## 2 Literature
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**References** & **Mutual Authentication Scheme** & **Entity’s Involved in the Authentication Process** & **Cryptography (Enc/Dec) or Message Communication** & **Protocol Implementation Scenario** \\ \hline \multirow{4}{*}{Vehicle-to-grid (V2G) [14]} & Physical unclonable function (PUF)-based secure user key exchange authentication (SUKA) & Vehicle, aggregator, and grid server & A function designed to perform XOR, addition, scalar multiplication, and exponential computation & A vehicle smart grid ecosystem (V2G) \\ \hline \multirow{4}{*}{Remote health monitoring [15]} & A signature-based two-factor authentication protocol & The body sensors, personal devices (PDs), the medical server (MS), and the user (doctor/family) & A function using a secret key, a prime number, a generator of the cyclic group, a pseudo-random value, a hash function, an XOR operation, a concatenation operation, and nonce values & Remote health monitoring \\ \hline \multirow{4}{*}{5G security [16]} & A signature-based mutual authentication protocol for m-health systems, which symptomatic D2D communication within the 3 GPP infrastructure & A health center, a cloud server, patients with and without sensors, patients’ devices, doctors, 3 GPP access technology, evolved node B (eNB), and the 3 GPP evolved packet core (EPC), represented by the home subscriber server (HSS) & Symmetric key with a random number, bi-linear pairing, and a signature & Mobile health (m-health) and telecare medicine information systems (TMISs) \\ \hline \multirow{4}{*}{Public key (ECC)-based two-factor framework} & Enhanced elliptic-curve- cryptography (ECC)-based two-factor authentication framework & Elliptic curve discrete logarithms problem (ECDLP) and elliptic curve computational (ECCDHP) & Elliptic curve discrete logarithms problem (ECDLP) and elliptic curve computational & Smart card authentication \\ \cline{1-1} \cline{2-5}  & A novel mode-based hash-chain mutual authentication protocol & A cloud server, a university gateway server, a department server, and a user/device & Symmetric key with the lightweight encryption system (LES) & A fog/edge model for inter-university student authentication \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with the recent approaches. On the computational complexity of combinatorial problems, [PERSON] et al. [17] presented the problem of the maximum number of requests that can be made simultaneously within a network using the concept of edge-disjoint paths (EDP) or computing the maximum flow, which has been proven to be NP-complete. Ultimately, we wanted to overcome this problem by using cryptographic techniques and mathematical functions that can give high security with as few calculations as possible, to achieve a large amount of mutual authentication within a network containing millions of devices in the least possible time. Authentication is best served by ZKP, as shown by [PERSON] [18] and [PERSON] [19]. We surveyed various works in the literature to study ZKP applications and the use of mathematical methods within it. A complete ZKP ensures maintaining the three properties of completeness, soundness, and zero-knowledge. ZKP has a wide variety of authentication applications that include field programmable gate arrays (FPGAs), cloud computing, RFID, P2P systems, E-auction, etc. The following survey presents a short note about some well-known methods. FPGA design verification using intellectual property (IP) marks by using the zero-knowledge protocol was presented by [PERSON] et al. [20]. The objective of this work was the trusted proof of embedding desired watermarks within the FPGA. This was achieved by non-disclosure of the details of the mark's position and the details of the embedded signature string as marks. Multi-cloud storage verification of integrity for data possession by cooperative proving was presented by [PERSON] et al. [21].