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Table 4 Detailed computation and communication costs

From: Location-sharing protocol for privacy protection in mobile online social networks

Protocol

Communication costs

Computation costs

Location updation

Location query

Location updation

Location query

Nan Shen [21]

\((k\,+\,1)\lambda\)

(3p + 3)\(\lambda\)

k.Enc-asym + k.Dec-asym

p.Enc-sym + Enc-asym + p.Dec-sym + Dec-asym

Jin Li [28]

\((n\,+\,n^{2})\lambda \,+\,\mu\)

\((n\,+\,n^{2}\,+\,2p)\lambda\)

n.Enc-asym +  n.Dec-asym + Sig + Ver

\((n\,+\,p)\).Enc-asym + (n + p).Dec-asym

Xi Xiao [30]

\((k\,+\,1)\lambda\)

\((2p\,+\,1)\lambda\)

k.Enc-asym + k.Dec-asym

\((p\,+\,1)\).Enc-asym + \((p\,+\,1)\).Dec-asym

Juan Chen [22]

\((k\,+\,1)\lambda\) + 2\(\mu\)

2p\(\lambda\) + 4\(\mu\)

k.Enc-asym + k.Dec-asym + Sig + Ver

p.Enc-asym + p.Dec-asym + Sig + Ver

Chang Xu [29]

\((2n^{2}+2n)\lambda \,+\,\mu\)

(\(n^{2}\,+\,t\,+\,2p\,+\,n)\lambda\)

2n.Enc-asym + 2n.Dec-asym +Sig + Ver

\((t\,+\,n\,+\,p)\)Enc-asym + \((t\,+\,p\,+\,n)\)Dec-asym

Our protocol

3\(\lambda\) + \(\mu\)

\((2p\,+\,4)\lambda\)

2.Enc-asym + 2.Dec-asym + 2.Sig + 2.Ver

3.Enc-asym + p.Enc-sym + 3.Dec-asym + p.Dec-sym

  1. \(\lambda\): the length of elements calculated by elliptic curve encryption operation
  2. \(\mu\): the length of elements calculated by elliptic curve signature operation
  3. p: In the location query stage of friends and strangers, the number of members meeting the requirements of the inquirer
  4. n: the number of location services
  5. Enc-sym: a symmetric encryption operation
  6. Enc-asym: an asymmetric encryption operation
  7. Dec-sym: a symmetric decryption operation
  8. Dec-asym: an asymmetric decryption operation
  9. Sig: a elliptic curve signature operation
  10. Ver: an operation to verify the validity of an elliptic curve signature
  11. k: one real location and \((k-1)\) virtual locations generated by k anonymous
  12. t: the number of friends assigned to each location server