Efficient Anonymization of the SocioNetwith the Aid of Rumor Riding

Hiroki IIZUKA1 and Satoshi FUJITA11Department of Information Engineering, Hiroshima University

Higashi-Hiroshima, 739-8527, Japan

Abstract— In this paper, we propose an anonymized objectsearch scheme for the SocioNet which is an unstructuredP2P based on the notion of the similarity of interests. Theproposed scheme is an application of a randomized objectsearch scheme proposed by Liu et al. called Rumor Riding(RR, for short). We propose two techniques to overcome theinefficiency of a simple application of the RR to the SocioNet.The performance of the proposed scheme is evaluated bysimulation. The simulation result indicates that the proposedscheme reduces the number of messages to a half of a simplecombination, and additionally, shows that the number ofdelegates selected in the RR severely affects the success rateof the overall scheme particularly when the TTL is not large.

Keywords: Peer-to-Peer content sharing, anonymity of users,object search, Rumor Riding, SocioNet.

1. IntroductionRecent advancement of network technologies enables us

to easily share various contents over the Internet. For exam-ple, YouTube attracts more than 1 billion unique user visitsper month and the upload of 100 hours of video every minutein 2014. A key issue to realize such a content sharing overa large network is how to find the location of a requestedobject. In particular, the support of an efficient object searchis a crucial issue for Peer-to-Peer (P2P) applications sincein those systems, objects are generally stored in the localstorage of each peer without being collected to a specificserver as in classical content sharing services.

Flooding of queries with a designated TTL (time to live) isa simple but commonly used technique to realize an efficientobject search in P2P networks. There are many proposalsconcerned with the variations of the query flooding, whichincludes LightFlood [3], Diff-Flooding [2] and UMPS [10].Among them, we are interested in the object search basedon an unstructured overlay reflecting the interest of theusers. SocioNet [4] and UIM [1] are representatives of suchapproaches. The key idea of such similarity-based overlaysis to connect peers to have similar interests by a link sothat the peer which issues a query, called questioner, canbe connected with a peer which has an object matching thequery, called respondent, through a path consisting of asmall number of links. By adopting such an overlay, the

efficiency of query flooding can be significantly improvedcompared with random overlays [4]. However, although itcertainly improves the efficiency, it causes a serious risk foreach user so that the fact of issuing a query, the fact ofresponding to the query and the content of the query andthe reply are disclosed to all peers to have similar interests.In other words, such a simple flooding could not preservethe privacy of users which is a crucial drawback of the mostof existing flooding-based object search schemes.

In this paper, we focus on the SocioNet as the underlyingsimilarity-based P2P, and propose a scheme to preserve theanonymity of users in the network. The proposed schemeis an application of a randomized method proposed byLiu et al. called Rumor Riding (RR, for short) [5]. Thekey idea of the RR is to select delegates through randomwalk and to make those delegates to conduct actual queryflooding and the response to the query (see Section 3 for thedetails). It is evaluated by simulation that such a randomizedapproach could certainly preserve the anonymity of userswhile keeping the cost reasonably low. However, a directapplication of the RR to the SocioNet is not efficient sincethe RR was originally proposed for random overlays and theapplication of the RR loses the benefit of the SocioNet sothat the distance between the questioner and the respondentis short. To overcome such an issue, this paper proposes twotechniques to improve the efficiency of the object search inthe SocioNet in terms of the number of messages which isnecessary to keep a high success rate.

The performance of the proposed scheme is evaluated bysimulation. The result of simulation indicates that it reducesthe number of messages to a half of a simple combination ofthe RR and the SocioNet, and additionally, it shows that thenumber of delegates severely affects the success rate whenthe given TTL is not large. More precisely, we found thatthe number of delegates, which can be controlled by tuningparameters used in the RR, should be at least three to attaina high success rate while keeping the number of messagessufficiently low.

The remainder of this paper is organized as follows.Sections 2 and 3 describe an overview of the SocioNet andthe basic flow of the RR, respectively. Section 4 describes theproposed scheme. Section 5 describes the simulation result.Finally, Section 6 concludes the paper with future work.

