1. A Key Management Scheme for Hierarchical Access Control in Group Communication
Qiong Zhang, Yuke Wang
Jason P, Jue
2008
International Journal of Network Security
Vol7
Tae Hoon Kim
Referenced ppt by
Seung-Tae Hong
A-Ra Jo

2. Contents 1. Introduction 2. Background and Related Work
2.1 Formalization of Partially ordered Relations
2.2 Related work
3. The HAC Scheme
4. Rekey Algorithm
5. Performance Analysis
5.1 Storage Overhead
5.2 Rekey Overhead
6. Performance Comparison
7. Conclusion

3. Introduction Emerging Internet application Access control
Teleconferencing, e-newspaper, IPTV
Based on group communication
In order to widely commercialize(Internet Application), the issue of access control must be addressed.
Access control
: User having different access rights to multiple data streams
Hierarchical access control
Include e-newspaper subscription and video multicast services
Commercialize :상업화

4. Moderate Video Quality
Introduction
Access Relation
Sports
Financial
Stock
Top News
Weather
Gold O
Silver Sport
Silver Finance
Basic
Access Relation
EL2
EL1 BL
Best Video Quality O
Moderate Video Quality
Basic
For Example, consider two types of service
E-newspaper subscription service
Video multicast service
BL : Best Layer
EL : Enhancement Layer

5. Introduction
What is need to implement access control for group communication?
Data encryption keys
Often used to encrypt data streams
User Access
If the user possesses the data encryption keys
Must be update data encryption keys
When a user dynamically joins or leaves a group
Use backward secrecy and forward secrecy[12]

6. Introduction Key management schemes aim
update the data encryption keys in order to ensure backward secrecy and forward secrecy
Two categories of key management scheme
Centralized
A centralized key server controls the entire group
Generates keys and distribute keys to legitimate users via rekey messages
Distributed
No centralized group controller and generate group keys based on the contribution of users in the group

7. Introduction
In this paper, focus on a centralized key management scheme
It is critical to minimize rekey overhead in order to reduce the cost for communication and computation and computation at the key server and users

8. Formalization of partially ordered relation
Notation
U : A set of users {u1, u2, …}
R : A set of data streams {r1, r2, …}
A : An access relation, where A ⊆ U × R
Ui : Membership group i consisting of a subset of users
Ri : Resource group i consisting of a subset of data streams
Partial order of users(In an access relation A)
If the data streams that user ui can access is a subset of data streams that user uj can access, then ui is smaller than uj
If users ui and uj can access exactly the same subset of data streams, both users are equivalent

9. Formalization of partially ordered relation
Partial order of users (cont.)
If the set of users that can access data stream rj is a subset of users that can access data stream ri, then ri is smaller than rj
If the set of users that can access data stream ri is exactly same as the set of users that can access data stream rj , the two data streams are equivalent
R:set of data
streams
U : set of Users
Sports
Financial
Stock
Top News
Weather
Gold O
Silver Sport
Silver Finance
Basic U1 R3 U2 R1 U3 U4 R2

10. Formalization of partially ordered relation
DAG(Directed Acyclic graph)[3]
The partially ordered relations of membership groups and resource groups can each be represented by a DAG

11. Formalization of partially ordered relation
Satisfy the following conditions
1)it must maintain the partial orders of the membership group DAG and the resource group DAG
2)a user u ∈ U has access to a resource r ∈ R iff vertex representing U is the same as the vertex representing R or is reachable to the vertex representing R in the unified DAG
3)the unified DAG is the smallest partial order satisfying the above conditions

12. Related work Logical key graph[22]
Important data structure to improve the efficiency of key management
Consisting of k-nodes, U-nodes
K-nodes : Represents a key
U-nodes : Represents a user

13. Related work Keyset(U1) = { k1,k7,k9, k11} Userset(k9) = {u1,u2,u3,u4}
K-node that has no outgoing edges
data encryption keys
Data encryption key
: used to
data streams encryption keys
key
Key encryption key
: used to
data encryption keys
Keyset(U1)
One or more outgoing edges
but no incoming edges
Userset(k9)
Keyset(U1) = { k1,k7,k9, k11}
Userset(k9) = {u1,u2,u3,u4}

