Sepandar D. Kamvar
Mario T. Schlosser
held by the author/owner(s).
WWW2003, May 20-24, 2003, Budapest, Hungary.
We describe an algorithm to decrease the number of downloads of inauthentic files in a peer-to-peer file-sharing network that assigns each peer a unique global trust value, based on the peer's history of uploads. We present a distributed and secure method to compute global trust values, based on Power iteration. By having peers use these global trust values to choose the peers from whom they download, the network effectively identifies malicious peers and isolates them from the network.
In simulations, this reputation system, called EigenTrust, has been shown to significantly decrease the number of inauthentic files on the network, even under a variety of conditions where malicious peers cooperate in an attempt to deliberately subvert the system.
C.2.4Computer-Communication NetworksDistributed Systems[Distributed applications]H.3.3Information SystemsInformation Storage and Retrieval[Selection]H.2.7Information SystemsDatabase Management[Security, integrity and protection]
Attacks by anonymous malicious peers have been observed on today's popular peer-to-peer networks. For example, malicious users have used these networks to introduce viruses such as the VBS.Gnutella worm, which spreads by making a copy of itself in a peer's Gnutella program directory, then modifying the Gnutella.ini file to allow sharing of .vbs files . Far more common have been inauthentic file attacks, wherein malicious peers respond to virtually any query providing ``decoy files'' that are tampered with or do not work.
It has been suggested that the future development of P2P systems will depend largely on the availability of novel methods for ensuring that peers obtain reliable information on the quality of resources they are receiving . In this context, attempting to identify malicious peers that provide inauthentic files is superior to attempting to identify inauthentic files themselves, since malicious peers can easily generate a virtually unlimited number of inauthentic files if they are not banned from participating in the network. We present such a method wherein each peer is assigned a unique global trust value that reflects the experiences of all peers in the network with peer . In our approach, all peers in the network participate in computing these values in a distributed and node-symmetric manner with minimal overhead on the network. Furthermore, we describe how to ensure the security of the computations, minimizing the probability that malicious peers in the system can lie to their own benefit. And finally, we show how to use these values to identify peers that provide material deemed inappropriate by the users of a peer-to-peer network, and effectively isolate them from the network.
There are five issues that are important to address in any P2P reputation system.
An important example of successful reputation management is the online auction system eBay . In eBay's reputation system, buyers and sellers can rate each other after each transaction, and the overall reputation of a participant is the sum of these ratings over the last 6 months. This system relies on a centralized system to store and manage these ratings.
In a distributed environment, peers may still rate each other after each transaction, as in the eBay system. For example, each time peer downloads a file from peer , it may rate the transaction as positive () or negative ( ). Peer may rate a download as negative, for example, if the file downloaded is inauthentic or tampered with, or if the download is interrupted. Like in the eBay model, we may define a local trust value as the sum of the ratings of the individual transactions that peer has downloaded from peer : .
Equivalently, each peer can store the number satisfactory transactions it has had with peer , and the number of unsatisfactory transactions it has had with peer , . Then, is defined:
Previous work in P2P reputation systems [6,1] has all been based on similar notions of local trust values. The challenge for reputation systems in a distributed environment is how to aggregate the local trust values without a centralized storage and management facility. While each of the previous systems cited above addresses this issue, each of the previous systems proposed suffers from one of two drawbacks. Either it aggregates the ratings of only a few peers and doesn't get a wide view about a peer's reputation, or it aggregates the ratings of all the peers and congests the network with system messages asking for each peer's local trust values at every query.
We present here a reputation system that aggregates the local trust values of all of the users in a natural manner, with minimal overhead in terms of message complexity. Our approach is based on the notion of transitive trust: A peer will have a high opinion of those peers who have provided it authentic files. Moreover, peer is likely to trust the opinions of those peers, since peers who are honest about the files they provide are also likely to be honest in reporting their local trust values.
We show that the idea of transitive trust leads to a system where global trust values correspond to the left principal eigenvector of a matrix of normalized local trust values. We show how to perform this eigenvector computation in a distributed manner with just a few lines of code, where the message complexity is provably bounded and empirically low. Most importantly, we show that this system is highly effective in decreasing the number of unsatisfactory downloads, even when up to 70% of the peers in the network form a malicious collective in an attempt to subvert the system.
