A Secure Two-Way Verification based Authentication Scheme with user Anonymity for Cloud Networks
* 1S.Mercy, 2R.Nagaraja , 3 M.Jaiganesh
1,2Department of Information Science and Engineering, Bangalore Institute of Technology, Bangalore, Karnataka, India.
3Department of Information Science and Engineering, Faculty of Engineering and Technology, Jain University, Bangalore, Karnataka, India.
1[email protected], 2[email protected], 3[email protected]
The cloud computing along with massive storage and privacy based services are upcoming technique.The information and communication technology connected with various handhold devices through Internet for performing thedata sharing between public networks with large size of users. The internet enabled devices are becoming more sophisticated applications for users in cloud computing environment. An important progression in today‟s cloud computing technology is the facility to connect both private and public networks for maintaining large resource or for handling large size of information. Integration of remote devices and cloud environmentbrings inclusiveusage for real-time application in many commercial products. The security alarms such as authentication and information confidentiality of these clouds computing environment plays an imperative role in successful integration of authentication and access controls. In this paper, we proposed a two-way authentication protocol using Discrete Logarithm. The proposed scheme satisfies all basic security requirements and provides mutual authentication. In this scheme, every new session a new session key will be produced for further communication. The detailed analysis of security for the proposed scheme demonstrates that it is withstand against various attacks.
In the earlier stage of 90‟s, storage systems are maintained by the single server and controlled by various authentication and confidentiality schemes. Lot of research publications and research activities are proposed by the researcher. Due to the large amount of storage purpose, later 2000 cloud computing comes to the commercial purpose usage. Many issues are identified by the developers and research peoples in cloud storage and service. Practical difficulties for providing better security in cloud computing are solved by applying various cryptographic techniques. The security needs in cloud computing has been classified into two main areas of confidentiality and authentication. Most of the cloud computing applications are designed with the combination of authentication and access control for user validation. As a service provider, the cloud computing environment has to provide efficient communication between cloud users and could servers.
The fast growing of IT technology, cloud computing environment has become one of the important research areas in recent years. The cloud computing services are quickly integrated with our daily lives due to its high service efficiency, high scalability and less expensive . The traditional model of service gets changed fundamentally for providing consumer access rights and services to resources: as a service granter of cloud computing.
This new technology efficientlyrallies the use of resources by maintain the centralized demands. The cloud customers are gaining the accessibility of using resources and decrease the using charge through on demand.
Due to this reason, big companies are build and maintain a individual cloud environment and provide services. For example, Google App Engine, Amazon Web services,
and IBM Smart Cloud  are maintaining and providing cloud service for all the customers with minimum cost. In addition to that, both the individuals and small level companies are enjoying the benefits of cloud services. In general, there are three types of cloud services are available the market: providing Infrastructure as a Service (IaaS), providing Platform for developing various applications as a Service (PaaS), providing various Software applications for the users as a Service (SaaS) .
Recently, most of the business solutions are transformed and changed to cloud application environment. The security issues become one of the prominent areas in cloud environment, due to the fast growing of cloud services. The following questions are most common in cloud service, how to protect user data from unauthorized access by the illegal users and how to provide user privacy. The preserving user privacy has become a challenging problem and hot area for the researchers.
These issues are solvable by applying user authentication verification schemes. The user authentication schemes are developed based on basic user verification method like, two- factor, three-factors. These schemes first verify the user identity and secret code (password, Pin number, Passcode, OTP). If the user verification successfully completed then the cloud server allow the user for accessing the cloud data and services.
In this scenario, user will be verified and malicious user request will be restricted. The cloud servers are validated by applying mutual authentication schemes. A secure authentication schemes must satisfy the above mentioned points. Once the authentication for user and cloud server is over then a session key will be established for further session secure communications.
The password-based authentication schemes are suitable for cloud environment by combine with cryptographic algorithms. In this authentication scheme, user has to register with the cloud server by including user identity and password.
2. Related Work
In 2011, Hao et al.  proposed the new authentication scheme with two-factor based on the combination of password and smart cards for the environments of cloud computing.
Lot of research articles has been published with enhanced versions [35-42], each scheme different in terms of security , user privacy , usage , and competence .
