An Anonymous User Authentication with Key Agreement Scheme without Pairings for Multiserver Architecture Using SCPKs

Abstract

With advancement of computer community and widespread dissemination of network applications, users generally need multiple servers to provide different services. Accordingly, the multiserver architecture has been prevalent, and designing a secure and efficient remote user authentication under multiserver architecture becomes a nontrivial challenge. In last decade, various remote user authentication protocols have been put forward to correspond to the multi-server scenario requirements. However, these schemes suffered from certain security problems or their cost consumption exceeded users’ own constrained ability. In this paper, we present an anonymous remote user authentication with key agreement scheme for multi-server architecture employing self-certified public keys without pairings. The proposed scheme can not only retain previous schemes’ advantages but also achieve user privacy concern. Moreover, our proposal can gain higher efficiency by removing the pairings operation compared with the related schemes. Through analysis and comparison with the related schemes, we can say that our proposal is in accordance with the scenario requirements and feasible to the multi-server architecture.

1. Introduction

In modern society, people’s life is highly dependent on the Internet, but the exposure of networks often causes great loss to users, which brings about that a secure user authentication mechanism has become the key issue to preserve valid remote clients in safety from being attacked. There is no doubt that the user authentication with smart card is one of the most widely used and the simplest approaches. When taking only one sort of service into account, some password authentication schemes for single-server environment have been proposed [1, 2].

Later with the rapid development of technology, different servers are needed to offer service via the network, and conventional methods need users to register with various servers repetitively and remember different identities and passwords. It is obvious that these traditional schemes make authentication inconvenient and cost much. Consequently, an appropriate multiserver user authentication mechanism has turned into a concern. In 2001, Li et al. [3] gave a remote user authentication scheme in neural networks for the first time, which opened up the gateway access to the multiserver architecture.

Considering the system environment without loss of generality, the multiserver architecture consists of multiple distributed service servers and remote clients with limited resource and capability. The service servers offer different access services such as e-commerce, online conference, network game, and remote medical system. If a remote client wants to access to these services, he/she needs to login these service servers through cellular network or wireless local area networks (WLANs).

Due to multiserver environment special characteristics and information security problem in public networks, designing a feasible user authentication scheme under multiserver architecture is a key issue, which can ensure the access of legitimate users and prevent invalid user from interfering with the service server. A practical user authentication scheme under the multiserver environment must address the following requirements. They consist of both the previous criteria [1] and new user anonymity issue.(1)No repetitive registration is needed for the multiserver environments.(2)No verification table is stored in the server.(3)Mutual authentication and session key agreement can be achieved between the users and the service servers to carry on subsequent communications.(4)Various possible attacks can be resisted.(5)User can choose identity and password freely and change his/her password freely.(6)The computational and communication cost is low since the energy resources and computing capability of a smart card are limited.(7)The user is not allowed to expose his identity privacy information to eavesdroppers. Assume that the adversary obtains a valid user’s identity, he/she can masquerade the user to enjoy the regular service without registration, which can cause losses for the valid user or even worse consequences. So the anonymous authentication should be implemented.

In order to satisfy all of these criteria, this paper proposes an anonymous remote user authentication scheme without pairings for multiserver architecture using self-certified public keys (SCPKs). We present public key-based user anonymous authentication scheme under the multiserver environment. Meanwhile, our proposal heightens efficiency increasingly accompanied by the removal of pairings operation; in contrast, the existing public key-based authentication schemes generally employ pairings function. Moreover, our proposal can avoid the server spoofing attack since the verification process relies on the server’s private key. Through security and performance analysis, our proposal not only achieves anonymous authentication with key agreement securely but also results more efficiently, remedying the weaknesses of previous authentication schemes which either encounter some attacks or fail to protect user privacy or cost relatively more energy. Compared with other related achievements, ours is more suitable for the remote user whose resources and capability are constrained under multiserver architecture.

The rest of this paper is organized as follows. Section 2 briefly describes some related works. Some preliminaries are given in Section 3. Our proposed secure and efficient user authentication scheme for multiserver architecture and corresponding analysis are presented in Sections 4 and 5, respectively. Finally, some conclusions are drawn in Section 6.