In this section, we describe the EigenTrust algorithm. In EigenTrust, the global reputation of each peer is given by the local trust values assigned to peer by other peers, weighted by the global reputations of the assigning peers. In Section 4.1, we show how to normalize the local trust values in a manner that leads to an elegant probabilistic interpretation and an efficient algorithm for aggregating these values. In Section 4.2, we discuss how to aggregate the normalized trust values in a sensible manner. In Section 4.3, we discuss the probabilistic interpretation of the local and global trust values. In Section 4.4 through Section 4.6, we present an algorithm for computing the global trust values.
In order to aggregate local trust values, it is necessary to normalize them in some manner. Otherwise, malicious peers can assign arbitrarily high local trust values to other malicious peers, and arbitrarily low local trust values to good peers, easily subverting the system. We define a normalized local trust value, , as follows:
This ensures that all values will be between 0 and 1. (Notice that if , then is undefined. We address this case in Section 4.4.) There are some drawbacks to normalizing in this manner. For one, the normalized trust values do not distinguish between a peer with whom peer did not interact and a peer with whom peer has had poor experience. Also, these values are relative, and there is no absolute interpretation. That is, if , we know that peer has the same reputation as peer in the eyes of peer , but we don't know if both of them are very reputable, or if both of them are mediocre. However, we are still able to achieve substantially good results despite the drawbacks mentioned above. We choose to normalize the local trust values in this manner because it allows us to perform the computation that we describe below without renormalizing the global trust values at each iteration (which is prohibitively costly in a large distributed environment) and leads to an elegant probabilistic model.
We wish to aggregate the normalized local trust values. A natural way to do this in a distributed environment is for peer to ask its acquaintances about their opinions about other peers. It would make sense to weight their opinions by the trust peer places in them:
We can write this in matrix notation: If we define to be the matrix and to be vector containing the values , then . (Note that as desired.)
This is a useful way to have each peer gain a view of the network that is wider than his own experience. However, the trust values stored by peer still reflect only the experience of peer and his acquantainces. In order to get a wider view, peer may wish to ask his friends' friends ( ). If he continues in this manner, ( ), he will have a complete view of the network after large iterations (under the assumptions that is irreducible and aperiodic, which we guarantee in practice and address in Section 4.5).
Fortunately, if is large, the trust vector will converge to the same vector for every peer i. Namely, it will converge to the left principal eigenvector of . In other words, is a global trust vector in this model. Its elements, , quantify how much trust the system as a whole places peer .
It is useful to note that there exists a straightforward probabilistic interpretation of this method, similar to the Random Surfer model of . If an agent were searching for reputable peers, it can crawl the network using the following rule: at each peer , it will crawl to peer with probability . After crawling for a while in this manner, the agent is more likely to be at reputable peers than unreputable peers. The stationary distribution of the Markov chain defined by the normalized local trust matrix is our global trust vector .
In this section, we describe the basic EigenTrust algorithm, ignoring for now the distributed nature of the peer-to-peer network. That is, we assume that some central server knows all the values and performs the computation. In Section 4.6, we describe how the computation may be performed in a distributed environment.
We simply wish to compute , for large, where we define to be the -vector representing a uniform probability distribution over all peers, . (In Section 4.2, we said we wish to compute , where is the normalized local trust vector of some peer . However, since they both converge to the principal left eigenvector of , we may use instead.)
At the most basic level, the algorithm would proceed as in Algorithm 1.
A priori notions of trust. Often, there are some peers in the network that are known to be trustworthy. For example, the first few peers to join a network are often known to be trustworthy, since the designers and early users of a P2P network are likely to have less motivation to destroy the network they built. It would be useful to incorporate such notions of trust in a natural and seamless manner. We do this by defining some distribution over pre-trusted peers. For example, if some set of peers are known to be trusted, we may define if , and otherwise.) We use this distribution in three ways. First of all, in the presence of malicious peers, will generally converge faster than , so we use as our start vector. We describe the other two ways to use this distribution below.
Inactive Peers. If peer doesn't download from anybody else, or if it assigns a zero score to all other peers, from Equation 1 will be undefined. In this case, we set . So we redefine as:
Malicious Collectives. In peer-to-peer networks, there is potential for malicious collectives to form . A malicious collective is a group of malicious peers who know each other, who give each other high local trust values and give all other peers low local trust values in an attempt to subvert the system and gain high global trust values. We address this issue by taking
The modified algorithm is given in Algorithm 2.