A remote user authentication protocol with biometrics identity is an authentication scheme in which a remote trusted server confirms the legality of a user over a public network using his biometric identity. Last few years, several research papers have been published by the scholars in the field of biometrics-based remote user authentication protocol using smart cards [11–24]. A remote user authenticationschemes with user biometric proposed for different kinds of real-time environment such as protected multi-server environments [25–29]
and Telecare Medicine Information System (TIMS) [30–33]. An effective three-factor authentication protocol for remote user verification are proposed in [34, 35] using Discrete Logarithm Problem (DLP) and Elliptic Curve Cryptosystem (ECC).
In 2010, Li and Hwang  introduced an efficient bio-metric based authentication scheme for remote users using smart cards. Later, Li et al.  and Das  shows that Li and Hwang's  scheme suffers with few security flaws and they have proposed two new improved authentication protocol based on the classical biometrics technology. In the proposed schemes, the user biometric identity is matched with the original biometric identity stored in the server system storage with basic security developments to overwhelm the noticed security defects.
In 2012, An  shows that Das‟s  scheme has some security weakness, like password guessing, user impersonation, and insider attacks. To overcome the security weakness in the Das‟s  scheme An  proposed an upgraded scheme. In 2013, Khan and
Kumari  pointed out that there some gaps are present in the An‟s  protocol and they have introduced an upgraded biometric-based remote user authentication scheme to overcome the pitfalls by incorporating the user anonymity property. Recently, Sarvabhatla et al.  and Wen et al.  pointed out that Khan and Kumari‟s  scheme is subject to against guessing of password attacks and user masquerade attacks. They have proposed two new authentication schemes to overwhelmed the security faintness of Khan and Kumari‟s 
scheme. The above illustrated protocols make use of user‟s biometrics identity to defend the user‟s password and improve the user‟s secrecy and privacy.
In 2013, Yang et al.  dedicated to introduce a secure authentication protocol for the environment of cloud computing, this scheme is weak to dictionary attack. Then Yang et al.
 introduced a new protocol; inappropriately, Chen et al.  revealed this scheme is subject to insider attack and impersonation attack. Chen et al  proposed a new version to protocol to overcome the weakness.Chen et al  scheme is broken by Wang et al. . Wang et al.  showed that Chen et al.‟s scheme  is vulnerable to offline dictionary attack and impersonation attack. Recently, Amin et al. shows that the security flaws in the schemes of Xue et al.  and Chuang et al. . These two schemes are fail to provide user anonymity and forward secrecy while being not able to resist against offline password guessing attack and so on. Therefore, they designed a new scheme that claims to overcome the security flaws of the two schemes and be secure to various attacks.
Most of the biometrics identity based or three-factor authentication schemes [3, 6, 7, 9, 10] are fails to withstand security issues, because of the using cryptographic hash function directly on the biometric identity. The hash digested values are computed directly from the biometric identities, but no two biometrics readings will have the same feature and they are rarely identical.
In 2015, Das and Goswami  proposed a robust remote authentication scheme based on biometric identity using smart cards. The biometric identity is protected by using fuzzy extractor techniques and Bio-Hashing function. Das and Goswami  scheme requires so expensive communication and computation and this schemeneeds the user has to remember a complex password. Zhao et al.  proposed a new method by applying a fuzzy negotiation structure by using the concept of fuzzy extractor technology to secure a Body Sensor Network (BSN). In the pre-stage process of the structure, each biosensor node has been preloaded with secret keys for the purpose of security and verify the commitment.
In 2016, Roy et al.  presented a remote user authentication by applying biometrics for a TMIS applications using Bio-Hashing function. Qi and Tang  proposed a new session initiation protocol based on biometrics authentication using a fuzzy extractor technique. Roy et al. and Qi and Tang schemes needs high computational and communication costs. In , Henniger and Waldmann proposed a method with biometric identity based authentication protocol using smart cards.
In recent years, extensive efforts have been taken for a secure and practical authentication scheme in cloud computing environment, some of the recent schemes are [26–
29]. Most of the researchers are claims that, these scheme are having security flaws more or less. Design and developing a secure authentication scheme is still a challengefor cloud computing environment. Recent years, many peoples are using cloud computing fir real-time application like, hospital, online-shopping, etc., the potential security pressures will lead to greater damage. This unacceptable situation motivates us to explore the inherent reasons of the failure in those schemes, find the basic method to fix the security flaws, and design a robust and efficient user authentication protocol for cloud computing environment.