2. Related Work

Until now, two categories of improved multiserver user authentication schemes, hash-based authentication and public key based authentication, have emerged successively. To hash-based authentication, some user password authentication suggestions [4–7] based on static ID have been proposed to conquer the weaknesses of Li et al.’s, yet these were proven easy to be traced. In 2009, Liao and Wang [8] raised a dynamic identity authentication protocol for multiserver environment to advance previous work. In the following years, many researchers [9–12] have developed and enhanced the user authentication scheme step by step. To public key-based authentication, employing public key cryptosystem into the password authentication, Das et al. [13] first proposed a remote user authentication protocol with smart card using bilinear pairings. Yet theirs had an obvious disadvantage: no mutual authentication and key agreement. To improve the security, a series of user authentication schemes [14–16] with bilinear pairings have been presented. To improve the efficiency, Tseng et al. [17] gave a low-cost pairing-based user authentication protocol for wireless users and claimed that theirs was efficient, easy password changing, and suitable for multiserver environment in distributed networks. Unfortunately, in 2013, Liao and Hsiao [18] pointed out that Tseng et al.’s scheme also lacked mutual authentication with session key agreement, suffered from insider attack, password guessing attack, and replay attack, and advanced a pairings-based user authentication scheme using self-certified public keys. Liao and Hsiao claimed that their proposal could withstand various possible attacks and was well suited for multiserver environment.

Regretfully, most of the existing related public key based authentication schemes under multiserver architecture mentioned previously did not pay attention to user anonymity issue. Moreover, their authentication schemes needed excessive energy consumption employing pairings operation and suffered from the server spoofing attack, which was not conducive to communication running and trapped in DoS attack easily.

3. Preliminaries

We now briefly review some basic concepts used in this paper, including bilinear pairings [19], related complexity assumptions [20], and self-certified public keys [21, 22].

3.1. Admissible Bilinear Pairing

Let 𝔾 be an additive group generated by 𝑃 with prime order 𝑞 and let 𝔾_𝑇 be a multiplicative group of the same order. A map 𝑒̂∶𝔾×𝔾→𝔾_𝑇 is said to be an admissible bilinear pairing if the following three conditions hold true.(1)Bilinearity: for all 𝑎,𝑏∈ℤ^∗_𝑞, we have 𝑒(̂𝑎𝑃,𝑏𝑃)=𝑒(̂𝑃,𝑃)^𝑎𝑏.(2)Nondegeneracy: 𝑒(̂𝑃,𝑃)≠1_𝔾𝑇.(3)Computability: 𝑒̂ is efficiently computable.

We refer readers to [19] for more details of such pairings.

3.2. Complexity Assumption

(1)Computational discrete logarithm (CDL) assumption: given 𝑄=𝑘⋅𝑃, where 𝑃,𝑄∈𝔾, there exists no probabilistic polynomial-time algorithm which can determine 𝑘.(2)Computational Diffie-Hellman (CDH) assumption: given two elements 𝑎𝑃, 𝑏𝑃 in a group 𝔾, where the unknown numbers 𝑎,𝑏∈ℤ^∗_𝑞 are selected at random, there exists no probabilistic polynomial-time algorithm which can compute 𝑎𝑏𝑃.(3)Elliptic curve factorization (ECF) assumption: given two elements 𝑃, 𝑄, where 𝑄=𝑎𝑃+𝑏𝑃 and 𝑎,𝑏∈ℤ^∗_𝑞, there exists no probabilistic polynomial-time algorithm which can obtain 𝑎𝑃 and 𝑏𝑃.