It should be emphasized that the pre-trusted peers are essential to this algorithm, as they guarantee convergence and break up malicious collectives. Therefore, the choice of pre-trusted peers is important. In particular, it is important that no pre-trusted peer be a member of a malicious collective. This would compromise the quality of the algorithm. To avoid this, the system may choose a very few number of pre-trusted peers (for example, the designers of the network). A thorough investigation of different methods of choosing pre-trusted peers is an interesting research area, but it is outside of the scope of this paper.
Here, we present an algorithm where all peers in the network cooperate to compute and store the global trust vector, and the computation, storage, and message overhead for each peer are minimal.
In a distributed environment, the first challenge that arises is how to store and . In previous sections, we suggested that each peer could store its local trust vector . Here, we also suggest that each peer store its own global trust value . (For presentation purposes, we ignore issues of security for the moment and allow peers to store their own trust values. We address issues of security in Section 5.)
In fact, each peer can compute its own global trust value:
Secondly, in most P2P networks, each peer has limited interaction with other peers. There are two benefits to this. First, the computation is not intensive, since most are zero. Second, the number of messages passed is small, since and are small. In the case where a network is full of heavily active peers, we can enforce these benefits by limiting the number of local trust values that each peer can report.
Second, we can specifically limit the number of local trust values that a peer reports. In the modified version of EigenTrust, each peer reports a subset of its total set of local trust values. Preliminary simulations have shown this scheme to perform comparably well as the algorithm presented here, where peers report all of their local trust values.
We combat this by implementing two basic ideas. First, the current trust value of a peer must not be computed by and reside at the peer itself, where it can easily become subject to manipulation. Thus, we have a different peer in the network compute the trust value of a peer. Second, it will be in the interest of malicious peers to return wrong results when they are supposed to compute any peer's trust value. Therefore, the trust value of one peer in the network will be computed by more than one other peer.
In the secure version of the distributed trust algorithm, M peers (dubbed score managers of a peer ) compute the trust value of a peer . If a peer needs the trust value of peer , it can query all M score managers for it. A majority vote on the trust value then settles conflicts arising from a number of malicious peers being among the score managers and presenting faulty trust values as opposed to the correct one presented by the non-malicious score managers.
To assign score managers, we use a distributed hash table (DHT), such as CAN  or Chord . DHTs use a hash function to deterministically map keys such as file names into points in a logical coordinate space. At any time, the coordinate space is partitioned dynamically among the peers in the system such that every peer covers a region in the coordinate space. Peers are responsible for storing (key, value) pairs the keys of which are hashed into a point that is located within their region.
In our approach, a peer's score manager is located by hashing a unique ID of the peer, such as its IP address and TCP port, into a point in the DHT hash space. The peer which currently covers this point as part of its DHT region is appointed as the score manager of that peer. All peers in the system which know the unique ID of a peer can thus locate its score manager. We can modify our initial algorithm such that it can be executed by score managers.
, is mapped into points covered by peers 2, 3 and 6, respectively, by hash functions , and . Thus, these peers become peer 1's score managers.
To cope with the inherent dynamics of a P2P system, we rely on the robustness of a well-designed DHT. For example, when a score manager leaves the system, it passes on its state (i.e., trust values or ongoing trust computations) to its neighbor peer in the DHT coordinate space. DHTs also introduce replication of data to prevent loss of data (in this case, trust values) in case a score manager fails.
Here we describe the secure algorithm to compute a global trust vector. We will use these definitions: Each peer has a number of score managers, whose DHT coordinates are determined by applying a set of one-way secure hash functions to the peer's unique identifier. are the coordinates of peer in the hash space. Since each peer also acts as a score manager, it is assigned a set of daughters - the set contains the indexes of peers whose trust value computation is covered by the peer. As a score manager, peer also maintains the opinion vector of its daughter peer (where ) at some point in the algorithm. Also, peer will learn which is the set of peers which downloaded files from its daughter peer : It will receive trust assessments from these peers referring to its daughter peer . Finally, peer will get to know the set which denotes the set of peers which its daughter peer downloaded files from: Upon kicking off a global trust value computation, its daughter peer is supposed to submit its trust assessments on other peers to its score manager, providing the score manager with .
Upsides of the secure algorithm in terms of increased security and reliability include:
Anonymity. It is not possible for a peer at a specific coordinate to find out the peer ID for whom it computes the trust values - hence malicious peers cannot increase the reputation of other malicious peers.