In this paper, we have proposed a two-way authentication scheme using Discrete Logarithm. The proposed scheme satisfies all basic security requirements and provides mutual authentication. In this scheme, every new session a new session key will be generated
for further communication. The security analysis of the proposed scheme demonstrates that it is secure against various attacks.
3. Proposed Two-way Authentication scheme
In this section, we providing some fundamental cryptographic properties, like Collision resistant property, Discreate Logarithm Problem and Bio-Metric Fuzzy Extractor.
1. Hash function with Collision resistant
In general, the definition for the collision resistant hash function as follows :
Definition : A cryptographic hash function is defined as follows, 0,1 ∗ : → 0,1 𝑘, this function known to be a collision resistant hash function if and only if, the following properties are satisfied:
a. Compression: The function . produces the output of 𝑥 with fixed length of 𝑘 − 𝑏𝑖𝑡𝑠 for the input of 𝑥 of random finite bit length.
b. Pre-image resistance: For all the specified outputs of . , it is computationally infeasible for finding any input 𝑥′ such that it produce 𝑥′ = 𝑦.
c. Collision resistant: It is computationally infeasible for finding any two different inputs 𝑥 and 𝑥′produce the same hash value, i.e. 𝑥 = 𝑥′ .
2. Discrete Logarithm Problem
Definition : The Discrete Logarithm Problem over a group 𝑍𝑝∗, can be illustrated as follows: Let us assume that 𝑍𝑝∗ is a finite cyclic group with respect to the order of 𝑝, here 𝑝 is sufficiently large prime number. Here 𝑔 is a generator of finite cyclic group 𝑍𝑝∗, and 𝑦 is a positive integer belongs to the group of 𝑍𝑝∗. Then the modular exponentiation for the 𝑦 is denotes as follows,
𝑥 = 𝑔𝑦 𝑚𝑜𝑑 𝑝 , 𝑥 ∈ 𝑍𝑝∗
Let us assume that, the known value of (𝑥, 𝑝, 𝑔) are public variable. From the known values finding of 𝑦 is computationally infeasible. This will takes polynomial time for solving the problem.
3.2. Proposed Scheme
The proposed authentication scheme has three phases, Registration Phase, Login Phase, Authentication and verification Phase. The following section explains proposed phases in detail. The registration phase will be executed only once during the user registration. The user may access the cloud services by executing login phase and each new login request the user will get new session key. This key can be used for further secure session communication.
a. Registration Phase
In the registration phase, theuser 𝑈𝑖, selects his identity 𝐼𝐷𝑖 and password 𝑃𝑊𝑖. The user 𝑈𝑖has to perform the following steps,
1. Compute 𝐶𝐼𝐷𝑖 = 𝐼𝐷𝑖||𝑇𝑅 and 𝐶𝑃𝑊𝑖 = 𝑃𝑊𝑖||𝑇𝑅
2. The user 𝑈𝑖 request the Cloud Server 𝐶𝑆 bysending a registration request along with the following parameters
𝐶𝐼𝐷𝑖, 𝐶𝑃𝑊𝑖, 𝑇𝑅
3. The Cloud Server𝐶𝑆receives the registration request and stores𝐶𝐼𝐷𝑖, 𝐶𝑃𝑊𝑖 and 𝑇𝑅in a database maintained by the Cloud Server
4. The Cloud Server send a accepted and conformation message to the user 𝑈𝑖 along with the Public Key of Cloud Server 𝐾𝑒𝑦𝑃 .
5. The user 𝑈𝑖maintain the Public Key of Cloud Server 𝐾𝑒𝑦𝑃 for further communication with the Cloud Server
b. Login Phase
The legal users are allows to enter into the Cloud Server through login phase only.
