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Simple efficient mutual anonymity protocols forpeer-to-peer network based on primitive roots

Source: Journal of Network and Computer Applications, vol. 30, pp. 662-676, 2007.Authors: Chin-Chen Chang, Chih-Yang Lin, and Keng-Chu LinSpeaker: Shu-Fen Chiou (邱淑芬 )

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Outline

Introduction Xiao et al.’s protocols Proposed method Conclusion

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Introduction

A Peer can act three roles Publisher Requester Provider (Responder)

Pub

Req Pro

1.mp3

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Introduction

Hybrid P2P

TTPP0

P1

P2

P3

File listRequester

1.mp3P1

provider

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Introduction

Pure P2P

P0

P1

P2

P5

1.mp3Requester

P3

1.mp3

provider

P5

P5

Download file

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Xiao et al.’s protocols Mix-based hybrid P2P protocol

provider

1. Generate symmetric secret key2. Select m peers for cover path, encrypt with their public key

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Xiao et al.’s protocols cont.

Pure P2P protocol

shortcut

provider

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Xiao et al.’s protocols cont.

Disadvantage Scalability TTP know the details of providers and

requesters.

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Primitive roots

p11 ( ( )) ( )11 10 4 {1,3,7,9}

2 is a primitive root

2 11 21 mod 2 11 83 mod 2 11 77 mod 2 11 69 mod

}6,3,7,9,10,5,8,4,2,1{11mod}2,...,2,2{ 1010 order

2 1 110 mod

2 2 111 mod

2 4 112 mod

2 8 113 mod

2 5 114 mod

2 10 115 mod

2 9 116 mod

2 7 117 mod

2 3 118 mod

2 6 119 mod

2 1 1110 mod

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Hybrid P2P mutual anonymity

System initialization Address (alias) of gi

j mod p, j=1~p-1

p=7, gi=3

U2, TTP, U3, U1, U4, TTP

31 mod 7=3 32 mod 7=2

6 4 5 1

TTP

Sub-path address table U2

TTP,U1,U4

TTP,U3,TTP

gi=5 5 4 6 2 3 1

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Hybrid P2P mutual anonymity

Peer initialization

Ui

Ni+1

Randomly selects one path Ni+2

{{FLi}KT,Ni}

…

TTPConstruct an index database

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Hybrid P2P mutual anonymity

provider

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Shortcut-responding protocol

Random probability pj>pi->shortcut node

provider

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Pure P2P mutual anonymity p=5, p-2=3 peers involved

Random select p-1 number x1, x2,.., xp-1

Peer gets gj generates alias gjxi

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Anonymity analysis

Total n peers Between two consecutive aliases of TT

P sn: smallest numbers of peers

ln: largest number of peers

TTP: guess requester -> 1/sn

guess provider -> 1/n-ln

TTP TTP. . .

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Anonymity analysis

Requester (or provider): 1/(n-1) Middle node: guess R or P -> 1/(n-1)

if know number of middle nodes k

guess R or P -> 1/(n-k) Local eavesdropper: guess R or P -> 1/(n-1) Cooperating peers: if k cooperating peers

guess R or P -> 1/(n-1)

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Conclusions

The covert paths can be dynamically generated.

It is guaranteed that all the peers and the TTP can pass any of the covert paths.

Different primitive roots generate different covert paths, which raises the level of flexibility and anonymity of the protocol.

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Comments

Nm

UjNq

Ui

TTP

1.Generate symmetric keys

{Ni, file_id, null, K}

{NTTP, file_id, true, K}

{Ni, file_id, true, K}

{Nn, file_id, true, {f}K}{Nj, file_id, true, {f}K}

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Comments

Pure P2P Initiator generates peers’ aliases and

transmits them to peers.