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### Optimizing Key Authentication in Wireless Sensor Networks with Hash Trees and Simulation Results ###

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This paper discusses the implementation of public key authentication in wireless sensor networks (WSAN) using optimal hash trees, addressing limitations associated with Merkle hash trees and incomplete Merkle trees. A direct conversion method is proposed for achieving maximum probability in node communication, detailing the root hash and symmetric structures for secure data exchange between nodes. Simulation results further illustrate communication probabilities and patterns, challenging real-world applicability while exploring theoretical constructs in a virtual environment. ###

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### Optimizing Key Authentication in Wireless Sensor Networks with Hash Trees and Simulation Results ###

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  1. Public Key Authentication in Wireless Sensor Network (3) Jeonil Kang(dreamx@seclab.inha.ac.kr)

  2. Optimal Hash Tree • Limitation of Merkle Hash Tree • Incomplete Merkle trees : where the number of leaves is not 2^n. - Direct conversion Optimal for the maximum possible probability that a node has AP length less than maximum

  3. Least Path (LP) Protocol Root Hash • Using Symmetric Structure A  B : A’s ID, A’s PK, A[1], A[2] B : h(h(h(A’s ID || A’s PK) || A[1]) || A[2]) ?= B[3] B  A : B’s ID, B’s PK, B[1], B[2] A : h(h(B[1] || h(B’s ID || A’s PK)) || B[2]) ?= A[3] A[3] B[3] B[2] A[2] A B A[1] B[1]

  4. Simulation Results Probabilistic Distribution (?)

  5. WSAN • Wireless Sensor and Actor Network a a a cluster …. a a actor node : cluster head H(ID || PK) sensor nodes a trim down …. H(ID XOR LOC || PK)

  6. Missed Sensor Nodes Aj 3) {key_group_i}key_session 2) {ACCEPT Sij}key_session Build new Merkle sub-tree Ai 1) {ID, LOCi, PK, Proofs}key_group_i Sij 4) {Trust Aj, LOCj, key_group_j}key_group_i

  7. Communication vs. Memory d : trim down levels

  8. BONUS : M-D GBS M-1 intersection nodes [1][2][3]…[M] Communication Probability (X) Is This Possible in the Real World? NO. Can We Imagine Communication Pattern? Absolutely NO. Is This Possible in the Virtual? YES.

  9. BONUS : (M-1).5-D GBS • Communication Pattern • Property in the Real World • up to 3 Dimensions [*][1][1][1] [*][1][1][2] [*][1][1][3] [*][1][1][4] [*][1][1][1] [*][1][1][2] [*][1][1][3] [*][1][1][4] [1][2][3][4] [*][1][1][1] [*][1][1][2] [*][1][1][3] [*][1][1][4] [*][1][1][1] [*][1][1][2] [*][1][1][3] [*][1][1][4] [*][1][2][1] [*][1][2][2] [*][1][2][3] [*][1][2][4] [2][1][4][3] [*][1][2][1] [*][1][2][2] [*][1][2][3] [*][1][2][4] [*][1][2][1] [*][1][2][2] [*][1][2][3] [*][1][2][4] [*][1][2][1] [*][1][2][2] [*][1][2][3] [*][1][2][4] [*][1][3][1] [*][1][3][2] [*][1][3][3] [*][1][3][4] [2][2][3][4] [*][1][3][1] [*][1][3][2] [*][1][3][3] [*][1][3][4] [*][1][3][1] [*][1][3][2] [*][1][3][3] [*][1][3][4] [2][1][4][4] [*][1][3][1] [*][1][3][2] [*][1][3][3] [*][1][3][4] [2][1][3][4] [*][1][4][1] [*][1][4][2] [*][1][4][3] [*][1][4][4] [*][1][4][1] [*][1][4][2] [*][1][4][3] [*][1][4][4] [*][1][4][1] [*][1][4][2] [*][1][4][3] [*][1][4][4] [*][1][4][1] [*][1][4][2] [*][1][4][3] [*][1][4][4]

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