14. Related work Logical key graph be used to
Maintained at key server in order to efficiently distribute keys to dynamically joining or leaving users
Many key management schemes[2,7,8,10,16,22,23]
Proposed to construct a logical key graph and to update keys in the logical graph efficiently
Problem : only provide key management for equivalent users and equivalent data stream

15. Related work
Constructing a single logical key graph for hierarchical access control[17,19,24]
[19] : User have different level and higher-level users can access more data streams than lower-level users
Problem : higher-level user are able to access all data streams
[24] : Chinese Reminder Theorem based hierarchical access control scheme
Problem : only suitable for users having a tree-based partially ordered hierarchy
[17] : Users form a partially ordered relation while the data streams are not partially ordered(MG Scheme)

16. Related work MG Vs. HAC scheme
MG HAC
Data stream2 : Financial
Data stream3 : Stock
HAC(Hierarchical Access control)

17. The HAC Scheme Four steps to construct the logical key graph
Next slide
In the key graph
Users in Ui form a balanced binary tree
mki is root represents the memebership-group Key
Ri is Resource group
Encrypted by a resource-group key, dki
The membership-group-keys are connected with resource-group keys by the relation subgraph
Use greedy algorithm
To explore the unified DAG
For constructing the sub graph

18. R1 R2 R3 Unified DAG Relation subgraph dk3 rk4 k25 dk2 dk1 rk1 rk3 rk2
① For each resource group, encrypt all data streams in the resource group with a single data encryption key, called the resource-group key
Unified DAG
dk3
rk4
Relation
subgraph
k25
dk2
dk1
rk1
rk3
rk2
④ Connect the roots of membership-group subtrees to the corresponding resource-group keys
② For each membership group, construct a balanced logical key tree called the membership-group subtree, where each user is represented by a u-node and the root of the subtree is associated with a key, called the membership-group key
③ Construct a relation subgraph to connect the resources-group keys based on a unified DAG
Balanced logical key tree
(membership-group subtree)

19. Greedy algorithm of the HAC Scheme
Notation
M = set of membership group in Vi
K = set of k-nodes; cover disjoint set of membership group
C = set of membership group in M; that has been covered by k-nodes in K
U = set of uncovered membership groups in M
RK = set of representative k-nodes; has been generated
Userset = set of membership groups covered by a representative k-node rkj

20. Rekey Algorithm Update the keys in the key graph
User join, leave, or switch membership groups dynamically
The service provider changes access relations dynamically
Case1)User u8 switches from U2 to U1
k26 k8
k20
k17
dk1
mk1
mk2
dk3
k26
dk2 k8
Send
{k26}k8 to u8
{k26}k1 to u1
Send
{mk’2}k19 to u5, u6
{mk’2}k7 to u7 u8

21. Rekey Algorithm
Case2)Update the access relations(new data stream, new membership group) R4
dk3’
rk4’
dk4
rk5

22. Performance Comparison
Experiment environment
Compare the performance of the HAC scheme with the MG scheme
Measured storage overhead and rekey overhead
Develop a simulation model to construct logical key graphs with d =2 based on access relation and to simulate user actions in the system
Consider three cases where equivalent data streams to group, and the number of data streams per resource group is shown in Table3

23. Performance Comparison
Note that, Case III is
much higher than the
differerce between the
HAC scheme and Case II
Why HAC experiment is only one?
All data streams in a resource group are encrypted by the same resource-group key
HAC Scheme 1 1 1 3 1 1 1 3

24. Performance Comparison
We can see that
HAC scheme results in less rekey overhead than the MG Scheme
HAC Scheme 1 1 1 3 1 1 1 3

25. Conclusion In the HAC scheme In the key graph Future work
Proposed a hierarchical access control key management scheme for group communication
Employed an algorithm to construct a key graph based on a unified relation of membership groups and resource group
Can handle complex access relations
In the key graph
Equivalent data streams are grouped in a resource group and are encrypted by a single data encryption key
Future work
To employ the batch rekeying[23] scheme in order to further improve the key management efficiency