Table 1.

Notations used in this paper.

Notations	Description
$S{M}_j$	j-th smart meter
$NG$	Neighborhood gateway
$I{D}_j$	$S{M}_j$’s identification
$m_i^j$	i-th message for $S{M}_j$
$D_i^j$	Data report of i-th $S{M}_j$
$V_i^j$, $V_i^{\prime j}$	Verification
$K_i^j$	i-th secret key for $S{M}_j$
$r_i^j$	i-th random number for $S{M}_j$
h ($·)$, H ($·)$	One-way hash function
$X\Vert Y$	Concatenation operator
⊕	Bitwise XOR operator
$T_{NG}$, $T_j$	Timestamp for $NG$ and $S{M}_j$