During the client login phase, the user 𝑈𝑖 has to enter his/her Identity𝐶𝐼𝐷𝑖 and Password 𝐶𝑃𝑊𝑖through service request login page. The client login page will perform the following steps,
1. The client login paper computes 𝐶𝐼𝐷𝑖𝑛𝑒𝑤 = 𝐼𝐷𝑖 ⊕ 𝑇𝐶 and 𝐶𝑃𝑊𝑖𝑛𝑒𝑤 = 𝑃𝑊𝑖⊕ 𝑇𝐶 2. The client computes 𝐶1 = (𝐶𝐼𝐷𝑖𝑛𝑒𝑤||𝐶𝑃𝑊𝑖𝑛𝑒𝑤) and encrypt the 𝐶1 by using public
key of Cloud Server 𝐾𝑒𝑦𝑃 as follows 𝐸1 = 𝐸𝑛𝑐𝐾𝑒𝑦𝑃(𝐶1)
3. Select a random nonce 𝑟 and compute the following value, 𝐶2 = (𝐶1||𝑇𝐶||𝑟) 4. Encrypt the 𝐶2 by using public key of Cloud Server as follows, 𝐸2 = 𝐸𝑛𝑐𝐾𝑒𝑦𝑃(𝐶2) 5. The login request message has been generated along with the following parameters,
𝐿𝑜𝑔𝑖𝑛 𝑅𝑒𝑞𝑢𝑒𝑠𝑡 𝑀𝑒𝑠𝑠𝑎𝑔𝑒 = 𝐸1, 𝐸2, 𝑇𝐶 c. Verification and Mutual Authentication Phase
In this phase, the Cloud Server 𝐶𝑆 receives the login request message and verifies it as follows
1. The Cloud Server CS receives the login request message 𝐸1, 𝐸2, 𝑇𝐶 at 𝑇𝐶∗and verify the authentication as follows,
a. If 𝑇𝑐 − 𝑇𝑐∗ ≤ ∆𝑇 then ACCEPT the Login request and proceed further b. Else REJECT the login request message
c. The Cloud Server decrypts the received message by using the private key 𝐾𝑒𝑦𝑃𝑟as follows,
𝐷1 = 𝐷𝑒𝑐𝐾𝑒𝑦𝑃𝑟 𝐸1 and𝐷2 = 𝐷𝑒𝑐𝐾𝑒𝑦𝑃𝑟 𝐸2
d. If 𝐷1 == (𝐶𝐼𝐷𝑖𝑛𝑒𝑤||𝐶𝑃𝑊𝑖𝑛𝑒𝑤) then ACCEPT the Login request and go to Step 2
e. Else REJECT the request
2. The Cloud Serverselects a random number 𝑟2 and compute session key as follows 𝑆𝐾𝑁𝑒𝑤 = 𝑔 𝐷2⊕𝑟2⊕𝑇𝑆 (𝑚𝑜𝑑 𝑃)
3. The Cloud Server computes𝐶3 = (𝐷2||𝑟2||𝑇𝑆) and 𝐸3 = 𝑆𝐸𝑛𝑐𝑆𝐾𝑁𝑒𝑤(𝐶3)
4. The Cloud Server generate a mutual authentication message 𝑀𝐴𝑁𝑒𝑤 = 𝐸3, 𝑟2, 𝑇𝑆 5. The Client user𝑈𝑖 receives the message 𝑀𝐴𝑁𝑒𝑤 = 𝐸3, 𝑟2, 𝑇𝑆 at 𝑇𝑆∗from the Cloud
Server CS and perform the following checking process,
a. If 𝑇𝑠− 𝑇𝑠∗≤ ∆𝑇 then ACCEPT the Login request and proceed further b. Else REJECT the mutual authentication message
c. Compute session key as follows, 𝑆𝐾𝑁𝑒𝑤 = 𝑔 𝐸2⊕𝑟2⊕𝑇𝑆 𝑚𝑜𝑑 𝑃 , here 𝑟2 and 𝑇𝑆values are taken from 𝑀𝐴𝑁𝑒𝑤.