3.3. Self-Certified Public Key

Here, we describe a self-certified public key process briefly; more details can be found in [21, 22].(1)Initialization: given a group 𝔾 on an elliptic curve 𝐸, 𝑃 is a based point generator of prime order 𝑞, the system authority (SA) selects a random value 𝑠∈ℤ^∗_𝑞 as its private key and computes the public key 𝑃_pub=𝑠⋅𝑃. Publish the related parameters and keep 𝑠 secret.(2)Partial private key and private key generation: the user 𝑈_𝑖 chooses a number 𝑘_𝑖 randomly, computes 𝐾_𝑖=𝑘_𝑖⋅𝑃, and sends (ID_𝑖,𝐾_𝑖) to SA over a secure channel. SA calculates 𝑊_𝑖=𝐾_𝑖+𝑤_𝑖⋅𝑃 as the witness using a random number 𝑤_𝑖. Then, SA computes the user’s partial private key 𝑠_𝑖=𝐻(ID_𝑖‖𝑊_𝑖)⋅𝑠+𝑤_𝑖 and submits (𝑠_𝑖,𝑊_𝑖) to 𝑈_𝑖. 𝑈_𝑖 can obtain its private key 𝑠_𝑖=𝑠_𝑖+𝑘_𝑖.(3)Public key extraction: 𝑈_𝑖’s public key can be computed by Pub_𝑖=𝑠_𝑖⋅𝑃. Any entity, who communicates with 𝑈_𝑖 and receives the witness 𝑊_𝑖, can authenticate 𝑈_𝑖’s public key Pub_𝑖 as long as he/she calculates the equation: Pub_𝑖=𝐻(ID_𝑖‖𝑊_𝑖)⋅𝑃_pub+𝑊_𝑖.

4. The Proposed Scheme

In this section, we propose an anonymous remote user authentication scheme for multiserver environment without pairings, which consists of five phases: server registration phase, user registration phase, login phase, verification phase, and password change phase. Three entities are involved: user (𝑈_𝑖), service server (𝑆_𝑗), and registration center (RC). RC chooses the system private/public key pair 𝑠/𝑃_pub, where 𝑠 is a random number in ℤ^∗_𝑞 and 𝑃_pub=𝑠⋅𝑃. Then publish the system parameters Params={𝔾,𝑃,𝑞,𝑃_pub,𝐻(⋅)} and keep 𝑠 secret. The notations used in this section are listed in Table 1. Some detailed steps will be described as follows and shown in Figure 1.

Table 1 

Notations used in proposed scheme.

Figure 1 

The proposed scheme.

4.1. Server Registration Phase

When the service server wants to access to the multiserver architecture, it needs to register first. In this phase, RC uses the self-certified public key (SCPK) to generate the related credentials.

Step S1. 𝑆_𝑗 chooses a random value 𝑘_𝑗∈ℤ^∗_𝑞, computes 𝐾_𝑗=𝑘_𝑗⋅𝑃, and sends (SID_𝑗,𝐾_𝑗) to RC.

Step S2. After receiving the message (SID_𝑗,𝐾_𝑗), RC generates a 𝑤_𝑗∈ℤ^∗_𝑞 randomly, calculates 𝑊_𝑗=𝐾_𝑗+𝑤_𝑗⋅𝑃, 𝑠_𝑗=𝐻(SID_𝑗‖𝑊_𝑗)⋅𝑠+𝑤_𝑗, and issues (𝑊_𝑗,𝑠_𝑗) to 𝑆_𝑗.

Step S3. 𝑆_𝑗 can obtain its private key with 𝑠_𝑗=𝑠_𝑗+𝑘_𝑗 and verify the validity of the message by computing Pub_𝑗=𝑠_𝑗⋅𝑃=𝐻(SID_𝑗‖𝑊_𝑗)⋅𝑃_pub+𝑊_𝑗.

If the equation holds, the issued values are valid, and vice versa.

4.2. User Registration Phase

Supposing that the user 𝑈_𝑖 wants to get service granted only from 𝑆_𝑗, he/she needs to register to the same RC that 𝑆_𝑗 did, by submitting his identity ID_𝑖 and password PW_𝑖 to RC. Then, RC returns the smart card back to 𝑈_𝑖. The communication between 𝑈_𝑖 and RC is through a secure channel. The steps are performed as follows.

