Security Comm. Networks. 2008; 1:301–308
Published online 26 June 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/sec.26
A bilateral remote user authentication scheme that
preserves user anonymity
Huei-Ru Tseng, Rong-Hong Jan and Wuu Yang∗,†
Department of Computer Science, National Chiao Tung University, Hsinchu 30010, Taiwan
Summary
Smart card-based authentication is one of the most widely used and practical solutions to remote user authentication. Compared to other authentication schemes, our proposed scheme aims to provide more functionalities and to resist well-known attacks. These crucial merits include (1) a user can freely choose and change his passwords; (2) our scheme provides mutual authentication between a server and a user; (3) it achieves user anonymity; (4) a server and a user can generate authenticated sessions keys. Moreover, our scheme can resist replay attacks, forgery attacks, insider attacks, reflection attacks, and parallel session attacks. Copyright
©
2008 John Wiley & Sons, Ltd.KEY WORDS: smart card; authentication; passwords; anonymity
1. Introduction
A remote user authentication scheme is a mechanism that authenticates remote users and allows legitimate users to access network services over an insecure com-munication network. In a distributed network, when a remote user requests for a service, the server should authenticate the user first. Due to high portability, low cost, and limited cryptographic capabilities of smart cards, a number of smart card-based remote authen-tication schemes have been proposed [1–22]. In 1981, Lamport [1] proposed the first password authentication scheme for remote users over an insecure channel. Since then, several schemes [2–22] have been proposed to improve security, efficiency, and functionality. Past experience has shown that constructing a secure user authentication scheme is not trivial because lots of proposed schemes were subsequently broken by well-known attacks [3,6–8,10,11,13,16].
*Correspondence to: Wuu Yang, Department of Computer Science, National Chiao Tung University, Hsinchu 30010, Taiwan.
†E-mail: [email protected]
Traditionally, if a remote user wants to log into a server, he has to submit his identity and password to the server. On receiving the login request, the server first checks the validity of the identity and computes a one-way hash value of the received password, and then checks the computed value against the server’s verification table. Since this approach clearly incurs the risk of tampering and the cost of managing the table, several schemes [2,4,5,9,12,14,15,17–22] have been proposed that do not depend on a verification table.
Due to the constrained resources in smart cards, the computation and communication overhead must be low in practical implementation. Sun [19] proposed an efficient authentication scheme that adopts only simple hashing operations. In 2002, Chien et al. [4] proposed another authentication scheme that improves on Sun’s in two ways: it achieves mutual authentication and it allows users to choose their passwords freely.
After a user is authenticated, the messages between the user and the server must be encrypted when transmitted over the public network. They have to agree on a session key. Juang [9] proposed an authentication scheme that provides a key agreement function. In various e-commerce applications, user anonymity is also crucial. Das et al. [5] first proposed a dynamic identity-based authentication scheme that preserves user anonymity. However, Chien and Chen [2] pointed out that Das et al.’s scheme [5] fails to protect user anonymity.
In order to reduce the risk of single-point failures, Choi and Youn [23] proposed a novel data encryption and distribution approach based on LU decomposition in 2004. The scheme allows higher security and avail-ability compared with the mirroring scheme [24–26], and provides a solution for failures and malicious compromises of storage nodes, client systems, and user account. Pathan et al. [17,18] also proposed two bilateral authentication schemes based on LU decomposition. However, their schemes have several security weaknesses, including (1) they cannot resist replay attacks; (2) passwords could be revealed by the server; (3) they cannot preserve user anonymity; and (4) the server and users cannot agree on a session key. To conquer these weaknesses, we propose a bilateral user-authentication scheme that not only fixes these weaknesses, but also aims to achieve more functionalities and resists well-known attacks. These crucial merits include (1) users can freely choose and change their passwords; (2) it provides mutual authentication between a server and a user; (3) it achieves user anonymity; (4) a server and a user can generate authenticated sessions keys. Moreover, the scheme is secure against replay attacks, forgery attacks, insider attacks, reflection attacks, and parallel session attacks.
The rest of this paper is organized as follows: In Section 2, we state the basic terms and preliminaries for our scheme. Our proposed scheme is presented in Section 3. Then, we shall analyze our proposed scheme, show that our scheme can resist several attacks, and provide a comparative study with other authentication schemes in Section 4. Finally, we will conclude our paper in Section 5.