2. SocioNet2.1 Overview

The SocioNet is an unstructured P2P based on the notionof similarity of interests. Each link in the SocioNet is eithera similarity link or a random link. The former is intended toconnect peers to have similar interests so that a query issuedby a peer easily hits a target object with high probabilitywhich is expected to be held by a peer to have similar interestto the questioner, and the latter is intended to connect apair of remote peers so that the resulting network has ashort diameter. Random links are established by rewiringsimilarity links with a certain probability β through randomwalk, as in the Watts and Strogatz’s scheme to constructsmall-world networks [9] (the value of parameter β is set toaround 0.2 to 0.3 in the SocioNet).

The search of a target object is done through the floodingof a query as in conventional P2Ps, while the existenceof similarity links could significantly reduce the number ofmessage transmissions required for attaining a given hit ratecompared with random overlays such as Gnutella [8].

2.2 Similarity of PeersThe similarity of peers is defined as follows. Let Oi be

the set of objects held by peer i. Assume that each objectis attached tags representing the attributes of the object,e.g., a music file of the performance of Benny Goodmanwill be attached tags Jazz, Clarinet and Swing. Let T ={t1, t2, . . . , tj , . . .} denote the (universal) set of tags. Foreach peer i and tag tj ∈ T , let Oi,tj denote the set ofobjects attached tag tj in set Oi. Then, the relevance of tagtj with peer i is defined as

wi,tjdef=

|Oi,tj ||Oi|

.

For example, if peer i has 100 objects and 50 of them areattached tag Jazz, then wi,Jazz = 50100 = 0.5. The profile ofpeer i, denoted by w⃗i, is a vector of relevances, i.e.,

w⃗idef= (wi,t1 , wi,t2 , . . . , wi,tj , . . .).

With the above notions, the similarity of peer j for peer i isdefined as follows

sim(i, j)def=

|Oi||Oj |

× 1cos(w⃗i, w⃗j)

, (1)

where peer j with a smaller sim(i, j) is more favorable forpeer i as an adjacent peer connected by a similarity link.The reader should note that the above notion of similarity isnot symmetrical. If fact, even if two peers a and b have thesame profile w⃗ = w⃗a = w⃗b, when |Oa| < |Ob|, we have

sim(a, b) < 1 < sim(b, a),

that is, b would be favorable for a but the reserve is not true.

Questioner

Sower

Flooding of decrypted query

Random walk of query rumors

rC

rK

Fig. 1: Steps 1 and 2 in the Rumor Riding.

2.3 Update ProcedureWith the above notions, the SocioNet establishes similar-

ity links in two different ways. The first way is to use a serverwhich keeps the similarity for all pairs of peers to select pairsto have high similarity in a centralized manner. The secondway, which will be adopted in the proposed scheme, is touse random walk. More concretely, each peer i which wishesto update its similarity links first conducts x independentrandom walks, where x is the (maximum) degree of thepeer in the overlay. At any peer in the random walk, it stopswith probability c/ logN for some constant c so that theexpected length becomes O(logN), where N is the numberof peers in the network, and the peer at the stopped point isregarded as the candidate for new neighbors. Among those xcandidates and the currently adjacent x peers, peer i selectsx peers to have highest similarity to peer i, and updatesneighbors so that it is connected to the selected x peers.

3. Rumor RidingRumor Riding (RR) is a scheme to realize an anonymous

object search in unstructured P2Ps. The basic idea of theRR is to delegate the roles of the flooding of a query andthe reply to the query to randomly selected peers calledsowers. With such a randomized mechanism, we can keepthe anonymity of the questioner and the respondent. Inaddition, to keep the security of message transmissions, eachmessage is encrypted by the sender of the message using thepublic key of the receiver.

The protocol for the object search in RR consists of fivesteps. In the following, we explain each step in detail.

Step 1: Generation of Query RumorsLet i be the questioner. At first, peer i generates a public

key K+i and inserts it to the content of the query, whereK+i will be used to encrypt the reply to the query by therespondent. Let q be the plain text of the resulting messageincluding K+i . Peer i then encrypts q with a symmetric keyK into a cipher text C, then organizes two query rumors rK

rC’

Questioner

Sower

Direct forwarding of decrypted reply

Random walk of rumors

rC

rK

Sower

Respondent

rK’

Fig. 2: Step 3 in the Rumor Riding.

and rC , where rK and rC are messages containing K and C,respectively. Those rumors are sent out to different neighborsof peer i and start an (independent) random walk with anappropriate TTL (more precisely, peer i generates k suchpairs of rumors to increase the probability of those rumors“meeting” at a peer, where k is an appropriate parameter;it is experimentally verified that k and the TTL should bedetermined so that their product is from 100 to 200, i.e., ifk is four then the TTL should be from 25 to 50 [5]). SeeFigure 1 for illustration.

