. 2023 Jan 18;23(3):1122. doi: 10.3390/s23031122

Table 4.

The proposed scheme.

User( $U_{i}$ )	Gateway	Sensor Node( ${SN}_{j}$ )
{User Registration}
(1) Enter: $I D_{i}$ , $P W_{i}$ , $B_{i}$
Generate: $r_{U}^{1}$	(2) Generate: $r_{G W}^{1}$ , $r_{G W}^{2}$ , $r_{G W}^{3}$
Compute: $G e n (B_{i}) = (R_{i}, R_{b i})$ ,	Compute:
$H P W_{i} = h (P W_{i} ‖ R_{i} ‖ r_{U}^{1})$	$T I D_{i} = h (I D_{i} ‖ r_{G W}^{1} ‖ K_{G W})$ ,
Transmit: $I D_{i}$ ⟶	$S_{i}^{1} = h (I D_{i} ‖ r_{G W}^{2} ‖ K_{G W})$ ,
	$S_{i}^{2} = h (I D_{i} ‖ r_{G W}^{3} ‖ K_{G W})$
(3) Compute:	Store: $I D_{i}$ , $T I D_{i}$ , $S_{i}^{1}$ , $S_{i}^{2}$
$U_{i} M_{1} = T I D_{i} \oplus H P W_{i}$ ,	⟵ Transmit: $T I D_{i}$ , $S_{i}^{1}$ , $S_{i}^{2}$
$U_{i} M_{2} = S_{i}^{1} \oplus H P W_{i}$
$U_{i} M_{3} = S_{i}^{2} \oplus H P W_{i}$
$U_{i} M_{4} = h (P W_{i} ‖ R_{i} ‖ I D_{i}) \oplus r_{U}^{1}$
$U_{i} M_{5} = h (r_{U}^{1} ‖ T I D_{i} ‖ S_{i}^{1} ‖ S_{i}^{2})$
Store: $U_{i} M_{1}$ , $U_{i} M_{2}$ , $U_{i} M_{3}$ , $U_{i} M_{4}$ , $U_{i} M_{5}$
{Sensor Node Registration}
	(2) Generate: $r_{G W}^{4}$	⟵(1) Transmit: $S I D_{j}$
	Compute:
	$T S I D_{j} = h (S I D_{j} ‖ r_{G W}^{4} ‖ K_{G W})$
	Store: $S I D_{j}$ , $T S I D_{j}$
	Delete: $S_{i}^{2}$
	Transmit: $T S I D_{j}$ , $T I D_{i}$ , $S_{i}^{2}$ ⟶	(3) Store: $S I D_{j}$ , $T S I D_{j}$ , $T I D_{i}$ , $S_{i}^{2}$
{Authentication and Key distribution}
(1) Verify Password
Enter: $I D_{i}$ , $P W_{i}$ , $B_{i}$
Compute: $R_{i} = R e p (B_{i}, R_{b i})$ ,	(2) Verify the user
$r_{U}^{1} = h (P W_{i} ‖ R_{i} ‖ I D_{i}) \oplus U_{i} M_{4}$ ,	Retrieve: $r_{U}^{2} = U_{i} M_{6} \oplus S_{i}^{1}$
$H P W_{i} = h (P W_{i} ‖ R_{i} ‖ r_{U}^{1})$	Compute:	(3) Verify the gateway
$T I D_{i} = U_{i} M_{1} \oplus H P W_{i}$ ,	$U_{i} M_{8}^{*} = h (r_{U}^{2} ‖ T I D_{i} ‖ t s_{U})$	Retrieve: $r_{G W}^{5} = G M_{1} \oplus T S I D_{j}$
$S_{i}^{1} = U_{i} M_{2} \oplus H P W_{i}$ ,	Verify: $r_{U}^{2}$ ’s freshness, $t s_{U}$	$T I D_{i} = G M_{2} \oplus r_{G W}^{5}$
$S_{i}^{2} = U_{i} M_{3} \oplus H P W_{i}$ ,	$U_{i} M_{8}$ = ? $U_{i} M_{8}^{*}$	$T I D_{i}^{n e w} = G M_{3} \oplus r_{G W}^{5}$
