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Table 4 Comparison of computation costs

From: A secure electronic medical record authorization system for smart device application in cloud computing environments

Protocol

Chiou et al. [13]

Mohit et al. [14]

Kumar et al. [15]

Li et al. [16]

The proposed scheme

Patient visiting doctor phase

\(\begin{aligned} 1T_{Sign} + 3T_{P} + \hfill \\ 2T_{S} + 7T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 3T_{S} + \hfill \\ 11T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 3T_{S} + \hfill \\ 10T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 3T_{S} + \hfill \\ 11T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 4T_{Sign} + 4T_{A} + \hfill \\ 2T_{S} + 2T_{H} \hfill \\ \end{aligned}\)

Electrical medical record search phase

\(\begin{aligned} 3T_{Sign} + 4T_{M} + \hfill \\ 8T_{P} + 6T_{S} + \hfill \\ 18T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 4T_{Sign} + 4T_{S} + \hfill \\ 19T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 4T_{Sign} + 12T_{S} + \hfill \\ 20T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 5T_{Sign} + 10T_{S} + \hfill \\ 20T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 8T_{Sign} + 8T_{A} + \hfill \\ 4T_{S} + 2T_{H} \hfill \\ \end{aligned}\)

Diagnosis phase

\(\begin{aligned} 1T_{Sign} + 2T_{S} + \hfill \\ 8T_{H} + 2T_{P} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 2T_{S} + \hfill \\ 5T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 5T_{S} + \hfill \\ 10T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 1T_{Sign} + 2T_{S} + \hfill \\ 8T_{H} \hfill \\ \end{aligned}\)

\(2T_{A}\)

Total cost

\(\begin{aligned} 5T_{Sign} + 4T_{M} + \hfill \\ 13T_{P} \hfill \\ \end{aligned}\)

\(\begin{aligned} 6T_{Sign} + 9T_{S} + \hfill \\ 35T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 6T_{Sign} + 20T_{S} + \hfill \\ 40T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 7T_{Sign} + 15T_{S} + \hfill \\ 36T_{H} \hfill \\ \end{aligned}\)

\(\begin{aligned} 12T_{Sign} + 14T_{A} + \hfill \\ 6T_{S} + 4T_{H} \hfill \\ \end{aligned}\)

  1. \(T_{Sign}\): The time is taken to execute/verify a signature. \(T_{A}\): The time is taken to calculate an asymmetric encryption/decryption operation. \(T_{M}\): The time is taken to calculate a multiplication operation. \(T_{P}\): The time is taken to calculate a bilinear pairing operation. \(T_{S}\): The time taken to calculate a symmetric encryption/decryption operation. \(T_{H}\): The time is taken to calculate a one-way hash function