Step U1. 𝑈_𝑖 freely chooses a password PW_𝑖 and a random number 𝑏_𝑖 to compute 𝐴_𝑖=𝐻(PW_𝑖‖𝑏_𝑖) and 𝐼_𝑖=𝐻(ID_𝑖‖𝑏_𝑖). Then, 𝑈_𝑖 submits (ID_𝑖,𝐴_𝑖,𝐼_𝑖) to RC for user registration via a secure channel.

Step U2. RC calculates?𝐵_𝑖=𝑠⋅𝐻(ID_𝑖‖𝐼_𝑖)+𝑥,?𝐶_𝑖=𝐵_𝑖⊕𝐻(𝐴_𝑖),?𝐷_𝑖=𝐵_𝑖⊕𝐻(ID_𝑖)⊕𝐴_𝑖,?𝑋=𝑥⋅𝑃,?𝐸_𝑖=𝐻(ID_𝑖‖𝐴_𝑖)⋅𝑃−𝑋,stores (𝐶_𝑖,𝐷_𝑖,𝐸_𝑖,𝐻(⋅)) in 𝑈_𝑖’s smart card, and submits it to 𝑈_𝑖. Then 𝑈_𝑖 keys 𝑏_𝑖 into the smart card.

4.3. Login Phase

When 𝑈_𝑖 wants to login to the server 𝑆_𝑗, he/she first inserts his/her own smart card to a card reader and then inputs the identity ID_𝑖 and password PW_𝑖. The log-in details with respect to this smart card are as follows.

Step L1. The smart card computes 𝐴^′_𝑖=𝐻(PW_𝑖‖𝑏_𝑖), 𝐵^′_𝑖=𝐷_𝑖⊕𝐻(ID_𝑖)⊕𝐴^′_𝑖, and 𝐶^′_𝑖=𝐵^′_𝑖⊕𝐻(𝐴^′_𝑖) and checks whether 𝐶^′_𝑖=𝐶_𝑖. If the answer is yes, it means that the smart card matches to 𝑈_𝑖.

Step L2. The smart card generates a random value 𝑟_𝑖∈ℤ^∗_𝑞 and computes ?𝑊_𝑖=𝐻(ID_𝑖‖𝐼_𝑖),?CID_𝑖=𝑊_𝑖⊕𝐵_𝑖,?𝑅_𝑖=𝑟_𝑖⋅𝑃.

Step L3. The smart card submits the login request message (CID_𝑖,𝑅_𝑖) to 𝑆_𝑗 over a public channel.

4.4. Verification Phase

After receiving the login request message from 𝑈_𝑖, 𝑆_𝑗 performs the following tasks to authenticate the user.

Step V1. 𝑆_𝑗 checks whether CID_𝑖 conforms to the fixed format. If the format is wrong, 𝑆_𝑗 outputs the reject message; otherwise it calculates?𝐾_𝑗𝑖=𝑠_𝑗⋅𝑅_𝑖,?𝑅_𝑗=𝑟_𝑗⋅𝑃,?𝑇_𝑗𝑖=𝑟_𝑗⋅𝑅_𝑖,?𝑀_𝑗=𝐻(CID_𝑖‖𝐾_𝑗𝑖‖𝑅_𝑖‖𝑅_𝑗),where 𝑟_𝑗 is a random value, chosen by 𝑆_𝑗. Then 𝑆_𝑗 sends (SID_𝑗,𝑊_𝑗,𝑅_𝑗,𝑀_𝑗) to 𝑈_𝑖.

Step V2. Receiving the message (𝑊_𝑗,𝑅_𝑗,𝑀_𝑗), 𝑈_𝑖 first verifies the public key of 𝑆_𝑗 by the equation Pub_𝑗=𝐻(SID_𝑗‖𝑊_𝑗)⋅𝑃_pub+𝑊_𝑗. Only under the case the equation holds, 𝑈_𝑖 continues to calculate 𝐾_𝑖𝑗=𝑟_𝑖⋅Pub_𝑗, 𝑇_𝑖𝑗=𝑟_𝑖⋅𝑅_𝑗. Then 𝑈_𝑖 needs to check whether 𝑀=_𝑗^?𝐻(CID_𝑖𝑗‖𝐾_𝑖𝑗‖𝑅_𝑖‖𝑅_𝑗). When the verification can pass, 𝑈_𝑖 authenticates 𝑆_𝑗 and computes?𝑃_𝑖𝑗=𝐵_𝑖⊕𝐻(𝐾_𝑖𝑗‖𝑇_𝑖𝑗),?𝑋=𝐻(ID_𝑖‖𝐴_𝑖)⋅𝑃−𝐸_𝑖.