Randomization. Peers that enter the system cannot select at which coordinates in the hash space they want to be located (this should be a property of a well-designed DHT) - hence it is not possible for a peer to, for example, compute the hash value of its own ID and locate itself at precisely this position in the hash space to be able to compute its own trust value.
Redundancy. Several score managers compute the trust value for one peer. To assign several score managers to a peer, we use several multi-dimensional hash functions. Peers in the system still take over a particular region in the coordinate space, yet now there are several coordinate spaces, each of which is created by one multi-dimensional hash function. A peer's unique ID is thus mapped into a different point in every multi-dimensional hash space.
A couple of points are important to note here. First, the issue of secure score management in P2P networks is an important problem, with implications for reputation management, incentive systems, and P2P micropayment schemes, among others. An extended discussion of secure score management in P2P networks, and various concrete score management schemes (including a variant of the one presented above), are given in . The main contribution of this work is not in the secure score management scheme, but rather in the core EigenTrust algorithm. We discuss the secure score management scheme because some secure score management scheme is essential to the EigenTrust algorithm. However, it is important to note that the core EigenTrust algorithm may be used with many different secure score management schemes.
Second, the secure protocols proposed here and in  describe how to use large collections of entities to mitigate singular or group-based manipulation of the protocol. These protocols are not secured in the traditional sense; rather, we can show that the probability is small that a peer is able to get away with misreporting a score. This is discussed further in .
Isolating Malicious Peers. When peer issues a query, the system may use the trust values to bias the user towards downloading from more reputable peers. One way to do this would be to have each peer download from the most highly trusted peer who responds to its query. However, such a policy leads to the most highly trusted peers being overloaded, as shown in Section 7. Furthermore, since reputation is built upon sharing authentic files, this policy does not enable new peers to build up reputation in the system.
A different strategy is to select the peers from whom to download probabilistically based on their trust values. In particular, we can make type probability that a peer will download a file from responding peer be directly proportional to the trust value of peer .
Such a policy limits the number of unsatisfactory downloads on the network, while balancing the load in the network and allowing newcomers to build reputation. The experiments in Section 7 validate this.
It should be noted here that peers may easily choose to bias their choice of download by a convex combination of the global trust values and their own local trust assessments of other peers (and use the trust values given by the vector , where is a constant between 0 and 1. This way, a peer can avoid downloading from a peer that has given it bad service, even if it gives the rest of the network good service.
Incenting Freeriders to Share. Secondly, the system may reward peers with high trust values. For example, reputable peers may be rewarded with increased connectivity to other reputable peers, or greater bandwidth. Rewarding highly trusted peers has a twofold effect. First, it gives users an incentive to share files, since a high global trust value may only be achieved by sharing authentic files. In the current Gnutella network, less than 7% of the peers are responsible for over 50% of the files, and as many as 25% of peers on the network share no files at all . Incentives based on trust values should reduce the number of free riders on peer-to-peer networks. Some such incentives are discussed in .
Second, rewarding highly trusted peers gives non-malicious peers an incentive to delete inauthentic files that they may have accidentally downloaded from malicious peers, actively keeping the network tidy. This makes it more difficult for inauthentic files to replicate in the system.
Network model. We consider a typical P2P network: Interconnected, file-sharing peers are able to issue queries for files, peers can respond to queries, and files can be transferred between two peers to conclude a search process. When a query is issued by a peer, it is propagated by broadcast with hop-count horizon throughout the network (in the usual Gnutella way), peers which receive the query forward it and check if they are able to respond to it. We interconnect peers by a power-law network, a type of network prevalent in real-world P2P networks .
Node model. Our network consists of good nodes (normal nodes, participating in the network to download and upload files) and malicious nodes (adversarial nodes, participating in the network to undermine its performance). In our experiments, we consider different threat models, where a threat model describes the behavior of a malicious peer in the network. Threat models will be described in more detail later on. Note also that, based on the considerations in Section 4.5, some good nodes in the network are appointed as highly trusted nodes.