d. The user 𝑈𝑖 decrypts 𝐸3as follows, 𝐷3 = 𝑆𝐸𝑛𝑐𝑆𝐾𝑁𝑒𝑤 𝐸3 and compute 𝐷4 = (𝐶2||𝑟2||𝑇𝑆)
e. The user 𝑈𝑖compare 𝐶3 and 𝐷4 as follows,
𝑖𝑓 𝐶3 == 𝐷4 𝑡𝑒𝑛 𝐴𝐶𝐶𝐸𝑃𝑇 f. Else REJECT the Mutual Authentication message
The common session key will be agreed upon with the user 𝑈𝑖and Cloud Server CS 4. Security Analysis
a. User Anonymity and maintaining Session Key
In the proposed authentication scheme, the attackers cannot obtain any user private information like the user‟s identity form the known information of login request 𝐿𝑜𝑔𝑖𝑛 𝑅𝑒𝑞𝑢𝑒𝑠𝑡 𝑀𝑒𝑠𝑠𝑎𝑔𝑒 = 𝐸1, 𝐸2, 𝑇𝐶 .In this login request message, both 𝐸1 and 𝐸2 has been encrypted by using servers public key. If an attacker captures the login request message and tries to decrypt the 𝐸1 for identify the user identityMutual authentication
The user 𝑈𝑖has been verified by the server and the server has been verified by the user 𝑈𝑖, this process known as mutual authentication. The mutual authentication verification has been included in the proposed authentication scheme during the Authentication and verification message. During this phase Session for the future session communication has been created. The session key has been created by using the following method 𝑆𝐾𝑁𝑒𝑤 = 𝑔 𝐷2⊕𝑟2⊕𝑇𝑆 (𝑚𝑜𝑑 𝑃) and we have used discrete logarithm concepts.
Assume, an attacker tries to generate original session key from the collected information from the login request and mutual authentication messages. Due to the discrete logarithm problem, it is highly impossible for the attackers for calculating the exact session key.
b. Resistance against replay attacks
A replay attack is a kind of message fabrication for making an illegal message conversation between two legal parties. In the proposed, the attacker capture the previously generated login request message 𝐿𝑜𝑔𝑖𝑛 𝑅𝑒𝑞𝑢𝑒𝑠𝑡 𝑀𝑒𝑠𝑠𝑎𝑔𝑒 = 𝐸1, 𝐸2, 𝑇𝐶 and send the message with current time stamp to the server. The server decrypt the 𝐸1 and 𝐸2 by using his private key and check with the recalculated values. This will not be match, due to the new time stamp. The login request message will be a new one for every new login session. Both 𝐸1 and 𝐸2 are generated based on the current time stamp only. In the proposed authentication scheme replay attack is not possible
c. Resistance against forgery attacks
From the legal userside, he/she attempts to act as another legal user in the same cloud. The attacker has generate a forged a authenticate request message𝐿𝑜𝑔𝑖𝑛 𝑅𝑒𝑞𝑢𝑒𝑠𝑡 𝑀𝑒𝑠𝑠𝑎𝑔𝑒 = 𝐸1, 𝐸2, 𝑇𝐶 and send to the server. However, the forged messages will not be authenticated by the server due to the message freshness along with user identity and password. The login request message has been created with 𝐸1 = 𝐸𝑛𝑐𝐾𝑒𝑦𝑃(𝐶1) and 𝐸2 = 𝐸𝑛𝑐𝐾𝑒𝑦𝑃(𝐶2)and these values could not be created by any legal user for other legal user.
d. Resistance against denial-of-service attacks
During the login phase, any one of the attacker tries to implement the denial of service for any legal user by capturing the login. If an attacker generate an illegal replay message and send to the user, then the user verifies the mutual authentication and ignore the replay message from the illegal sever.
e. Resistance to server spooﬁng attacks
If an attacker attempts to impersonate like server by replaying a forged mutual authentication message for the login request message 𝐿𝑜𝑔𝑖𝑛 𝑅𝑒𝑞𝑢𝑒𝑠𝑡 𝑀𝑒𝑠𝑠𝑎𝑔𝑒 = 𝐸1, 𝐸2, 𝑇𝑐 . This is not possible in the proposed authentication scheme due to the verification technique. Both user and the server verifies the time stamp and encrypted request, if any one of the verification is fails then user can easily come to know server service spoofed.
f. Forward secrecy
The session key has been created by the server will not be shared directly with user, instead of that a small portion of information has been shared. The user has to generated the same session key with this shared information. This will be verified by the user and server during the mutual authentication phase. If an attacker tries to capture the session communication and tries to guess the post session key, then it is not possible in the proposed authentication scheme, due to the freshness in the session key. The new session has been started with new time stamp and nonce value. So, the forward secrecy has been maintained by the proposed scheme.
