Computation Complexity. It is the computational resources required by the honest parties during a protocol execution; and (d)
Computation Complexity. For LKE and iLKE, the computational expenses on a worker sensor come from two stages: (i) to establish a secure channel to the associated service sensor and decrypt the received polynomial shares during polynomial share distribution, (ii) to calculate shared keys with other worker sensors in pairwise key establishment. To obtain polynomial shares securely from a service sensor, a worker sensor needs to encrypt a secret key Ks with Xxxxx’x algorithm (one squaring only) and decrypt the received poly- nomial share with a symmetric cryptography algorithm (AES, DES, etc.). Note that the asymmetric Xxxxx’x cryptosystem, with a comparable security with RSA, shifts a large amount of the computational overhead to service sensors and thus lengthens the lifetime of worker sensors. To compute a pairwise key with sensor j at (x , y ), [12] X. Xxxxxxxxxx and X. X. Xxxxxx, “A key-management scheme for distributed sensor networks,” in ACM CCS’02, pp. 41-47. [13] X. Xxxx and X. X. Xxxx, “GPSR: greedy perimeter stateless routing for j j wireless networks,” in ACM MobiCom 2000, pp. 243-254. sensor i instantiates the λ-degree polynomial share with kj = Hash(xj, yj), which requires λ modular multiplications and λ modular additions. The computation process has been tailored for sensor networks by [14] which greatly reduces the computation overhead by transforming onto a smaller finite field.
Computation Complexity. For the space complexity, the DPCopula-MLE algo- rithm takes O(mn) (i.e. the size of the original dataset), where m is the number of dimensions, n is the number of records in the original dataset. For the time i=1 complexity, computing all DP marginal histograms take O(Σm (AilogAi + n)) = O(mAlogA + mn) due to [47], where A = max{A1, . . . , Am}. DP MLE takes l2 l O(l × m2n2 ) = O(m2n2 ). DPCopula-MLE takes O(mAlogA + m2n2/l).
Computation Complexity. For the space complexity, DPCopula-Xxxxxxx is the same with DPCopula-MLE. For the time complexity, the complexity of each Xxxxxxx’x τ takes O(nlogn) using a fast Xxxxxxx’x τ computation method. The total time complexity is O(mAlogA+m2nlogn). When the number of records is large, computing Xxxxxxx’x τ is very time consuming. A natural technique is to compute Xxxxxxx’x τ only on nˆ sample records of the full data to reduce the computation complexity which requires O( 4 ) Laplace noise on each coefficient. This sampling method guarantees differential privacy by enlarging the Laplace noise from O( 4 ) to O( 4 ). Here the n+1 nˆ+1 selection of nˆ should guarantee that the Laplace noise O( 4 ) be sufficiently small nˆ+1 compared to the scale of original correlation coefficients that is [−1, 1]. In practice, setting nˆ ≥ (50m(m − 1)/s2) − 1 is adequate. Thus, no matter how large n is, the time complexity will be fixed to O(mAlogA + m2).
Computation Complexity. Until this work is proposed, there is no contribution that involved the social profile in the smart IoT industrial context. For the overhead, we compare our scheme with others in the aspects of setup/mutual authentication, key generation, renewing of VID phases. In Table 4, we only compare the time cost in the registration and mutual authentication phase between SE and the Fog. Table 4. Computation comparisons Computation cost Setup and mutual authentication Key Generation Renewing of VID Xxxxxxxx et al. [25] 3Tmul + 1TH + 1Tenc 1 TH + 1Tmul n.a 3TAsymenc+ enc+1Asym dec 2Tenc+1Tdec+4 Arij et al [21] 4Tmul+9TH Tmul 1TH n.a Xxxxx et al. [23] 9Tenc + 2TH n.a n.a Xxx et al. [24] 12TH + TF + 2Thmac + 1Tenc 1TH + 1Tenc 4TH Xxxxx et al.[26] 3TH + 1Tenc 1TH + 1Tenc 1TH Ours 11 TH+ 1Tenc 1 TH 1 TH Xxxxxxxx et al. [22] 6TH + 4Tmul+ 1Tenc+1Tdec+1TAsym 1TAsym dec+2TH+
