## 6 Discussion
### Communication, Computation, and Storage Overhead of the 5 GAKA-LCCO Protocol  
In order to evaluate the communication overhead, we will compute the transmitted message size. According to [2; 3; 4; 26; 27], the sizes with respect to various fields of the transmitted messages are presented in Table 2.  
A comparative analysis between the 5 GAKA-LCCO protocol and the recently improved 5G AKA protocols [23; 24; 26; 28] regarding the communication, computation, and storage overhead is given in Table 3.  
In Table 3, the communication overhead represents the total communication overhead of the transmitted messages among the UE, SN, and HN, including the transmitted messages in both the synchronization failure procedure and the MAC failure procedure. For the 5G AKA protocol, the total communication overhead = \(448+576+496+368+128+128+400+208+336+16+16=3120\) bits. For the protocol in [23], the total communication overhead = \(384+640+496+368+128+128+400+208+336+16+16=3248\) bits. For the protocol in [24], the total communication overhead = \(448+576+496+368+128+128\) + \(400+256+256+208+208=3472\) bits. For the protocol in [26], the total communication overhead = \(576+192+192+768+1088+576+128+128+16=3664\) bits. For the protocol in [28], the total communication overhead = \(448+704+1008+560+192+1  
\(272+336=3664\) bits. For our proposed 5 GAKA-LCCO protocol, the total communication overhead = \(192+448+768+880+368=2656\) bits.  
In Table 3, _ECDH_ denotes the generation and verification of an elliptic curve Diffie-Hellman (ECDH) exchange. _PED_ denotes the generation and verification of a public key encryption and decryption process. _ED_ denotes the generation and verification of a symmetric key encryption and decryption process. \(F\) denotes the generation and verification of a key function, a key derivation function, a MAC function, or a hash function, which are grouped into one category because they require the same amount of calculation [27]. _XOR_ denotes the generation and verification of an XOR value.  
The storage overhead is composed of three parts: Public parameters, identity information, and keys [34]. Hence, the storage overhead in Table 3 represents the total storage overhead of the public parameters, identity information, and keys on the UE, SN, and HN. For the 5G AKA protocol, the total storage overhead = \(1408+512+1408=3328\) bits. For the protocol in [23], the total storage overhead = \(1920+2688+3072=7680\) bits. For the protocol protocol in [24], the total storage overhead = \(2432+512+256=5504\) bits. For the protocol in [26], the total storage overhead = \(1408+576+1408=3392\) bits. For the protocol in [28], the total storage overhead = \(1408+512+1408=3328\) bits. For our proposed 5 GAKA-LCCO protocol, the total storage overhead = \(1408+512+1472=3392\) bits.  
From Table 3, the communication overhead of the 5 GAKA-LCCO protocol is considerably less than that of the 5G AKA protocol and the recently improved 5G AKA protocols [23; 24; 26; 28]. According to [26], _PED_ > _ECDH_ > _ED_ > \(F\) > _XOR_ in computation overhead, so the computation overhead of the 5 GAKA-LCCO protocol is also lower than that of the 5G AKA protocol and the recently improved 5G AKA protocols [23; 24; 26; 28]. Hence, our proposed 5 GAKA-LCCO protocol has less communication and computation overhead than the 5G AKA protocol and the recently improved 5G AKA protocols. In addition, the storage overhead of the 5 GAKA-LCCO protocol is slightly more than that of the 5G AKA protocol and the improved 5G AKA protocol in [28] and is equivalent to that of the improved 5G AKA protocol in [26]. However, the storage overhead of the 5 GAKA-LCCO protocol is considerably less than that of the two improved 5G AKA protocols in [23; 24].