Abstract-----i
Acknowledgements-----ii
Contents-----iii
List of Figures-----v
List of Tables-----vi
1 Introduction-----1
　　1.1 The Use of Virtual Private Networks-----1
　　1.2 Drawbacks of the Modern VPN Security Mechanism-----2
　　1.3 A Brief Introduction to Synchronized Choice Petri Nets-----7
　　1.4 Applying Synchronized Choice Petri Nets as a Security Algorithm to VPN-----9
　　1.5 Research Method and Framework-----10
2 Literature Review-----13
　　2.1 Security Algorithms in Virtual Private Network-----13
　　　　2.1.1 Symmetric-key Algorithms-----13
　　　　2.1.2 Asymmetric-key Algorithms-----21
　　　　2.1.3 IPsec-----26
　　2.2 Synchronized Choice Petri Net-----33
　　　　2.2.1 Preliminaries-----33
　　　　2.2.2 Analysis Techniques-----37
　　　　2.2.3 Subclasses of Petri nets-----40
　　　　2.2.4 Additional Structural Properties of Petri Nets-----41
　　　　2.2.5 Liveness for Synchronized Choice Petri Nets-----43
　　　　2.2.6 Formal Proof of Liveness Conditions-----46
　　　　2.2.7 The Algorithm for Verification of SNC and Liveness-----48
3 System Analysis and Design-----50
　　3.1 System Overview-----50
　　3.2 System Module Analysis-----51
　　 3.3 System Module Design-----53
4 Prototype System Implementation-----57
　　4.1 Development Platform-----57
　　4.2 Development Tools57
　　　　4.2.1 Access Database System-----57
　　　　4.2.2 Borland C++ Builder Component-----58
　　4.3 The Core of SNC Security-----59
　　 　　4.3.1 Data Representation of SNC net-----60
　　　　4.3.2 Generating a New Marking-----61
　　　　4.3.3 Checking Firability-----62
　　　　4.3.4 Generating a Firing Sequence-----63
　　　　4.3.5 Using a Marking as an Encryption Key-----64
5 Conclusions and Suggestions-----66
　　5.1 Conclusions-----66
　　5.2 Suggestions-----66
　　5.3 Research Limitations-----67
Bibliography-----68

List of Figures
Figure 1.1 The concept of VPN-----1
Figure 1.2 The use of Petri nets for the modeling and analysis of systems-----7
Figure 1.3 The mutual exclusion problem modeled by Petri nets-----8
Figure 1.4 The research framework-----12
Figure 2.1 The symmetric-key encryption model-----14
Figure 2.2 The simplified depletion of DES-----16
Figure 2.3 The asymmetric-key encryption model-----22
Figure 2.4 An example of elliptic curves-----25
Figure 2.5 Classes of elliptic curves used by cryptographers-----25
Figure 2.6 Host-to-host and gateway-to-gateway secure communication-----27
Figure 2.7 Transport and tunnel modes of IPsec-----28
Figure 2.8 (a) AH transport mode (b) AH tunnel mode (c) ESP transport mode (d) ESP tunnel mode-----31
Figure 2.9 (a) an example of a Petri net (b) the reachability tree of (a)-----38
Figure 2.10 (a) an example of a Petri net (b) the incidence matrix of (a)-----39
Figure 2.11 The bridge B and the subhandle H_s-----45
Figure 3.1 The architecture of the prototype system-----50
Figure 3.2 The idea of dynamic identity generation-----51
Figure 3.3 The idea of dynamic encryption key generation-----51
Figure 3.4 The design of user authentication module-----51
Figure 3.5 The design of data encryption module-----53
Figure 3.6 The design of the SNC crypto engine-----55
Figure 4.1 A simplified database system environment-----56
Figure 4.2 The concept of SNC security-----58
Figure 4.3 The transpose of incidence matrix A in figure 2.10 (b)-----60
Figure 4.4 The code snippet of transferring the incidence matrix into the transpose of incidence matrix-----60
Figure 4.5 (a) a Petri net in figure 2.10 with a marking state (b) the marking vector of (a) (c) the firing transition vector of (a)-----61
Figure 4.6 The code snippet of generation of a new marking-----62
Figure 4.7 The code snippet of checking firability-----63
Figure 4.8 The code snippet of generation of a firing sequence-----64
Figure 4.9 Using a marking as an encryption key-----65

List of Tables
Table 1.1 Drawbacks of security algorithms or of security concepts-----6
Table 2.1 Other DES replacements-----21