Step 2: Sowers Concerned with the QuestionerIn the RR, a peer which receives both rK and rC serves as

a delegate of the questioner called sower. More concretely,after decrypting message q from K and C, each sower startsthe flooding of q to its neighbors and waits for the reply tothe query from an appropriate respondent. After receiving areply message from the respondent, which is encrypted withthe public key K+i of the questioner i and is separated intotwo rumors similar to the separation of q into rK and rC ,it sends back those rumors to the questioner along the pathstraveled by rK and rC , respectively, in the reverse direction.The reader should note that to enable such a behavior of thesower and the other intermediate peers, the RR should forceevery peer to cache all rumors passing through the peer fora certain time so that it is expired after the reply message issuccessively received by the questioner.

Step 3: Reply from the RespondentSuppose that query q transmitted by a sower s is received

by a peer j holding an object matching the query. Afterreceiving q, peer j generates a reply message and encryptsit with the public key K+i of the questioner i. Let R bethe resulting cipher text. Peer j then encrypts R and the IPaddress of s with a symmetry key K ′ into a cipher text C ′,then organizes two reply rumors rK′ and rC′ similar to Step1. Those rumors are sent out to different neighbors and startan (independent) random walk, as before. If a peer receivesboth rK′ and rC′ from its neighbors, then the peer serves

Questioner

Sower

Direct forwarding of decrypted ACK

Random walk of rumors

Sower

Respondent

Fig. 3: Step 4 in the Rumor Riding.

as the sower concerned with the respondent as follows: 1) itdecrypts R and the IP address of s from reply rumors, and2) it directly forwards reply rumors to sower s. See Figure2 for illustration.

Step 4: ACK MessageAfter receiving reply rumors rK′ and rC′ , the questioner i

decrypts R from C ′ with symmetry key K ′ and then decryptsthe reply message from R with the secret key of peer i.Then peer i sends an ACK message to the respondent jin the following manner: 1) it encrypts the ACK messageinto a cipher text with the public key of j (which shouldbe contained in the reply message); 2) it organizes tworumors from the cipher text as in previous steps; and 3) itsends out those rumors to different neighbors, as before. Thesower conceded with the ACK message directly forwardsthe received rumors to the sower concerned with the replymessage described in Step 3, which will be delivered to therespondent j by traveling the path used in the random walkin the reverse direction. See Figure 3 for illustration.

Step 5: Transmission of ObjectAfter receiving the (encrypted) ACK message, the respon-

dent j decrypts it into plain text with the symmetry keycontained in a rumor and the secret key of j. After that,it moves to the actual transmission of the requested objectusing digital envelope. More concretely, after encryptingthe object into a cipher text F , peer j transfers it tothe questioner through random walk of two rumors, directforwarding of the rumors to the sower concerned with theACK message, and the delivery of rumors by traveling thepath used in the random walk of Step 4 in the reversedirection.

4. Proposed Method4.1 Design Issues

This section describes the details of the proposed scheme.The goal of the scheme is to realize an anonymous object

Sower

Similarity link

Random link

Fig. 4: Dynamic switch of the mode of flooding during thequery propagation.

search in the SocioNet using the notion of the RR describedin Section 3. However, if we directly apply the techniquesused in the RR to the SocioNet, we will face to the followingissues: 1) As was described in Section 2, the SocioNet isdesigned in such a way that the questioner is located inthe neighborhood of the respondent. However, the directapplication of the RR to the SocioNet loses such a benefitof the SocioNet, since in the RR, the actual flooding isconducted by a sower which is randomly selected from allpeers in the network, i.e., we cannot guarantee that the soweris in the neighborhood of the respondent. 2) The search inthe RR is based on a simple flooding, i.e., it repeats theforwarding of a received query to all neighbors until theTTL given to the query exhausts. However, such a simplescheme does not fully utilize the structure of the SocioNetso that two types of links play different roles in the overlay,i.e., random link connects remote peers and similarity linkconnects peers to have similar interests. This means that toimprove the efficiency of the object search, the propagationof a query from the selected sower should be conducted bycarefully considering the difference of the role of links.

In the following subsections, we propose two techniquesto overcome those issues.