Then 𝑈_𝑖 transmits (𝑃_𝑖𝑗,𝑋) to 𝑆_𝑗.

Step V3. Next, 𝑆_𝑗 undoes 𝐵^′_𝑖=𝑃_𝑖𝑗⊕𝐻(𝐾_𝑗𝑖‖𝑇_𝑗𝑖), 𝑊^′_𝑖=CID_𝑖⊕𝐵^′_𝑖 and examines 𝑋=^?𝐵^′_𝑖⋅𝑃−𝑊^′_𝑖⋅𝑃_pub. If it is not the case, 𝑆_𝑗 rejects the message and stops the session. Otherwise, 𝑆_𝑗 successfully authenticates 𝑈_𝑖.

Step V4. Finally, the user 𝑈_𝑖 and the service server 𝑆_𝑗 agree on a common session key as ?SK=𝐻(𝑊_𝑖‖𝐾_𝑖𝑗‖𝑇_𝑖𝑗).

4.5. Password Change Phase

The password change phase is invoked when the user wants to change his/her password PW_𝑖 to a new password PW^∗_𝑖. The user first inserts his/her smart card into a card reader and enters ID_𝑖, PW_𝑖. The smart card computes 𝐴_𝑖=𝐻(PW_𝑖‖𝑏_𝑖), 𝐵^′_𝑖=𝐷_𝑖⊕𝐻(ID_𝑖)⊕𝐴_𝑖 and 𝐶^′_𝑖=𝐵^′_𝑖⊕𝐻(𝐴_𝑖). Then, the smart card checks if the 𝐶^′_𝑖 is the same as 𝐶_𝑖. If both values are the same, the user is asked to input a new password PW^∗_𝑖. The smart card calculates new information 𝐴^∗_𝑖=𝐻(PW^∗_𝑖‖𝑏_𝑖), 𝐶^∗_𝑖=𝐶_𝑖⊕𝐻(𝐴_𝑖)⊕𝐻(𝐴^∗_𝑖), 𝐷^∗_𝑖=𝐷_𝑖⊕𝐴_𝑖⊕𝐴^∗_𝑖, 𝐸^∗_𝑖=𝐻(ID_𝑖‖𝐴^∗_𝑖)⋅𝑃+𝐸_𝑖−𝐻(ID_𝑖‖𝐴_𝑖)⋅𝑃. At last, the smart card replaces 𝐶_𝑖,𝐷_𝑖,𝐸_𝑖 with the new 𝐶^∗_𝑖,𝐷^∗_𝑖,𝐸^∗_𝑖 to accomplish changing password. In this phase, RC is not needed to participate and the user can freely complete changing password by himself.

5. Analysis of Our Scheme

In this section, we first analyze the functionality features of our proposed scheme based on the requirements of the remote user authentication for multiserver architecture, which have been presented in Section 1. Then we evaluate the performance of the proposed scheme and make comparisons with some related works [8, 9, 11, 12, 17, 18].

5.1. No Repetitive Registration

In our scheme, before the user wants to login to the server under multiserver environment, they must run the user registration with his/her information to the registration center. Then, the user can access to all the service without submitting registration request once again.

5.2. No Verification Table

Throughout the protocol process, it is not difficult to find that RC and 𝑆_𝑗 have no need to maintain any verification or password table, which can cost much and whose leakage may cause serious disruption. Meanwhile, our scheme does not need to store the user’s password or public key with certificate, too.

