MB/s?

If you calculate the probability of picking a certain OR, you can use the weighted Bandwidth, because a OP is picking random ORs for the circuit, besides other characteristics proportional to its weighted Bandwidth. If you want to calculated the probability whether an malicious OR will be picked, I would draw the conclusion, that you can use the total of malicious (weighted)Bandwidth.

Example: Lets say the attacker Bob uses a 5 ORs, each 1MB/s bandwidth (total bandwidth 5 MB/s). And attacker Lucy uses only one OR with a total bandwidth of 5 MB/s. Would there be a difference in terms of probability? What is more likely? An OR of Bob being picked or from Lucy?

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There are multiple practical reasons where five ORs of bandwidth X MB/s each could be superior to one OR of bandwidth 5X MB/s. There are some restrictions and exceptions to this point in general. This list is not meant to be the comperhensive list of all possible advantages and/or disadvantages, but give you enough clues to get the idea. Let us start and list some of them:

  1. Down times

Any system would have down time for variety of reasons. Five distributed system is much less prone to catastrophic failure than one centeral system. This is straight out of a basic reliability manual. In this case at down times Lucy would have zero probability of success, while Bob would have some probability of success. This assumes all five systems will not go down simultaneously.

  1. Distribution

It is clear that one 5X system can be located at a single location, while five systems can be distributed worldwide. One scenario may look at distribution of relays worldwide and distribute the five relays at the top five locations that relays are located at (Germany, France, US, etc.). Now the attacker can make sure that folks who may reject certain locations due to their convictions, still have a chance of falling into trap.

  1. Efficency

Having 5X amount of bandwidth does not necessarily means that it is fully being utilized. If anybody for any reason suspect an specific relay or a country that a given relay is located at, it maybe avoided. This can go to a point that the relay is no longer working efficiently. Distributing the system to several smaller units at different locations and under different names will alleviate this problem. In addition each relay can be configured to accept or reject specific tasks independently. This makes the analysis of data much faster.

In Short it is not enough to produce a 5X MB/s relay. One need to gain the trust or at least the perceived trust of Tor and its users to be efficiently effective attacker (or non attacker for that matter). This can be facilitated by starting a large number of relays rather than a small number of relays even at constant capacity.

Obviously, there maybe a cost disadvantage to running multiple relays even at constant capacity.

Some of the restrictions and exceptions to this analysis are:

  1. The total bandwidth should not be so low that when you divide it into several parts it become unusable. I believe, if not mistaken, the minimum advisable relay bandwidth per Tor guidlines is currently about 250 kB/s.

  2. The cost analysis should not be so prohibitive that make this exercise untenable. If you can increase the capacity with some of this fund you may do so and make the best compromizes.

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