5. Performance Analysis
In this section, we have provided the detailed study on performance analysis for the proposed authentication scheme. The performance analysis phase includes basic cryptographic operations with respect to the execution time taken. The related authentication schemes are compared with proposed authentication for login and authentication phases. We have not consider the registration phase for the performance analysis. Following related authentication schemes are consider for performance analysis,Juang et al.‟s scheme , Sun et al.‟s scheme , Singh et al.‟s scheme , and Li et al.‟s scheme .
The following table 1 provides basic cryptographic operations with respect to the execution time. The execution time has been calculated from the basic computing environment with Windows 3 64-bit PC, Intel Core i5-8250U CPU of 1.60 GHz, 4GB RAM.
The cryptographic functions/cryptography operations are developed with core JAVA cryptographic functions. The Java Cryptographic Architecture (JCA) is a cryptographic platform, which provides a set of Application Program Interface (API‟s) for hash functions, point multiplications, modular inverse, key generation and random number generation. These API‟s are allowed the developers to develop and integrate the security needs. In the proposed method, we have used basic cryptographic operations directly and the performance has been measured with respect the milliseconds.
𝑇𝐻: Execution time taken to perform Hash Operation
𝑇𝑅𝑆𝐴: Execution time taken to perform Encryption/Decryption using RSA 𝑇𝐸𝐶𝐶: Execution time taken to perform Encryption/Decryption using ECC
𝑇𝑆𝑦𝑚: Execution time taken to perform Encryption/Decryption using Symmetric Algorithm
𝑇𝐷𝐿𝑃: Execution time taken to perform aDiscrete Logarithm Problem
Cryptography Operations Execution time in Milliseconds
𝑇𝐻 0.54 𝑚𝑠
𝑇𝑅𝑆𝐴 15.75 𝑚𝑠
𝑇𝐸𝐶𝐶 17.55 𝑚𝑠
𝑇𝑆𝑦𝑚 7.55 𝑚𝑠
𝑇𝐷𝐿𝑃 13.55 𝑚𝑠
Table 1: Execution Time for each Cryptography Operations
The following Table 2, provides the execution time comparison for the related schemes.
The Huang et al  scheme requires3𝑇𝐻 + 1𝑇𝑆𝑦𝑚 for login phase and 1𝑇𝐸𝐶𝐶 + 1𝑇𝑆𝑦𝑚 for authentication phase.Juang et al.‟s scheme  needs3𝑇𝐻 + 1𝑇𝑆𝑦𝑚 for login phase and1𝑇𝐸𝐶𝐶 + 2𝑇𝑆𝑦𝑚 for authentication phase.Sun et al.‟s scheme  required 2𝑇𝐸𝐶𝐶 + 4𝑇𝐻 for login phase and 2𝑇𝐸𝐶𝐶 + 1𝑇𝑆𝑦𝑚 for authentication phase.
Singh et al.‟s scheme  needs2𝑇𝐸𝐶𝐶 + 4𝑇𝐻 and 2𝑇𝐸𝐶𝐶 + 1𝑇𝑆𝑦𝑚 for login and authentication phase respectively. Li et al  scheme required 8𝑇𝐻+ 4𝑇𝑆𝑦𝑚 for login phase and 1𝑇𝐸𝐶𝐶 + 10𝑇𝑆𝑦𝑚 for authentication phase. Lu et al  scheme needs 1𝑇𝑃𝑀+ 5𝑇𝐻 and 3𝑇𝑃𝑀+ 6𝑇𝐻 for login and authentication phases respectively. Sutrala et al  scheme required 7𝑇𝐻+ 1𝑇𝑒 for login phase and 9𝑇𝐻 + 1𝑇𝑒 for authentication phase. The proposed authentication scheme required 2𝑇𝐻 + 2𝑇𝑅𝑆𝐴 for login phase and 2𝑇𝐻+ 1𝑇𝐷𝐿𝑃+ 1𝑇𝑆𝑦𝑚 for authentication phase. The following table 3 and the figure 1 illustrate the performance analysis for the related authentication schemes with proposed authentication scheme.