5.3. Mutual Authentication with Session Key Agreement

In the verification phase of the proposed scheme, the service server 𝑆_𝑗 can authenticate the validity of 𝑈_𝑖 by checking if 𝑋=𝐵^′_𝑖⋅𝑃−𝑊^′_𝑖⋅𝑃_pub holds. 𝑈_𝑖 can verify the public key of 𝑆_𝑗Pub_𝑗=𝐻(SID_𝑗‖𝑊_𝑗)⋅𝑃_pub+𝑊_𝑗 with 𝑊_𝑗 to confirm that 𝑆_𝑗 is the objective service server; meanwhile check the equation 𝑀^′_𝑗=𝑀_𝑗 to affirm that the login message is received by 𝑆_𝑗. Only when all previous equations are satisfied, the session continues and the communication parties agree on a shared session key SK=𝐻(𝑊_𝑖‖𝐾_𝑖𝑗‖𝑇_𝑖𝑗). For the aforementioned analysis, our scheme can achieve mutual authentication with session key agreement.

5.4. No Synchronization Clock

In our scheme, both the user and the service server employ the random points 𝑅_𝑖,𝑅_𝑗 to interactive with each other. The timestamp does not appear in the proposed scheme; therefore the synchronization clock problem can also be abstained in the session key.

5.5. Anonymity

In the user registration phase, the identity of the remote user can be protected from disclosure by the secure channel between 𝑈_𝑖 and RC. In the login and authentication phase, 𝑈_𝑖’s identity is submitted with CID_𝑖 substituting ID_𝑖, nobody can learn the user’s real identity, and 𝑆_𝑗 can only verify the user’s validity cannot obtain the real ID_𝑖 with the received message. To general adversary, he/she can extract the smart card and intercept the login message, but he can do nothing to crack the user’s identity due to the resistance to collision of the hash function. Therefore, we claim that our scheme can provide the user anonymity.

5.6. Security of the Session Key

(1)Perfect Forward Secrecy and Backward Secrecy. In this scheme, the session key is established by 𝑊_𝑖, 𝐾_𝑖𝑗, 𝑇_𝑖𝑗, where 𝐾_𝑖𝑗 and 𝑇_𝑖𝑗 rely on the random values 𝑟_𝑖 and 𝑟_𝑗. 𝑟_𝑖 and 𝑟_𝑗 are independently generated in each session, are also changed for each authentication phase and are not correlated. The adversary cannot use current session key to derive forward and backward session key. Hence, we claim that our scheme achieves perfect forward secrecy and backward secrecy.(2)Known Session Key Security. In this scheme, the session key SK=𝐻(𝑊_𝑖‖𝐾_𝑖𝑗‖𝑇_𝑖𝑗) is composed of 𝑊_𝑖, 𝐾_𝑖𝑗 and 𝑇_𝑖𝑗. Assume that the adversary can seize a session key SK_𝑚𝑛; he cannot obtain the parameters 𝑊_𝑚, 𝐾_𝑚𝑛, and 𝑇_𝑚𝑛 attributed to the one-way hash function 𝐻(⋅). Since 𝐾_𝑚𝑛 and 𝑇_𝑚𝑛 consist of 𝑅_𝑚, 𝑅_𝑛, which are independent for each session, no session keys rely on each other. Furthermore, though the adversary can intercept the current transmitted message 𝑅^′_𝑚, 𝑅^′_𝑛, he cannot compute the new session key SK_𝑚𝑛’s components 𝐾^′_𝑚𝑛 without the server’s private key or 𝑇^′_𝑚𝑛 due to the CDH problem’s difficulty.(3)No Key Control. In this scheme, the session key consists of 𝑊_𝑖, 𝐾_𝑖𝑗, 𝑇_𝑖𝑗, where partial parameters 𝐾_𝑖𝑗, 𝑇_𝑖𝑗 are generated by Diffie-Hellman key exchange form; thereby the fairness of the session key can be guaranteed. More specifically, 𝐾_𝑖𝑗=𝑠_𝑗⋅𝑅_𝑖=𝑟_𝑖⋅Pub_𝑗, 𝑇_𝑖𝑗=𝑟_𝑗⋅𝑅_𝑖=𝑟_𝑖⋅𝑅_𝑗, 𝑅_𝑖 and 𝑅_𝑗 are respectively provided by the user and the server; therefore either party is in vain attempting to preselect or control the session key.

