A Key Management Scheme for Hierarchical Access Con-

trol in Group Communica-tion

Qiong Zhang, Yuke WangJason P, Jue

2008International Journal of Network Security

Vol72013. 05. 13

Tae Hoon Kim

Referenced ppt by Seung-Tae HongA-Ra Jo

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

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Introduction Emerging Internet application

Teleconferencing, e-newspaper, IPTV Based on group communication

In order to widely commercialize(Internet Application), the is-sue 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

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Introduction

For Example, consider two types of service E-newspaper subscription service Video multicast service

Access Rela-tion Sports Finan-

cial Stock Top News

Weather

Gold O O O O OSilver Sport O O O

Silver Fi-nance O O O O

Basic O OAccess Rela-tion EL2 EL1 BL

Best Video Quality O O O

Moderate Video Quality O

Basic O O

• BL : Best Layer• EL : Enhancement Layer

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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]

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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

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Introduction In this paper, focus on a centralized key man-

agement scheme It is critical to minimize rekey overhead in order to reduce

the cost for communication and computation and computa-tion at the key server and users

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Formalization of partially or-dered 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

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Formalization of partially or-dered 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 O O O OSilver Sport O O O

Silver Finance O O O OBasic O O

R1

R2

R3U1

U2

U3

U4

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Formalization of partially or-dered relation

DAG(Directed Acyclic graph)[3] The partially ordered relations of membership groups and

resource groups can each be represented by a DAG

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Formalization of partially or-dered relation

Satisfy the following condi-tions

1)it must maintain the partial or-ders of the membership group DAG and the resource group DAG

2)a user u U has access to a re-source r R iff vertex representing U is the same as the vertex repre-senting R or is reachable to the vertex representing R in the uni-fied DAG

3)the unified DAG is the smallest partial order satisfying the above conditions

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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

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Related work

Keyset(U1) = { k1,k7,k9, k11} Userset(k9) = {u1,u2,u3,u4}

One or more outgoing edges but no incoming edges

K-node that has no outgoing edges data encryption keys

key

Data encryption key: used to data streams encryp-tion keys

Key encryption key: used to data encryption keys Keyset(U1)

Userset(k9)

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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

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Related work Constructing a single logical key graph for hier-

archical access control[17,19,24] [19] : User have different level and higher-level users can ac-

cess 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 par-tially ordered hierarchy

[17] : Users form a partially ordered relation while the data streams are not partially ordered(MG Scheme)

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Related work MG Vs. HAC scheme

MG HAC Data stream2 : Financial Data stream3 : Stock

HAC(Hierarchical Access control)

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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

R1 R2 R3

dk3

dk1 dk2

k25Relationsubgraph

Balanced logical key tree(membership-group subtree)

Unified DAG

① For each resource group, encrypt all data streams in the resource group with a singledata encryption key, called the resource-group key

② For each membership group, con-structa balanced logical key tree called the membership-group subtree, where each user is represented by a u-node and the root ofthe subtree is associated with a key, calledthe membership-group key

③ Construct a relation subgraph to con-nectthe resources-group keys based on a unified DAG

rk1rk2

rk3

rk4

④ Connect the roots of membership-group subtrees to the corresponding re-source-group keys

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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

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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

k8k26 k17mk1

dk1

dk2 dk3

k20

mk2

k8

k26

Send {mk’2}k19 to u5, u6{mk’2}k7 to u7

Send {k26}k8 to u8{k26}k1 to u1

u8

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Rekey Algorithm Case2)Update the access relations(new data

stream, new membership group)

R4

dk4rk5

dk3’rk4’

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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 ac-tions 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

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Performance Comparison

Why HAC experiment is only one? All data streams in a resource group are encrypted by the

same resource-group key

11

11

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HAC Scheme

Note that, Case III is much higher than the differerce between theHAC scheme and Case II

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Performance Comparison

We can see that HAC scheme results in less rekey overhead than the MG

Scheme

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11

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33

HAC Scheme

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Conclusion In the HAC scheme

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