An Efficient-Communication Private Matching Scheme in Client-Server Model

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研究生：	羅艷華 Monica Law Chu
論文名稱：	An Efficient-Communication Private Matching Scheme in Client-Server Model 在用戶端與伺服器架構底下的效率傳輸私密配對方法
指導教授：	孫宏民 Sun, Hung-Min
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 資訊系統與應用研究所 Institute of Information Systems and Applications
論文出版年：	2010
畢業學年度：	98
語文別：	英文
論文頁數：	37
中文關鍵詞：	私人匹配、不經意傳輸、通用散列函數、通信複雜性
外文關鍵詞：	Private matching, Oblivious Transfer, Universal hash function, Communication Complexity
相關次數：	點閱：2 下載：0
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In this thesis, we propose an efficient- communication solution for private matching problem in Client-Server model. We consider the Client-Server environment, the client C has the dataset X of m elements and Server S has the dataset of n elements. However, it has shown to be not efficient, because the client’s dataset is smaller than the server’s dataset, i.e., m << n. Previously, the best result for solving PM problem requires the communication complexity O (m + n), which is linearly increasing with n.
Our proposed scheme is based on Oblivious Transfer. The communication complexity will only require O (m • log2 n), which is linearly increasing with log2 n. The technology is to construct a small universe, called hashed universe, by applying the universal hash function to the based universe of X and Y. We show that running the PM protocol will output the same result both in the based universe and the hashed universe. Our proposed scheme can perform more efficient when log2 (m +n) = O (n/m), for some security parameter ∆ > 0. We have to point out that our method can control the Error probability of choosing a PM applicable function to be very small. Compared to the previous PM protocol, our method is much more communication-efficient in the Client-Server model.

本論文的目標在找出一個有效率的傳輸複雜度再私密配對的方法。我們分析過去最好的方法為O(m+n)，其中m是伺服器端的資料個數，而n是用戶端的資料個數。然而，這在一般的用戶端與伺服器端的架構底下是很沒有效率的。一般來說，伺服器的資料個數遠遠大於用戶端的資料個數，這會使得私密配對的複雜度隨著n呈線性成長。
在本論文裡，我們提出一個有效率傳輸的私密配對方法。我們的方法尤其適用在用戶端與伺服器端架構底下。我們利用模糊傳輸協定(OT)的技巧去設計私密配對，並達到了O (m • log2 n)的傳輸複雜度。此外，我們並証明此方法在log2 (m +n) = O ( )會表現的比傳統的方法來的更有效率。我們採用 Universal hash function的技巧，將原本用戶端與伺服器端基於的資料集合X和Y映射到較小的資料集合，且經過由基於模糊傳輸協定的私密配對後，仍會有與原來配對X和Y相同的結果，因此達到具有傳輸效率的私密配對方法。

Aknowledgement    I
Abstract (in Chinese).    II
Abstract (in English).    III
Contents    IV
List of Tables.    V
List of Figures    V
Chapter 1  Introduction    1
1.1 Introduction to Private matching    1
1.2 Objective of the thesis        3
1.3 Overview of the Thesis        3
Chapter 2  Related Work      4
2.1 AgES Protocol              4
2.2 HL Protocol       5
2.3 FNP Protocol     6
Chapter 3  Preliminaries       8
3.1 Notation                     8
3.2 Security Models           8
      3.2.1 Semi-honese Adversaries      9
      3.2.2 Malicious Adversaries      9
      3.2.3 Ideal Model               10
      3.2.4 Trusted Third Party      10
3.3 Homomorphic Cryptosystem      11
      3.3.1 Additively homomorphic encryption             13
              3.3.1.1 Paillier Cryptosystem             13
      3.3.2 Multiplicative homomorphic encryption    15
              3.3.2.1 ElGamal Cryptosystem             15
3.4 Oblivious Transfer                               17
3.5 Introduction to Hash Function                      18
Chapter 4  Private matching based on Oblivious Transfer    21
4.1 Introduction to Lipmma method to implement our (m, n)-PM                                                  21
4.2 Implementing (m, n)-PM: A Na□ve Method             22
      4.2.1 Na□ve method against Semi-honest Adversaries                                       23
      4.2.2 Na□ve method against Malicious Adversaries    24
4.3 Applying Universal Hash Function : (m, n)-PMUH    24
      4.3.1 The Analysis of (m, n)-PM in Hashed Universe    25
            4.3.1.1 PM-applicable function    27
            4.3.1.2 The Universal hash family                                                  28
      4.3.2 Construction of (m, n)-PM ¬UH             30
      4.3.3 Communication Complexity of (m, n)-PMUH    31
Chapter 5  Comparisons in Communication Complexity    32
Chapter 6  Conclusions  34
6.1 Summary and Discussions  34
6.2 Future Research  35
References  36


List of Tables

Table 1: Comparisons in Communication Complexity of private matching protocol                                        33


List of Figures
Figure 1: The Based Universe and the Hashed Universe    25
Figure 2: Three mapping cases                      26

                                

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