Conclusions and Future Work

In this paper, we first employ the cryptographic technique which used to solve the problem of secure comparison for finding maximum/minimum in wireless sensor networks. In our scheme, we use the symmetric privacy homomorphism purposed by Domingo-Ferrer. It is feasible to process operations over the ciphertext in a wireless sensor network. Our protocol has some properties as follows:

 Providing end-to-end privacy: if the adversaries are semi-honest and only compromise the same kind of nodes (aggregator or sensing node), no private information of uncompromised nodes is disclosed. If the adversary compromise aggregators and sensing nodes, it only effect in localizing the possible damage. In terms of security, the result of our scheme is better than the preceding scheme in [8].

 Efficiency: our scheme can work with data aggregation and reduce energy consumption.

We have proved that our scheme is correct and provide data privacy. For the future work, there are two purposes we desire to achieve. First, we want to expand our scheme to defeat against the malicious adversary. Second, we expect to minimize the damage of node compromised attack.

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Reference

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Appendix A

In the following, we give an example for explanation.

Numerical Example for Secure Comparison

For simplification, this example focuses on aggregating the encrypted data. Assume there are two participants sx and sy with private readings vx and vy, respectively. We will compare two data in encrypted form with following parameters:

Case 1: vx > vy , vx = 5 = 1012 = X2X1X0, vy = 3 = 0112 = Y2Y1Y0

For illustration, we choose unrealistic small values:

Public parameters: d = 2, a modulus g = 28 Secret parameters: K = (x, q) , x = 3 and q = 7

The public aggregation function MAX is f(v_x, v_y) = max{v_x, v_y}

38 The sensing node decrypts f ’ by computing

 

 

     

Case 2: v_x = v_y , v_x = 3 = 011₂ = X₂X₁X₀, v_y = 3 = 011₂ = Y₂Y₁Y₀

and sends to AG with additional information (the ciphertext of ―1‖ (24,7) ).

39 The sensing node decrypts f ’ by computing

 

 

     