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Table 6 Computation complexity analysis of the protocol

From: Protecting the grid topology and user consumption patterns during state estimation in smart grids based on data obfuscation

Client side computations

Cloud computations

Utility provider \(\mathcal {U}\)

S i1

S ij

 

KeyGen - O(m+n+T)

–

–

Computeψ([F1],[Z1]) - O(n1m1T)

MatrixTrans ψK(.) - O(n1m1+n1m2+n2m1+n2m2)=O(nm)

O(miT)

O(1)

Computeψ([F12],[Z2]) - O(n1m2T)

Verify - O(n1T+n2T)=O(nT)

O(miT)

–

Computeψ([F12],[Z2]) - O(n2m1T)

Unmask - O(n1T+n2T)=O(nT)

–

–

Computeψ([F2],[Z2]) - O(n2m2T)

MatrixAdd - O(n1T+n2T)=O(nT)

–

–

Computeψ([H+],[Z]) -, O(nmT)

Total client-side computation cost ≈O(nm+mT+nT)

Total cloud computation cost =O(nmT)