Content distribution model. Interactions between peers - i.e., which queries are issued and which queries are answered by given peers - are computed based on a probabilistic content distribution model. The detailed model will not be described here, it is presented in . Briefly, peers are assumed to be interested in a subset of the total available content in the network, i.e., each peer initially picks a number of content categories and shares files only in these categories. Reference  has shown that files shared in a P2P network are often clustered by content categories. Also, we assume that within one content category files with different popularities exist, governed by a Zipf distribution. When our simulator generates a query, it does not generate a search string. Instead, it generates the category and rank (or popularity) of the file that will satisfy the query. The category and rank are based on Zipf distributions. Each peer that receives the query checks if it supports the category and if it shares the file. Files are assigned probabilistically to peers at initialization based on file popularity and the content categories the peer is interested (that is, peers are likely to share popular files, even if they have few files). The number of files shared by peers and other distributions used in the model are taken from measurements in real-world P2P networks .
Simulation execution. The simulation of a network proceeds in simulation cycles: Each simulation cycle is subdivided into a number of query cycles. In each query cycle, a peer in the network may be actively issuing a query, inactive, or even down and not responding to queries passing by. Upon issuing a query, a peer waits for incoming responses, selects a download source among those nodes that responded and starts downloading the file. The latter two steps are repeated until a peer has properly received a good copy of the file that it has been looking for. Upon the conclusion of each simulation cycle, the global trust value computation is kicked off. Statistics are collected at each node, in particular, we are interested in the number of authentic and inauthentic up- and downloads of each node. Each experiment is run several times and the results of all runs are averaged. We run an experiment until we see convergence to a steady state (to be defined in the descriptions of the experiments), initial transient states are excluded from the data.
The base settings that apply for most of the experiments are
summarized in Table 1. The settings
represent a fairly small network to make our simulations
tractable. However, we have experimented with larger networks in
some instances and our conclusions continue to hold. That is,
schemes that do well in a small setting, do proportionately as
well as the network is scaled up. Also note that our settings
describe a pessimistic scenario with a powerful adversary:
Malicious peers connect to the most highly connected peers when
joining the network (see Section 7.3),
they respond to the top 20% of queries received and thus have a
large bandwidth, they are able to communicate among themselves in
most of our threat models, and they make up a significant fraction
of the network in most of our experiments. Yet, our experiments
indicate that our scheme works well in this hostile a scenario,
and thus will also work in less hostile
Before we consider the strengths of our scheme in suppressing inauthentic downloads in a P2P network, we examine if it leads to unwanted load imbalance in the network. In the following section, we also give a precise definition on how we use global trust values in downloading files.
If are the trust values of peers responding to a query, the deterministic and probabilistic algorithms proceed as follows.
To give new peers in the network - which start with a global trust value of 0 - the chance of building up reputation, the probabilistic algorithm assigns a fixed 10% chance to download from the group of responding peers with trust value 0. Otherwise, new peers would maybe never be chosen as download source, depriving them of the chance to become a trusted member of the network. Based on our experience, a probability of 10% strikes a balance between granting malicious peers (which might also have a trust value of 0) too high a chance of uploading inauthentic files and allowing new peers to prove themselves as download sources of authentic files.
We compare these download source selection algorithms to a network where no reputation system is deployed, i.e., among peers responding to a query a peer is picked as download source entirely at random. We examine the load distribution in these networks. We do not assume the existence of any malicious peers in this experiment.
Setup. We simulate a network consisting of 20 good peers, no pre-trusted peers and no malicious peers. Other than that, the standard settings in Table 1 apply. After running queries on the system for 20 query cycles, the load distribution is measured in Figures 3 and 4: For each peer 1 - 20 in the network, we depict its load share, i.e., the fraction of its uploads after a full run of the experiment divided by the total number of uploads in the entire network. The load distribution in a network using the deterministic download source selection algorithm is compared to the load distribution in a network using no reputation system at all in Figure 3, whereas a system employing the probabilistic download source selection algorithm is compared to the non-trust based network in Figure 4.
Discussion. Always choosing the responding peer with the highest global trust value as download source leads to a vast load imbalance in the network: Popular peers do not stop accumulating trust value and gain further popularity. In Figure 3, peer 2 will eventually become the download source for virtually all queries that it is able to answer. Also note that in each experiment we ran another peer turned out to be the most trusted peer. Choosing download sources probabilistically yields only a slight deviation in terms of individual load share of each peer from the case where trust values are not used to select download sources among responding peers, therefore leading to a much better natural load distribution in the network. In Figure 4, peer 2 becomes the download source for 8% of all queries in the system, and many other peers participate in sharing the load, mainly determined by the number of and popularity of files the peers share. Our measurements also show that the efficiency in suppressing inauthentic downloads does not vary between the two approaches. Thus, for the remaining experiments we use the probabilistic peer selection algorithm.
