Table 4.

Computational cost of proposed protocol.

	Phase I	Phase II	Total cost
User	$C_E$ + $C_D$ + $C_H$ + $C_{XOR}$	$C_E$ + $C_D$ + $4\ast C_{XOR}$	$2\ast C_E$ + $2\ast C_D$ + $C_H$ + $5\ast C_{XOR}$
$AS$	$2\ast C_E$ + $2\ast C_D$ + $C_H$ + $2\ast C_{ran}$ + $C_{XOR}$	-	$2\ast C_E$ + $2\ast C_D$ + $C_H$ + $2\ast C_{ran}$ + $C_{XOR}$
Gateway	$C_E$ + $C_D$ + $C_H$ + $C_{XOR}$	$C_E$ + $C_D$ + $3\ast C_{XOR}$	$2\ast C_E$ + $2\ast C_D$ + $C_H$ + $4\ast C_{XOR}$
Total Cost	$4\ast C_E$ + $4\ast C_D$ + $3\ast C_H$ + $2\ast C_{ran}$ + $3\ast C_{XOR}$	$2\ast C_E$ + $2\ast C_D$ + $7\ast C_{XOR}$	$6\ast C_E$ + $6\ast C_D$ + $3\ast C_H$ + $2\ast C_{ran}$ + $10\ast C_{XOR}$

Acronyms: C: Computation, E: Encryption, D: Decryption, $XOR$: Ex-or operation, H: Hash, $ran$: random number generation, $PhaseI$: User device registration, $Phase$$II$: Mutual authentication and secret key generation.