$U_{i} M_{5}^{*} = h (r_{U}^{1} ‖ T I D_{i} ‖ S_{i}^{1} ‖ S_{i}^{2})$		$r_{U}^{3} = U_{i} M_{7} \oplus S_{i}^{2}$
Verify: $U_{i} M_{5}$ = ? $U_{i} M_{5}^{*}$	Generate: $r_{G W}^{5}$	Compute:
	$T I D_{i}^{n e w} = h (I D_{i} ‖ r_{G W}^{5} ‖ K_{G W})$ ,	$G M_{4}^{*}$
Generate: $r_{U}^{2}$ , $r_{U}^{3}$ , $t s_{U}$	$G M_{1} = T S I D_{j} \oplus r_{G W}^{5}$ ,	$= h (r_{G W}^{5} ‖ T S I D_{j} ‖ T I D_{i} ‖ T I D_{i}^{n e w})$
Compute:	$G M_{2} = T I D_{i} \oplus r_{G W}^{5}$	Verify: $G M_{4}$ = ? $G M_{4}^{*}$
$U_{i} M_{6} = r_{U}^{2} \oplus S_{i}^{1}$ ,	$G M_{3} = T I D_{i}^{n e w} \oplus r_{G W}^{5}$
$U_{i} M_{7} = r_{U}^{3} \oplus S_{i}^{2}$	$G M_{4}$
$U_{i} M_{8} = h (r_{U}^{2} ‖ T I D_{i} ‖ t s_{U})$	$= h (r_{G W}^{5} ‖ T S I D_{j} ‖ T I D_{i} ‖ T I D_{i}^{n e w})$
Transmit:	Transmit: $G M_{1}$ , $G M_{2}$ , $G M_{3}$
$U_{i} M_{6}$ , $U_{i} M_{7}$ , $U_{i} M_{8}$ , $T I D_{i}$ , $t s_{U}$ ⟶	$G M_{4}$ , $U_{i} M_{7}$ ⟶	Generate: $S K$
		Compute:
	(4) Verify the sensor node	$S N_{j} M_{1} = S K \oplus S_{i}^{2}$
(5) Verify the gateway	Compute:	$S N_{j} M_{2} = h (S K ‖ T I D_{i}^{n e w} ‖ r_{U}^{3})$
Compute:	$S N_{j} M_{3}^{*}$	$S N_{j} M_{3}$
$T I D_{i}^{n e w} = G M_{6} \oplus S_{i}^{1}$ ,	$= h (S N_{j} M_{1} ‖ S N_{j} M_{2} ‖ T S I D_{j})$	$= h (S N_{j} M_{1} ‖ S N_{j} M_{2} ‖ T S I D_{j})$
$G M_{5}^{*} = h (T I D_{i} ‖ T I D_{i}^{n e w})$	Verify: $S N_{j} M_{3}$ = ? $S N_{j} M_{3}^{*}$	Replace: $T I D_{i} \leftarrow T I D_{i}^{n e w}$
$U_{i} M_{1}^{n e w} = T I D_{i}^{n e w} \oplus H P W_{i}$		Transmit: $S N_{j} M_{1}$ , $S N_{j} M_{2}$
Verify: $G M_{5}$ = ? $G M_{5}^{*}$	Compute:	⟵ $S N_{j} M_{3}$
Replace: $U_{i} M_{1} \leftarrow U_{i} M_{1}^{n e w}$	$G M_{5} = h (T I D_{i} ‖ T I D_{i}^{n e w})$ ,
	$G M_{6} = T I D_{i}^{n e w} \oplus S_{i}^{1}$
Retrieve: $S K = S N_{j} M_{1} \oplus S_{i}^{2}$	Replace: $T I D_{i} \leftarrow T I D_{i}^{n e w}$
Compute:	Transmit: $G M_{5}$ , $G M_{6}$ , $S N_{j} M_{1}$ ,
$S N_{j} M_{2}^{*} = h (S K ‖ T I D_{i}^{n e w} ‖ r_{U}^{3})$	⟵ $S N_{j} M_{2}$
Verify: $S N_{j} M_{2}$ = ? $S N_{j} M_{2}^{*}$