We start our experiments considering the simplest threat model, where malicious peers are not initially aware of other malicious peers and simply upload inauthentic files.
Threat Model A. Individual Malicious Peers. Malicious peers always provide an inauthentic file when selected as download source. Malicious peers set their local trust values to be , i.e., malicious peers value inauthentic file downloads instead of authentic file downloads.
Setup. We simulate a network consisting of 63 good nodes, 3 of which are highly trusted nodes, applying the standard settings from Table 1. In each experiment, we add a number of malicious peers to the network such that malicious nodes make up between 0% and 70% of all nodes in the network. For each fraction in steps of 10% we run experiments and depict the results in Figure 5. Upon joining the network, malicious peers connect to the 10 most highly connected peers already in the network in order to receive as many queries travelling through the network as possible. In practice, P2P protocols such as the Gnutella protocol enable nodes to crawl the network in search of highly connected nodes. We run the experiments on a system where download sources are selected probabilistically based on our global trust values and on a system where download sources are chosen randomly from the set of peers responding to a query. Bars depict the fraction of inauthentic files downloaded in one simulation cycle versus the total number of files downloaded in the same period of time. The results are averaged over the last 10 query cycles in each experiment.
Discussion. In the absence of a reputation system, malicious peers succeed in inflicting many inauthentic downloads on the network. Yet, if our scheme is activated, malicious peers receive high local trust values only from other malicious peers, and even that only occasionally - since malicious peers have to happen to get acquainted with each other through a file exchange. Because of their low trust values, malicious peers are rarely chosen as download source which minimizes the number of inauthentic file downloads in the network. We observed a 10% fraction of inauthentic downloads, mostly due to the fact that good nodes make mistakes once in a while and upload inauthentic files (for example, by not deleting a downloaded inauthentic file from their shared folders). Even if no malicious peers are present in the network, downloads are evaluated as inauthentic in 5% of all cases - this accounts for mistakes users make when creating and sharing a file, e.g., by providing the wrong meta-data or creating and sharing an unreadable file.
Note that, due to the fact that our current secure algorithm uses majority vote, a cooperating malicious collective that comprises over 40% of the network will be able to influence the assignment of global trust values values in the network during their computation. This is not represented in Figure 5, which assumes that the trust values are computed correctly. However, it is unlikely that over 40% of the peers in a network are in a single malicious collective, unless the malicious collective is a result of pseudospoofing (a.k.a. the Sybil attack ), where a single adversary initiates thousands of peers onto the network. This type of attack can be avoided by imposing a cost of entry into the network. For example, a peer wishing to enter the network may be required to solve a puzzle that a computer cannot solve [3,5]. Currently, YAHOO! requires a user to read some text from a JPEG file in order to open a YAHOO! Mail account.
Thus, in knowing that our scheme is present in a system, malicious peers know that they have to gain a somewhat high local trust value in order to be considered as download sources. Therefore, we will examine strategies on how malicious peers can increase their global trust value despite uploading inauthentic files.
Since malicious peers cannot expect to receive any high local trust values from non-malicious peers, they can try to increase their global trust value by teaming up as a malicious collective. In the experiment depicted in Figure 6, we vary the number of malicious peers in the network to assess their impact on the network's performance when they are aware of each other and form a malicious collective.
Threat Model B. Malicious Collectives. Malicious peers always provide an inauthentic file when selected as download source. Malicious peers form a malicious collective by assigning a single trust value of 1 to another malicious peer in the network. Precisely, if denotes the set of malicious peers in the network, each sets
Setup. We proceed exactly as in the previously described experiment, albeit with malicious nodes operating under threat model B. As shown in Figure 6, we run the experiments on a system where download sources are selected based on our global trust values and on a system where download sources are chosen randomly from the set of peers responding to a query.
Discussion. Our system performs well even if a majority
of malicious peers is present in the network at a prominent place.