4.2 Dynamic Switch of the Mode of FloodingThe first technique is to take into account the difference of

the role of links during the propagation of query messages.More concretely, we devolve the role of diversification torandom links in an early phase of the query propagation andthe role of intensification to similarity links in the remainingsteps of the query propagation.

The concrete operation proceeds as follows. Let s be asower concerned with the questioner which received twoquery rumors rK and rC from its different neighbors. Afterdecrypting message q from C with K, s starts the floodingof q to its neighbors by setting TTL to a small value, e.g.,

two to five, using both of random and similarity links. Eachcopy of the query stops the propagation when: 1) the TTLexhausts or 2) it arrives at a peer holding an object matchingthe query. In addition, if it arrives at a peer which has asimilar interest to the query, then it switches the mode offlooding so that it merely uses similarity links to realize anefficient intensification of the exploration.

The similarity of a peer j with a query q is calculated asfollows. Recall that in the SocioNet, each peer is associatedwith a profile representing its interests in the form of a vectorof relevances to the tags in T . The idea is to associatea set of tags to each query issued by the questioners1. Ifquery q is associated with a single tag t drawn from set T ,the similarity of the query with a peer j is calculated inthe following three steps: 1) extract the relevance wj,t of jwith tag t from the profile w⃗j ; 2) extract top α elementsfrom the profile with the maximum relevance; and 3) if wj,tis contained in the extracted α elements, then we judgethat the similarity between peer j and query q is high.If q is associated with two or more tags, we extend theabove scheme so as to check whether the majority of tagsassociated with the query are contained in the top α elementsin the profile vector.

Figure 4 illustrates a running example of the scheme. Inthis figure, the peer holding an object matching the queryissued by the questioner is painted red, and peers whichhas a similar interest with the query is painted orange.After decrypting the query from two query rumors receivedfrom different neighbors, the sower, which is painted green,initiates a flooding of the query by setting the TTL to a smallvalue. The flooded message uses all links within the TTL,and after arriving at an orange peer, which has a similarinterest to the query, it switches the mode to the floodingwithout random links.

4.3 Similarity-Based FilteringThe second technique is to filter queries at each similarity

link by the similarity of the receiver to the query. Supposethat peer j receives a query q associated with a set oftags. In the first technique, all similarity edges outgoingfrom j are used for the propagation of the query unless theTTL is exhausted. However, since the similarity of peers isdefined by the cosign similarity of profiles and the number ofobjects held by each peer (see Equation (1) for the details),a neighbor ℓ of j connected by a similarity edge (j, ℓ) mightnot be relevant to q even if peer j is relevant to q and thevalue of sim(j, ℓ) is small. For example, consider the casein which peers j and ℓ have 200 objects attached tag Jazz,peer j has 20 objects attached tag Clarinet and peer ℓ has

1The simplest way to realize such a situation is to ask questioners todesignate tags associated with the query. Another possible way is to adoptthe technique of automatic tag attachment which has been proposed in theliterature [7]. In the evaluation described in Section 5, we assume that eachquery is attached a single tag by the questioner.

Table 1: Parameters used in the simulation.The number of peers 10000

The number of objects 1000The number of peers holding matching object 100

Average degree of peers 6Rewiring probability 0.3

TTL of the first phase 2Threshold θ 0.8

no object attached tag Clarinet. In such a case, a query qwith tag Clarinet received by peer j should not be forwardedto peer ℓ, since ℓ has no object attached tag Clarinet andsuch a fact can be detected by analyzing the relevance ofthe receiver ℓ to the query.

The filtering of queries is conducted by using the cosignsimilarity. More concretely, each query q is associated witha binary vector q⃗ so that the ith element in the vector takesvalue 1 if and only if the ith tag (in set T ) is associated withq. Then, the similarity σ(q, ℓ) between peer ℓ and query qis calculated as σ(q, j) = cos(q⃗, w⃗ℓ), and the similarity linkconnecting to ℓ stops the forwarding of q if the value ofσ(q, j) is smaller than a predetermined threshold θ.

5. Evaluation5.1 Setup

We evaluate the performance of the proposed scheme bysimulation. The simulation is conducted by using PeerSimsimulator [6], and as the competitor, we use a simplecombination of the RR and the SocioNet in which eachsower concerned with the questioner initiates a flooding ofthe decrypted query with a designated TTL. In the following,we denote the above combined scheme as COMB and theproposed scheme with two techniques PROP, where for thereader’s reference, we also show the result for the schememerely with the first technique denoted as TECH1 and thatwith the second technique denoted as TECH2. The metricfor the evaluation is the number of messages and the successrate, which are averaged over 30 runs.

