“…Therefore, the total communication of our proposed scheme is 4673+4641 = 9314 bits.Next, in Kumar and Garg,6 the user starts the communication sent by the login request < A ui > to the satellite and then the satellite adds ID sat to the received message and transmits < A ui , ID sat > , where the sizes of A ui , ID sat are 4096 and 32 bit each, and the NCC sends the respond request < a ni , w ni ,b ni > to satellite, and satellite passes the message < a ni , w ni , b ni , ID sat > with its own identity to user, where the sizes of < a ni , w ni , b ni ,ID sat > are 4096, 1, 512, and 32 bits, respectively, and the end the user sends the last communication message < w ui , b ui , AID i , IDsat > to NCC, where the sizes of < w ui , b ui , AID i , IDsat > are 1, 512, 512, and 32 bits, respectively. Therefore, the total communication cost of Kumar and Garg 6 scheme is 9826 bits.Next, in Dharminder et al18 protocol, the mobile user sends login request < a ui , v ui , w ui , aid i > to the satellite via public channel, then the satellite adds id sat to the received message and transmits < a u i , v u i , w u i ,aid i > ,id sat > to NCC, where the sizes of a u i ,v u i , w u i ,aid i , id sat are 4096, 512, 1, 512, and 32 bits, respectively, and the NCC sends the respond request < b ni , w ni , a ni , id sat > to satellite, and satellite passes the message < b ni , w ni , a ni > to user U i , where the sizes of b ni ,w ni , a ni , id sat are 512, 1, 4096, and 32 bits, respectively. Therefore, the total communication of Dharminder et al scheme is 5153+4641 = 9794 bits.…”