The experiment clearly shows that forming a malicious collective
does not decisively boost the global trust values of malicious
peers: These peers are tagged with a low trust value and thus
rarely chosen as download source. The system manages to break up
malicious collectives through the presence of pre-trusted peers
(see Section 4.4): If pre-trusted
peers were not present in the network, forming a malicious
collective in fact heavily boosts the trust values of malicious
nodes. Under the presence of pre-trusted peers, the local trust values
of malicious peers are significantly lower than those of good
peers already after one simulation cycle. This minimizes the
number of inauthentic downloads, and the numbers are virtually
equal to the numbers in Figure 5
when peers do not form a malicious collective. For example, with
40% of all peers in a network being malicious, around 87% of all
file downloads will end up in downloading an inauthentic version
of the file in a normal, non-trusted network. Upon activation of
our scheme, around
10% of all file downloads return an inauthentic file.
Forming a malicious collective obviously does not increase the global trust values of malicious peers sufficiently in order for them to have impact on the network. This leaves malicious peers with one choice: They have to increase their local trust values by receiving positive local trust values from at least some good and trusted peers in the network. In the experiment in Figure 7, we consider a strategy for malicious peers that is built on the idea that malicious peers try to get some positive local trust values from good peers.
Threat Model C. Malicious Collectives with Camoflouge. Malicious peers provide an inauthentic file in % of all cases when selected as download source. Malicious peers form a malicious collective as described above.
Setup. We simulate a network consisting of 53 good peers, 3 of which are pre-trusted peers, and 20 type C malicious peers applying the standard settings in Table 1. In each experiment, we apply a different setting of parameter in threat model B such that the probability that malicious peers return an authentic file when selected as download source varies from 0% to 90%. We run experiments for each setting of parameter in steps of 10%. Running the experiments on both a non-trust based system and on our system yields Figure 7. Bars depict the fraction of inauthentic files downloaded in one simulation cycle divided by the total number of files downloaded in the same period of time.
Discussion. Malicious peers that operate under threat model C attempt to gain positive local trust values from some peers in the network by sometimes providing authentic files. Thus, they will not be assigned zero trust values by all peers in the network since some peers will receive an authentic file from them. This in turn provides them with higher global trust values and more uploads - a fraction of which will be inauthentic. Figure 7 shows that malicious peers have maximum impact on the network when providing 50% authentic files: 28% of all download requests return inauthentic files then. However, this strategy comes at a cost for malicious peers: They have to provide some share of authentic files, which is undesirable for them. First of all, they try to prevent the exchange of authentic files on the network, and in this strategy they have to participate in it; second, maintaining a repository of authentic files requires a certain maintenance overhead.
Figure 8 depicts the trade-off between authentic (horizontal axis) and inauthentic (vertical axis) downloads. Each scenario from Figure 7 is represented by one data point in Figure 8. For example, consider the fourth dark bar in Figure 7, corresponding to and our reputation scheme in place. In this scenario, malicious peers provide 1850 authentic downloads and 5000 inauthentic ones in a particular run. The value is plotted in Figure 8 as the fourth data point (left to right) on the lower curve, representing the case when our reputation scheme is used. The points on each curve represent increasing values, from left to right.
In Figure 8, malicious nodes would like to operate in the upper left quadrant, providing a high number of inauthentic downloads, and a low number of authentic downloads. However, the file sharing mechanism in place constrains malicious nodes to operate along one of the curves shown. Without our reputation scheme (top curve), malicious nodes can set to a small value and move to the upper left quadrant. On the other hand, with our scheme, malicious peers have no good choices. In particular, increasing beyond 20% does not make much sense to malicious peers since the incremental authentic uploads they have to host outnumber the increase in inauthentic downloads. Moreover, for all settings of parameter below 50%, malicious peers will lose all positive local trust values assigned by other peers in the long run - since on average they do provide more inauthentic than authentic files.
Notice that the lines cross at the lower right hand side. This does not show that the non-trust-based scheme works better for high values of . Rather, it shows that, when the trust-based scheme is implemented, malicious peers must upload more authentic files in order to be able to upload the same number of inauthentic files. This is the desired behavior.
The previous experiment has shown that malicious peers can increase their impact by partly concealing their malicious identity. Yet over time, their malicious identity will be uncovered and they lose their impact on the network. In the experiment in Figure 9, we consider a team effort strategy that malicious peers can use to work around this drawback. Two different types of malicious peers are present in the network: Malicious nodes of type B and of type D.