Parameters used in the simulation are given as follows.The number of peers and the number of objects are fixed to10000 and 1000, respectively, where each object can haveseveral copies in the overlay. The number of copies held byeach peer follows a Poisson distribution with mean λ = 6.The popularity of the object matching a query is set to 1%,i.e., we consider a situation in which among 10000 peers,only 100 peers hold the object matching the query. Theoverlay network consisting of similarity links is generated bythe Barbási-Albert (BA) model so that the average degree ofeach peer is six and the probability of rewiring a similaritylink into a random link is set to 0.3. TTL of the first phaseof the query forwarding used in the first technique is set totwo. Finally, we fix threshold θ used in the second techniqueto 0.8. Those parameters as summarized in Table 1.

0

500

1000

1500

2000

2500

3000

2 3 4 5

Aver

age

num

ber o

f mes

sage

s

TTL

COMB PROP TECH1 TECH2

Fig. 5: The average number of messages issued in fourschemes.

0

10

20

30

40

50

60

70

80

90

100

2 3 4 5

Suc

cess

rate

[%]

TTL

COMB

PROP

Fig. 6: The success rate of two schemes obtained by dividingthe number of successful runs by the total number of runs.

5.2 Number of MessagesFigure 5 illustrates the result on the number of messages.

The horizontal axis is the TTL of the flooding and fourcurves correspond to the result for COMB, PROP, TECH1and TECH2, respectively. Although there is no big differ-ence among four schemes when TTL is two, we could find asignificant reduction of the number of messages as the TTLbecomes large. In particular, the amount of improvement ofCOMB by PROP is about 50% when TTL is five.

5.3 Success RateFigure 6 compares the success rate of COMB and PROP,

which is calculated by dividing the number of successfulruns by the total number of runs in the simulation, wherethe horizontal axis is the TTL of query flooding, as before.The success rate of COMB monotonically grows as the TTLincreases, which reaches 100% when TTL is four. However,the success rate of PROP is not stable with respect to themonotonic change of the TTL; e.g., the success rate when

0

10

20

30

40

50

60

70

80

90

100

2 3 4 5

Suc

cess

rate

[%]

TTL

COMB PROP TECH1 TECH2

Fig. 7: Comparison of the success rate of four schemes whichis calculated by excluding runs with two or less sowers.

TTL is three seems to be too small compared with thesuccess rate for other TTLs.

A reason of such an instability of the success rate is dueto the small number of sowers generated by the RR. SeeFigure 7 for illustration. This figure redraws the curves ofthe success rate after excluding simulation runs in whichthe number of sowers generated by the random walks is twoor less. As shown in the figure, by excluding such runs,we have a reasonable grow of the success rate, and canmake the following observations: 1) the use of the secondtechnique reduces the success rate (recall that the secondtechnique stops the forwarding of the query to a peer to havea profile which is not similar to the query); and 2) COMBis better than TECH2, i.e., the simultaneous use of the firsttechnique with the second technique relaxes the badness ofthe second scheme. The conjecture such that the number ofsowers affects the success rate is confirmed by Figure 8,which illustrates the impact of the number of sowers to thesuccess rate by fixing the TTL to three.

6. Concluding RemarksThis paper proposes an anonymized object search scheme

for the SocioNet. More precisely, we propose two techniquesto overcome the inefficiency of a simple application of theRumor Riding to the SocioNet, where the first techniqueis to dynamically switch the kind of links used for thequery propagation and the second technique is to filterqueries at each similarity link by the similarity of thereceiver to the query. The performance of the scheme isevaluated by simulation. The simulation result indicates thatthe proposed scheme reduces the number of messages of asimple combination of the SocioNet and the Rumor Ridingto a half without significantly reducing the success rate.

A future work is to verify the effect of the popularity ofthe searched object to the performance, which was fixed to1% in the current simulation. Another key issue is to conduct

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4

Suc

cess

rate

[%]

Number of sowers

COMB

PROP

Fig. 8: Impact of the number of sowers to the success rate(TTL is fixed to three).

a detailed analysis of the behavior of the proposed scheme,since in the current work, we merely evaluate the averagenumber of messages and the success rate.

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