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Key Predistribution Using Transversal Design on a Grid of Wireless Sensor Network

Key Predistribution Using Transversal Design on a Grid of Wireless Sensor Network. Author: S. Ruj, S. Maitra and B. Roy Source: Ad Hoc & Sensor Wireless Networks, vol. 5, no. 3-4, pp. 247-264, 2008. Presenter: Yung-Chih Lu ( 呂勇志 ) Date: 2010/10/08. Outline. Introduction

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Key Predistribution Using Transversal Design on a Grid of Wireless Sensor Network

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  1. Key Predistribution Using Transversal Design on a Grid of Wireless Sensor Network Author: S. Ruj, S. Maitra and B. Roy Source: Ad Hoc & Sensor Wireless Networks, vol. 5, no. 3-4, pp. 247-264, 2008. Presenter: Yung-Chih Lu (呂勇志) Date: 2010/10/08

  2. Outline • Introduction • Partially Balanced Incomplete Block Designs • Proposed Scheme • Performance Evaluation • Security Analysis • Conclusion • Comment

  3. Introduction (1/3) • Key Pre-distribution in WSN • Key pool={0,1,2,3,4,5,6} 2,3,5 (8x7)/2 = 28 Connectivity ratio= 27/28 = 0.9642 E(c)= (7+6+4) / 27 = 0.2593 V(c) = = 1/6 = 0.1667 x 3,4,5 1,2,4 c1 0,3,6 0,2,6 c2 0,4,5 0,1,3 1,5,6 :Sensor node WSN: Wireless Sensor Network c: c1 and c2 E(c): Fraction of links broken when c nodes are compromised V(c): Fraction of nodes disconnected when c nodes are compromised

  4. Introduction (2/3) R.H. Bruck, H.J. Ryser, "The nonexistence of certain finite projective planes", Canadian J. Math. vol.1, pp.88–93, 1949 • Bruck–Chowla–Ryser theorem • λ-(v,b,r,k) • q: sum of two square numbers • q mod 4 = 1 or 2 • If v=b= q2+q+1 , then r=k=q+1 • Example: q=2, λ-(v,b,r,k)=1-(7,7,3,3) • Key -pool = {0, 1, 2, 3, 4, 5, 6} • S1=(1,2,4) ．S5=(5,6,1) • S2=(2,3,5 ) ．S6=(6,0,2) • S3=(3,4,6 ) ．S7=(0,1,3) • S4=(4,5,0) v: key-pool size b: number of sensor nodes r: number of nodes in which a given key occurs k: number of keys in a node λ: number of nodes which contain a given pair of keys S: sensor node

  5. Introduction (3/3) • Goal • Key agreement • Key Pre-distribution Phase • Resilience against node capture attack • High connectivity

  6. Partially Balanced Incomplete Block Sushmita Ruj and Bimal Roy, "Key Predistribution Using Partially Balanced Designs in Wireless Sensor Networks", ISPA , p.p.431-445, 2007 • Key Pre-distribution • Block 1: (2, 3, 4, 5, 6, 7) Block 2: (1, 3, 4, 5, 8, 9) • Block 3: (1, 2, 4, 6, 8, 10) Block 4: (1, 2, 3, 7, 9, 10) • Block 5: (1, 2, 6, 7, 8, 9) Block 6: (1, 3, 5, 7, 8, 10) • Block 7: (1, 4, 5, 6, 9, 10) Block 8: (2, 3, 5, 6, 9, 10) • Block 9: (2, 4, 5, 7, 8, 10) Block 10: (3, 4, 6, 7, 8, 9) Block: sensor node

  7. Proposed Scheme (1/5) Colbourn, C. J. and Dinitz, J. H. (Eds.). CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, p. 112, 1996. • Key Pre-distribution in Transversal Design • b = r2 ,v = rk , b=v, k=r • Example: b=32 = 9, v=3×3 = 9. • Key pool={1,2,3,4,5,6,7,8,9} 。Sensor keys 0 1 2 0 1 2 0 1 2 0 1 2 Si,j ={(x, xi + j mod r) : 0 ≦ x < k} i k r j v: key-pool size b: number of sensor nodes r: number of nodes in which a given key occurs (r is a prime power) S: sensor node k: number of keys in a node

  8. Proposed Scheme (2/5) • Shared-key establishement phase • xi+j≡xi’+j’ mod r • x(i-i’)≡j’-j mod r • If(i≠i’) and (x≡(j’-j)(i-i’)-1 mod r) • Then have a common key 0 1 2 0 1 2 Key identity 1,4,7 0,0 i ignore 2,5,8 0,1 1,5,9 2,6,7 j key identity = H(Key) 1,0 1,1 H(.): one way hash function

  9. Proposed Scheme (3/4) • Path-key establishment phase 1,4,7 0,0 2,5,8,4 E1[4] E5[4] 0,1 1,5,9 2,6,7 1,0 1,1

  10. Performance Evaluation (1/3) • Grid-based

  11. Performance Evaluation (2/3) • RF radius RF radius = ρ The maximun number of physical neighbors within the RF radius = Bρ =2ρ (ρ + 1) Number of key-sharing neighbors within the RF radius = Aρ Connectivity Ratio = Aρ/Bρ ((2ρ+ 1)2 -1)/2 = (4ρ(ρ+ 1))/2=2ρ(ρ+ 1). v: key-pool size b: number of sensor nodes RF: radio frequency r: number of nodes in which a given key occurs k: number of keys in a node S: sensor node number of nodes connected

  12. Performance Evaluation (3/3) • Connectivity ratio k: number of keys in a node

  13. Security Analysis (1/2) • Resilience against node capture attack b: number of sensor nodes b = r2 S: sensor node r: number of nodes in which a given key occurs k: number of keys in a node V(c): Fraction of nodes disconnected when c nodes are compromised

  14. Security Analysis (2/2) • Resilience against node capture attack b: number of sensor nodes b = r2 S: sensor node r: number of nodes in which a given key occurs k: number of keys in a node E(c): Fraction of links broken when c nodes are compromised

  15. Conclusion • they analyze the connectivity of the network taking the RF radius into account • Transversal Design is useful

  16. Comment • Suitable for small WSNs • 2ρ (ρ + 1) is not accuracy

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