Threat Model D. Malicious Spies. Malicious peers answer 0.05% of the most popular queries and provide a good file when selected as download source. Malicious peers of type D assign trust values of 1 to all malicious nodes of type B in the network. Precisely, if and denote the set of malicious type B peers resp. type D peers in the network, each sets
Setup. We simulate a network consisting of 63 good peers, 3 of which are pre-trusted peers, and 40 (39%) malicious peers, divided into two groups of malicious type B and type D peers. Otherwise, the standard settings from Table 1 apply. In each experiment, we consider a different number of type B and type D peers. Configurations considered are: I. 40 type B, 0 type D peers II. 39 type B, 1 type D peer III. 36 type B, 4 type D peers IV. 35 type B, 5 type D peers V. 30 type B, 10 type D peers VI. 25 type B, 15 type D peers VII. 20 type B, 20 type D peers VIII. 15 type B, 25 type D peers IX. 10 type B, 30 type D peers X. 5 type B, 35 type D peers. From left to right, we plot these data points in a graph that depicts the number of inauthentic file downloads versus the number of authentic file uploads provided by malicious peers, as in the previous experiment.
Discussion. Malicious peers establish an efficient division of labor in this scheme: Type D peers act as normal peers in the network and try to increase their global trust value, which they will in turn assign to malicious nodes of type B providing inauthentic files. The malicious nature of type D peers will not be uncovered over time since these peers do not provide inauthentic files - hence they can continue to increase the global local trust values of type B peers in the network. An interesting configuration for malicious peers would be configuration I: Malicious peers provide a fairly low number of authentic downloads (around 100), yet achieve almost the same number of inauthentic downloads in the network as in other configurations with a higher share of authentic downloads by malicious peers. In any configuration though, our scheme performs better than a system without trust-based download source selection. Also, this strategy would probably be the strategy of choice for malicious peers in order to attack a trust-based network: For example, by hosting 500 authentic file uploads in this strategy malicious peers achieve around 5000 inauthentic file downloads - as opposed to about 2500 inauthentic file downloads in the previous strategy, given the same effort on providing authentic uploads.
Threat Model E. Sybil Attack. An adversary initiates thousands of peers on the network. Each time one of the peers is selected for download, it sends an inauthentic file, after which it disconnected and replaced with a new peer identity.
Discussion. This threat scenario simply takes advantage of the fact that the fudge-factor that allows previously unknown users to obtain a reputation can be abused. Essentially, because there is no cost to create a new ID, the adversary can dominate that pool (with ghost identities). Because 10% of all traffic goes to the ``unknown'' pool, the malicious entity can behave arbitrarily without fear of losing reputation. To make matters worse, this kind of attack will prevent good peers from being able to garner a good reputation (they are so outnumbered that they will almost never be selected).
However, this threat scenario can be averted by imposing a cost to creating a new ID as discussed in Section 7.3 and . For example, if a user must read the text off of a JPEG (or solve some other captcha ), it will be costly for a single adversary to create thousands of users.
Threat Model F. Virus-Disseminators. (variant of threat model C) A malicious peer sends one virus-laden (inauthentic) copy of a particular file every 100th request. At all other times, the authentic file is sent.
Discussion. This is a threat scenario that is not addressed by EigenTrust. EigenTrust greatly reduces - but does not completely eliminate - corrupt files on a P2P network. This is useful on a file-sharing network where executables are not shared. If executables are introduced that have potential to do great damage, then malicious peers can develop strategies to upload a few of them. But it should be noted that no reputation system to date claims to completely eliminate all corrupt files on a P2P network in an efficient manner. It should also be noted that the main problem on today's P2P networks is not the distribution of malicious executables (i.e. viruses), but rather the flooding of the network with inauthentic files. This is likely because today's P2P networks are mostly used to trade digital media, and relatively few users make use of these networks to share executables.
An overview of many key issues in reputation management is given in . Trust metrics on graphs have been presented in  and . Beth et al. , also use the notion of transitive trust, but their approach is quite different from ours. Reputation systems for P2P networks in particular are presented in  and , and are largely based on notions similar to our local trust values. The contribution of this work is that it shows how to aggregate the local trust assessments of all peers in the network in an efficient, distributed manner that is robust to malicious peers.
We would like to thank the reviewers of this paper for detailed and insightful comments.
This paper is supported in part by the Research Collaboration between NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation and CSLI, Stanford University (research project on Concept Bases for Lexical Acquisition and Intelligently Reasoning with Meaning).