2005). We selected two proposals for the sake of 
comparison, as presented below. 
(Jie et al. 2015) designed an authentication 
protocol that preserves the privacy of users´ data in 
the connection of their electric vehicles for the 
charging or discharging of batteries in the V2G 
network. It also optimizes communications through 
aggregators and dynamically manages the system. It 
uses group signatures and a partially blind signature 
restrictive technique based on identity. The 
architecture comprises five entities, namely Central 
Aggregator (CAG),  LAG, Charging/discharging 
station (ST), Plug-in electric vehicle (PEV) and a 
trusted authority (TA). The protocol consists three 
phases: a) Initial Configuration; b) Generation of 
group blind certificate for each PEV; c) Access of 
PEV to the V2G network through ST.  
(Saxena et al. 2015) proposed authentication 
protocols for the access of EVs in the Smart Grid 
and the recharge and discharge of their batteries 
considering five entities: EVs, Charging Station 
(CS), LAG, Certification/Registration Authority 
(CA/RA) and Control Center (CC). The protocol 
consists of four parts: Initial configuration, where all 
entities generate a pair of public and private keys; 
Registration of EVs: each EV sends information to 
CA/RA and returns a temporary identity to the EV; 
LAG - CA/RA communication: all LAG must have 
the register of the temporary identities of all EVs 
registered in CA/RA, therefore, the communication 
between LAG - CA/RA occurs for updating the 
register of such entities; Protocol execution: when an 
EV must charge or discharge (sell) part of its energy, 
it approaches a CS, establishes communication with 
LAG and generates a session key that guarantees a 
mutual authentication between EV and LAG. The 
EV calculates an identity verification parameter and 
sends an encrypted message to the LAG with the 
session key. The LAG decrypts the researched 
message, adds information for the verification of the 
EV identity, and sends all parameters to the CA/RA 
in a message encrypted with the CA / RA digital 
signature generated by the LAG. Finally, CA/RA 
checks the EV identity and returns a message of 
commands to the EV.  The remaining messages 
exchanged between the EV and CA/RA are 
encrypted under asymmetrical encryption based on 
blind digital firms. 
3  PROTOCOL PROPOSAL 
For the proposal of the protocol, a V2G network 
architecture is considered, involving EVs 
recharging/discharging their batteries; 
Charge/Discharge Stations (CDS);  Aggregators 
(AGs) --- Local AG’s, and a Central AG; 
Authentication Servers (AS), including a Central 
Authentication Server (CAS) and several Substation 
Authentication Servers (SAS), used in large  SG 
networks;  Control Center (CC).  
Three phases are considered:  
1
st
. phase: Initialization of the System 
Two cyclic groups G and G
T
 of order q and P, and a 
generator element of group G are chosen. G and G
T
 
are supposedly related to a non-degenerative pairing 
and a bilinear map that can be efficiently computed: 
ê  : G × G → G
T
  such that ê(P, P) ≠ 1G
T
  and 
ê(aP
1
,bQ
1
)  =  ê(b P
1
,a Q
1
)  =  ê(P
1
, Q
1
)
ab
  ∈ G
T
  for 
every  a, b ∈  
∗
  and every P
1
, Q
1
  ∈ G (Menezes, 
2005). Moreover, the hash functions of the system 
are defined: 
:
{
0,1
∗
→,  
:→ℤ
∗
 and 
:
{
0,1
∗
→ℤ
∗
.   
Finally, the central authentication server (AS) 
and all aggregators (AG) define an elliptical curve 
on a finite field E (Fq) and parameters {G, G
T
, ê, P, 
H
1
, H
2
, H
3
} are published. AS then chooses a private 
key  
,∈
∗
 and calcultates its public key 
=
∗ to be published.  
2
nd
. phase: Registration 
All EVs and  must register on-site in the energy 
supplier´s system. An identity (
) must be 
chosen for the registration of AGs. The aggregator 
then chooses a random number 
∈Z
∗
 to be its 
private key and calculates a public key 
=
∗
.  sends AS a message containing the public key 
and the identity of the device {
,ID
}. CAS 
stores the data received 
 andID
, and 
calculates group private key  
=
|
|
∗
        (1) 
and temporary group identity   
=
∗
(
)
               (2) 
where LAI (local area identifier) identifies the area 
where the aggregator is located and 
∗
 are 
random numbers. 
The registration of an EV is initialized when it 
chooses an 
 identity and an 
∈
∗
 private 
key. It calculates 
=
∗ public key. The 
user sends a message containing the public key and