Table 10 Computed costs of various group AKA protocols with respect to the applied cryptographic operations, n is representing to the number of IoVT devices requesting AKA.

From: A secure group-based authentication protocol for IoVT in 5G-enabled smart transportation and road safety systems

Protocol

Computation cost (ms)

P1: GBAAM45

\(\hbox {T}_{xor}\) + n(4*\(\hbox {T}_{hash}\) + \(\hbox {T}_{rand}\) + 2*\(\hbox {T}_{Aenc}\)) + K*(6*\(\hbox {T}_{hash}\) + \(\hbox {T}_{xor}\))

P2: EMTC-AKA47

n(7\(\hbox {T}_{hash}\) + 4\(\hbox {T}_{Senc}\) + 2\(\hbox {T}_{xor}\)) + 2\(\hbox {T}_{hash}\) + \(\hbox {T}_{rand}\)

P3: Ouaissa’s AKA18

n(2\(\hbox {T}_{xor}\) + \(\hbox {T}_{rand}\)) + (12n + 6)\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{mul}\)

P4: Braeken’s AKA35

n(2\(\hbox {T}_{Senc}\) + 11\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{rand}\) + 2\(\hbox {T}_{Aenc}\))

P5: NAPV10

(n + 2)\(\hbox {T}_{rand}\) + n(2\(\hbox {T}_{xor}\) + 15\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{mul}\))

P6: Choi’s AKA46

\(\hbox {T}_{rand}\) + 4*\(\hbox {T}_{hash}\) + n(\(\hbox {T}_{xor}\) + 2*\(\hbox {T}_{mod}\) + 6\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{Senc}\)) + \(\hbox {T}_{xor}\)

P7: Shang’s AKA17

(n - 1)(\(\hbox {T}_{ver}\) + \(\hbox {T}_{sig}\)) + n(2\(\hbox {T}_{hash}\) + 5\(\hbox {T}_{sm}\) + 2\(\hbox {T}_{xor}\)) + (n + 3)\(\hbox {T}_{rand}\) + (3n + 6)\(\hbox {T}_{mul}\)

P8: Miao’s AKA16

n(7\(\hbox {T}_{xor}\) + 13\(\hbox {T}_{hash}\) + 6\(\hbox {T}_{cmm}\)) + 8\(\hbox {T}_{hash}\) + 4\(\hbox {T}_{ccm}\) + 2\(\hbox {T}_{xor}\)

P9: Liu’s AKA34

n(4\(\hbox {T}_{mul}\) + 3\(\hbox {T}_{rand}\) + 2\(\hbox {T}_{aenc}\) + 6\(\hbox {T}_{xor}\) + 11\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{senc}\))

P10: Fu’s AKA48

n(6\(\hbox {T}_{xor}\) + 3\(\hbox {T}_{rand}\) + 11\(\hbox {T}_{hash}\) + 4\(\hbox {T}_{mul}\)) + (\(\hbox {T}_{xor}\) + 2\(\hbox {T}_{rand}\) + 4\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{mul}\))

P11: \(\hbox {E}^{2}\)sec49

n(2\(\hbox {T}_{xor}\) + 10\(\hbox {T}_{hash}\) + \(\hbox {T}_{rand}\)) + 2\(\hbox {T}_{enc}\) + 2\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{mod}\)

P12: EG-AKA39

2\(\hbox {T}_{Aenc}\) + 3\(\hbox {T}_{mul}\) + 2\(\hbox {T}_{rand}\) + 8\(\hbox {T}_{hash}\) + n(2\(\hbox {T}_{rand}\) + 10\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{Aenc}\) + 3\(\hbox {T}_{mul}\))

P13: 5G-AKA33

n(17\(\hbox {T}_{hash}\) + 2\(\hbox {T}_{Aenc}\))

P14: Proposed Protocol

16\(\hbox {nT}_{hash}\) + 5(n - 1)\(\hbox {T}_{xor}\) + \(\hbox {T}_{rand}\) + 2\(\hbox {T}_{hash}\)

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