5.7. Various Common Attacks

Our proposed remote user authentication scheme for multiserver architecture cannot only meet the previous security features, but also be against various known attacks, such as impersonation attack, and stolen smart card attack. We will discuss the following extra four attacks, the others can refer to [11, 18].(1)Impersonation Attack. If an adversary tries to impersonate as a legitimate user to log into the server, he/she must first forge a valid login request message (CID_𝑖,𝑅_𝑖). However, the adversary cannot compute a new and legal login message without knowing ID_𝑖 or 𝐵_𝑖. Suppose that the adversary can steal the smart card of the user 𝑈_𝑖 by virtue of some approaches, he is still unable to calculate 𝐵_𝑖 for the reason that he has no information about 𝐴_𝑖 and ID_𝑖. Moreover, even if the adversary utilizes (CID_𝑖,𝑅_𝑖) to log into 𝑆_𝑗, he cannot pass the verification 𝑋=^?𝐵^′_𝑖⋅𝑃−𝑊^′_𝑖⋅𝑃_pub because he is unable to provide correct 𝑃_𝑖𝑗 without 𝐵_𝑖 or 𝐾_𝑖𝑗. The adversary cannot obtain the valid session key. Under the situation, our proposed scheme can withstand the impersonation attack.(2)Stolen Smart Card Attack. We assume that 𝑈_𝑖’s smart card is stolen or lost; the adversary picks it and has the ability to breach the information stored in the smart card (𝐶_𝑖,𝐷_𝑖,𝐸_𝑖,𝐻(⋅),𝑏_𝑖). Yet on the one hand, it is impossible to guess 𝐴_𝑖 and ID_𝑖 correctly at the same time, on the other hand, 𝑠 and 𝑥 are, respectively, private key and secret value of RC, so the adversary cannot derive 𝐵_𝑖. Consequently, the adversary cannot fabricate a valid login message or compute the session key. That is the reason that our proposed protocol is secure against the stolen smart card attack.(3)Off-Line Password Guessing Attack. Assume that the adversary guesses a password PW^′ from the dictionary; he can compute 𝐴_𝑖=𝐻(PW^′‖𝑏_𝑖), 𝐵_𝑖=𝐶_𝑖⊕𝐻(𝐴_𝑖) but fails to calculate other information without ID_𝑖 or 𝐾_𝑖𝑗. The adversary cannot examine whether the guessed password PW^′ is correct without comparing parameters. Hence, the adversary can extract the smart card information and intercept the transmitted message in public channel, but our proposed scheme can resist the off-line password guessing attack.(4)Man-in-the-Middle Attack. When an adversary wants to perform the man-in-the-middle attack, he can intercept the login message, communicate, and share the session key with the server. In the proposed scheme, even if the adversary gets the message in public channel, he cannot calculate 𝑊_𝑖, 𝐾_𝑖𝑗, or 𝑇_𝑖𝑗 without ID_𝑖 or other random values 𝑟_𝑖,𝑟_𝑗. Consequently, our scheme can resist the man-in-the-middle attack.(5)Server Spoofing Attack. When a valid but malicious server 𝑆_𝑚 wants to cheat 𝑈_𝑖 on behalf of 𝑆_𝑗 and obtain the session key, he needs to know both the witness and private key of 𝑆_𝑗. In our scheme, 𝑆_𝑚 cannot provide the correct witness, and the user 𝑈_𝑖 cannot pass the server’s public key verification. Even if 𝑆_𝑚 intercepts 𝑊_𝑗, he cannot check the equation 𝑋=𝐵^′_𝑖⋅𝑃−𝑊^′_𝑖⋅𝑃_pub since he does not obtain 𝐾_𝑗𝑖 without knowing the private key 𝑠_𝑗. Finally, the adversary fails to share the session key with the user 𝑈_𝑖. Therefore, our scheme can resist the server spoofing attack.

