Adaptive Random Key Distribution Schemes for Wireless Sensor Networks

1
Adaptive Random Key Distribution Schemes for
Wireless Sensor Networks

• Shih-I Huang
• Dept. of Comp. Sci. Info. Eng.
• National Chiao Tung University
• WADIS03

2
Outline

• Introduction
• Motivation
• Related Work
• Proposed Schemes
• Analysis
• Conclusion

3
Introduction

• Wireless Sensor Networks (WSNs)
• It consists of a set of small devices with
  sensing and wireless communication capabilities
• Those small devices are named sensor nodes, and
  are deployed within a special area to monitor a
  physical phenomenon.
• Ex Anthrax
• Multifunctional
• Depends on what sensors are attached
• Features
• Widely deployed. (1001M?)
• Low communication bandwidth
• Limited memory space and computation power

4
Motivation

• A large WSN consists of thousands of nodes
• Need shared communication keys to ensure secure
  peer-to-peer wireless communication
• Limited memory storage (512 bytes 4K)
• To deliver data without being compromised, WSN
  services rely on secure communication and key
  distribution

5
Conventional Scheme (Random Pair-wise)
K5
K2 K3 K4 K5 K6 K7
K1 K2 K3 K4 K6 K7
K1
K1 K2 K3 K5 K6 K7
K2
K4
K1 K3 K4 K5 K6 K7
K1 K2 K3 K4 K5 K6
K7
K3
K6
K1 K2 K4 K5 K6 K7
K1 K2 K3 K4 K5 K7
Requires a large storage space for keys in a
large WSN
6
Motivation

• The existing key distribution solutions require a
  large memory space in a large WSN
• We propose two symmetric key distribution schemes
  to minimize storage requirement
• Adaptive Random Pre-distributed scheme (ARP)
• Unique Assigned One-way Hash Function scheme
  (UAO)

7
Related Work
8
Random Graph Theory

• A Random Graph G(n, p) is a graph of n nodes, and
  the probability that a link exists between any
  two nodes is p.
• Given a desired probability Pc for the graph
  connectivity
• ex Pc0.99999 to get a connected graph.
• Then we can get a threshold of p to form a
  connected graph.
• . (1)
• The expected degree of a node
• 
  .(2)

The scheme only needs to select d keys to keep
a network connected under probability p
9
Random Key Based Schemes

• Basic Scheme
• L. Eschenauer, V. D. Gligor, A Key-Management
  Scheme for Distributed Sensor Networks, 9th ACM
  Conference on Computer and Communication
  Security, pp.41-47, November 2002. (CCS02)
• Each node randomly picks r keys from a unordered
  key pool S.
• Use the common shared key to establish a secure
  link.
• Relies on probabilistic key sharing among the
  nodes of a random graph.

B
B
B
A
A
A
C
C
C
D
D
D
Secure link
Map Random Graph Theory to key selecting
problem
10
Adaptive Random Pre-distributed Scheme (ARP
Scheme)

• The features of ARP scheme
• A Random Key based key distribution scheme for
  WSNs.
• To minimize the memory requirement.
• ARP scheme consists of
• Two-Dimension Key Pool
• Key Selecting Algorithm

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Two-Dimension Key Pool

• Use t one-way function F1, F2,,Ft and t seed
  keys K1,0, K2,0,,Kt,0 to generate t one-way key
  chains.
• For a key chain KCi, it consists of Ki,0,
  Ki,1,Ki,s-1.
• Where Ki,j Fi(Ki,j-1), and the length of KCi is
  s.
• The key pool size s t.

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Key Selecting

• Each node randomly choose a one-way key chain,
  and memorized its one-way function Fi and its
  seed key Ki,0.
• Randomly select d-t key chains KCt1,
  KCt2,,KCt(d-t), from the rest of key chains.
• For each key chain KCtj selected, randomly pick a
  key Ktj,sj from KCtj and memorized Ktj,sj.

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Unique Assigned One-way Hash Function Scheme (UAO
Scheme)

• The features of UAO scheme
• Provide node-to-node authentication.
• Great resistance to node capture.
• The maximum supported network size is greater
  than the existing schemes.
• The UAO scheme consists of
• Key Decision Algorithm
• Node-to-Node Authentication Protocol

14
Key Decision Algorithm

• Suppose each sensor node SNi has a unique
  identity IDi.
• First, we assign a unique one-way hash function
  Fi to each sensor node SNi.
• Second, SNi randomly selects d other sensor
  nodes.
• Third, each selected node use following formula
  to generate the unique key for SNi.
• Finally, SNi memorizes those unique keys and the
  generating identities.

IDi
Fi
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Node-to-node Authentication Protocol
1
2
3
4

• SNi broadcasts its identity
• SNj verifies its key ring, if IDi is combined
  with any key then
• SNi calculates the Ks Fi(IDj), and decrypts the
  message, then sends the ACK and challenge
  message.
• SNj receives the challenge and sends the response

16
Analysis of ARP Scheme

• We analyze the ARP scheme in following aspect
• Probability of connectivity.
• Analyze the link probability of using
  Two-Dimension Key Pool.
• The link probability is equal to 1 Prany two
  nodes do not share any key

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Probability of Connectivity (1/2)

• To calculate the probability that any two nodes A
  and B do not share any common key
• As one-way key chain does not match with Bs
  one-way key chain.
• As one-way key chain does not match with any Bs
  selected keys.
• The probability of above two parts is equal to
• As selected keys do not match with Bs one-way
  key chain.
• The probability is equal to
• As selected keys do not match with any Bs
  selected keys.
• The probability is equal to
• The link probability is equal to
  
• 
  (3)

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Probability of Connectivity (2/2)
Key pool size 100,000
ARP needs fewer keys to achieve the same
connectivity probability
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Analysis of UAO Scheme

• The link probability p can be evaluate by 1
  Pr.two nodes do not have any key derived from
  the others one-way function
• p is equal to
• Substitute p by a function of d
• Substitute d by a function of n
• Evaluate the root of the above equation

r Key ring size
20
Evaluation of UAO Scheme
Key size 128 bits Pc0.99999
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Conclusion

• Key distribution is a critical and fundamental
  issue for the security service in WSNs.
• The pre-distributed and symmetric cryptosystem
  based scheme is well suitable for the resource
  constrained sensor networks.
• We propose two schemes based on one-way function
  and Random Graph theory to provide memory
  efficient key distribution for WSNs.
• ARP scheme
• Provide efficient trade-off between memory space
  and security strength.
• UAO scheme
• Provide node-to-node authentication.
• Great resistant to node capture.
• If there is enough memory space, we suggest using
  UAO scheme as the key distribution scheme for
  WSNs.
• Otherwise, we suggest using ARP scheme.
• To achieve an efficient trade-off between memory
  space and security strength.