Login Phase Authentication and Key Agreement Phase
Huang et al  3𝑇𝐻 + 1𝑇𝑆𝑦𝑚 1𝑇𝐸𝐶𝐶+ 1𝑇𝑆𝑦𝑚 3𝑇𝐻 + 1𝑇𝐸𝐶𝐶 + 2𝑇𝑆𝑦𝑚 Juang et al  3𝑇𝐻 + 1𝑇𝑆𝑦𝑚 1𝑇𝐸𝐶𝐶+ 2𝑇𝑆𝑦𝑚 3𝑇𝐻 + 1𝑇𝐸𝐶𝐶 + 3𝑇𝑆𝑦𝑚 Sun et al  2𝑇𝐸𝐶𝐶 + 4𝑇𝐻 2𝑇𝐸𝐶𝐶+ 1𝑇𝑆𝑦𝑚 4𝑇𝐻 + 4𝑇𝐸𝐶𝐶 + 1𝑇𝑆𝑦𝑚 Singh et al  2𝑇𝐸𝐶𝐶 + 4𝑇𝐻 2𝑇𝐸𝐶𝐶+ 1𝑇𝑆𝑦𝑚 4𝑇𝐸𝐶𝐶 + 4𝑇𝐻+ 1𝑇𝑆𝑦𝑚
Li et al  8𝑇𝐻 + 4𝑇𝑆𝑦𝑚 1𝑇𝐸𝐶𝐶 + 10𝑇𝑆𝑦𝑚 8𝑇𝐻 + 14𝑇𝑆𝑦𝑚
Lu et al  1𝑇𝑅𝑆𝐴+ 5𝑇𝐻 3𝑇𝑅𝑆𝐴 + 6𝑇𝐻 4𝑇𝑅𝑆𝐴 + 11𝑇𝐻
Sutrala et al  7𝑇𝐻 + 1𝑇𝐸𝐶𝐶 9𝑇𝐻 + 1𝑇𝐸𝐶𝐶 16𝑇𝐻 + 2𝑇𝐸𝐶𝐶 Proposed Scheme 2𝑇𝐻+ 2𝑇𝑅𝑆𝐴 2𝑇𝐻 + 1𝑇𝐷𝐿𝑃+ 1𝑇𝑆𝑦𝑚 4𝑇𝐻+ 2𝑇𝑅𝑆𝐴+ 1𝑇𝐷𝐿𝑃
+ 1𝑇𝑆𝑦𝑚 Table 2: Computational cost comparison with the related schemes
Total Cost Total Execution Time
Huang et al  3𝑇𝐻 + 1𝑇𝐸𝐶𝐶 + 2𝑇𝑆𝑦𝑚 34.27 𝑚𝑠 Juang et al  3𝑇𝐻 + 1𝑇𝐸𝐶𝐶 + 3𝑇𝑆𝑦𝑚 41.82 𝑚𝑠
Sun et al  4𝑇𝐻 + 4𝑇𝐸𝐶𝐶 + 1𝑇𝑆𝑦𝑚 79.91 𝑚𝑠
Singh et al  4𝑇𝐸𝐶𝐶 + 4𝑇𝐻+ 1𝑇𝑆𝑦𝑚 79.91 𝑚𝑠
Li et al  8𝑇𝐻+ 14𝑇𝑆𝑦𝑚 + 1𝑇𝐸𝐶𝐶 127.57 𝑚𝑠
Lu et al  4𝑇𝑃𝑀+ 11𝑇𝐻 68.94 𝑚𝑠
Sutrala et al  16𝑇𝐻 + 2𝑇𝐸𝐶𝐶 43.74 𝑚𝑠
Proposed Scheme 4𝑇𝐻+ 2𝑇𝑅𝑆𝐴+ 1𝑇𝐷𝐿𝑃+ 1𝑇𝑆𝑦𝑚 54.76 𝑚𝑠 Table 3: Execution Time comparison with the related schemes
Figure 1: Performance Analysis for the related authentication schemes with proposed scheme 0
20 40 60 80 100 120 140
Time in Mille Second
Execution Time (ms)
In this paper, we have proposed an authentication scheme using simple password along with public key cryptographic algorithm for cloud computing environment. The proposed authentication scheme has three basic phases. The login and authentication verification phase has been executed for every new login session. The proposed authentication scheme is two- factor authentication scheme with user identity and password. The session key has been created with discrete logarithm. The proposed authentication scheme is secure with various kinds of attacks in cloud environment. We have provided a informal security analysis for the proposed authentication scheme. The proposed scheme requires minimum computational cost and communication cost. In future, the proposed scheme may be improved with different public key cryptographic algorithms.
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