5.8. Local Password Verification

In our scheme, 𝑈_𝑖 can account whether the used smart card matches with himself by checking 𝐶^′_𝑖=𝐶_𝑖 before logging into 𝑆_𝑗, and thus accomplish the user password verification locally. Through the previous equation, 𝑈_𝑖 can avoid network resource wasting caused by wrong password. Because until the authentication phase 𝑆_𝑗 can authenticate user’s validity and password appropriateness; in other words, wrong password cannot be detected until the authentication phase. Therefore, our scheme can achieve local password verification.

At last, the functionality comparisons among our and other previously proposed schemes, such as [8, 9, 11, 12, 17, 18], are listed in Table 2. In particular, we can clearly see that the other schemes do not assist in the impersonation attack except our proposed scheme. Thus, it is obvious that our proposed scheme is superior to the others in accordance with all of essential comparative items. In addition, unlike the other related public key-based multiserver authentication schemes [17, 18], ours can achieve the user anonymity and local password verification. On the whole, our proposal is the only one that can satisfy all the functionalities for the multiserver architecture.

Table 2 

Functionality and security comparison with the related schemes.

5.9. Performance

Under multiserver architecture, the computational cost is a key issue to evaluate whether a remote user authentication scheme is efficient because of mobile devices’ constrained resources and computing capability. Before analyzing the computational cost of each phase, define some notations and equivalence relationship first:(i)𝑇_𝑒: the time to compute a bilinear pairing map;(ii)𝑇_𝑀: the time to compute a point multiplication on the elliptic curve group;(iii)𝑇_𝐴: the time to compute a point addition on the elliptic curve group;(iv)𝑇_𝐻: the time to compute a hash function;(a)𝑇_𝑒=20𝑇_𝑀;(b)𝑇_𝑀=6𝑇_𝐴.

The XOR operation, modular multiplication, and modular addition operation are negligible during evaluating the performance. In the following, we will give the computational cost of five phases individually. In the server registration phase, the computational cost is 5𝑇_𝑀+4𝑇_𝐴+2𝑇_𝐻. The user registration phase consumes 2𝑇_𝑀+2𝑇_𝐴+6𝑇_𝐻. When the user logs into the server, it costs 𝑇_𝑀+4𝑇_𝐻. During verification of each other between the server and the user, 9𝑇_𝑀+3𝑇_𝐴+6𝑇_𝐻 is demanded. The computational cost of the password change phase is 2𝑇_𝑀+2𝑇_𝐴+8𝑇_𝐻. The detailed cost comparisons with the related authentication schemes [17, 18] are illustrated in Table 3. At the same time, we show the implementation result in Figure 2, which can show the computational cost contrast more intuitively. Table 3 and Figure 2 can clearly indicate that our proposal needs no pairing operation, while [18] contains 4𝑇_𝑒 and [17] contains 2𝑇_𝑒. Because the relative computational cost of a pairing is approximately 20 times higher than that of the point multiplication over elliptic curve group, we can find that the computational cost of ours is obviously much less than that of others by removing pairing operation.

Table 3 

Cost comparison with the related schemes.

Figure 2 

Performance comparison between our scheme and others.

From Tables 2 and 3, we can make a conclusion that our remote authentication scheme has more security features and lower computational cost among the existing related works, which satisfies the requirements for the multiserver architecture.

6. Conclusions

An anonymous and efficient remote user authentication scheme for the multiserver architecture is proposed in this paper and the self-certified public keys are employed. Our scheme can satisfy all of the requirements needed for achieving secure authentication in multiserver environments, as compared with the previously proposed schemes. Moreover, the proposal succeeds to both achieve the user’s identity anonymity and remove the pairing operation, which makes that the proposed scheme can provide more advantages and be more practical for the actual applications. Additionally, we analyze the security and performance of our proposal and make comparisons with other related works. From these analysis and comparisons, we can reach a conclusion that our proposed scheme owns more functionalities and attains higher efficiency.

Acknowledgments

This work is supported by NSFC (Grant nos. 61272057, 61202434, 61170270, 61100203, 61003286, and 61121061) and the Fundamental Research Funds for the Central Universities (Grant nos. 2012RC0612 and 2011YB01).