2. Preliminaries
Our scheme is based on LU decomposition of matrices [27]. The decomposition re-writes a matrix as the product of a lower and an upper triangular matrices. In
the LU decomposition, an n× n matrix A is written as
A= L · U (1)
where L is a nonsingular lower triangular matrix, and
U is a nonsingular upper triangular matrix.
In our scheme, a symmetric key matrix An×n is
generated by the server during system initialization, where n is the number of users that could be supported. This matrix is a secret of the server. In order to reduce the risk of single-point failures, with LU decomposition, the server can separate the symmetric key matrix An×n to a lower and an upper triangular
matrices and store these matrices in other servers. Each element aijis a key from a key pool. We assume
that aij = aji, for 1≤ i ≤ n and 1 ≤ j ≤ n. Since A is
symmetric, the product of the x-th row of matrix L and the y-th column of matrix U is as same as that of the
y-th row of matrix L and the x-th column of matrix U.
For example, given A as follows:
A= 1 2 4 5 2 5 8 9 4 8 15 17 5 9 17 20 (2)
we perform elementary row operations to get the lower matrix L and upper matrix U as follows:
L= 1 0 0 0 2 1 0 0 4 0 −1 0 5 −1 0 −3 and U= 1 2 4 5 0 1 0 −1 0 0 1 3 0 0 1 2 (3)
Given x= 2 and y = 3, we can compute a23 and a32 as follows:
a23= LR(2)× UC(3)
=2 1 0 0×4 0 1 1T = 8 (4)
a32= LR(3)× UC(2)
=4 0 −1 0×2 1 0 0T = 8 (5) Since matrix A is symmetric, a23 = a32. Note that
LR(2) denotes the 2nd row of matrix L and UC(3)
denotes the 3rd column of matrix U. ©
Table I. Notations. Symbol Definition
Ui User i IDi User i’s identity PWi User i’s chosen password Ks The server’s secret key
AKi The authenticated session key computed by the server
and Ui
n The number of users that could be supported by the system
An×n A symmetric key matrix
T The timestamp
h(·) A one-way hash function
p A prime number and p is divisible by q− 1
g A generator of order q ⊕ An XOR operation
Pathan et al. [17,18] proposed two bilateral authen-tication schemes based on LU decomposition. Their proposed schemes are divided into four phases: regis-tration, login, authentication, and password-changing phases. However, their schemes have several security weaknesses, including (1) they cannot resist replay at-tacks; (2) passwords could be revealed by the server; (3) they cannot preserve user anonymity; and (4) the server and users cannot agree on a session key. Therefore, we propose a bilateral user-authentication scheme that not only fixes these weaknesses, but also aims to achieve more functionalities and resists well-known attacks.
3. Our Proposed Scheme
Our bilateral user authentication scheme is divided into four phases: registration, login, authentication, and password-changing phases. The notations and their corresponding definitions are listed in Table I. 3.1. Registration Phase
Suppose a new user Uiwith the identity IDi wants to
register with a server for remote-access services. Ui
randomly chooses his password PWi and sends the
pair (IDi, h(PWi)) to the server. Almost all existing
user authentication schemes [3,7,10–13,15,17–20,22] presume the existence of a secure channel in the registration phase. This usually means the private registration data are submitted in person or through an existing secure channel. Upon receiving the registration message, the server takes the following steps:
1. Generate two random numbers xi, yibetween 1 and
n, and select the xi-th row from matrix L (denoted as
LR(xi)), the xi-th column from matrix U (denoted
as UC(xi)), and the yith column from matrix U
(denoted as UC(yi)).
2. Compute the pair (Kxiyi, θi) as follows: (⊕ means
the exclusive-or operation)
Kxiyi= LR(xi)× UC(yi) (6)
θi= h(IDi⊕ Kxiyi)⊕ h(PWi)⊕ h(Ks) (7)
3. Issue a smart card containing (Kxiyi, θi, UC(xi), vi, h(·), g, p) to Ui, where vi= h(Ks)⊕ yi.
In the registration and password-changing phases, in order to keep a user’s password secret and resist insider attacks, the user transmits his password in hashed form, rather than as plain text. Note that Pathan et al.’s schemes [17,18] make use of plain text for transmitting passwords. In addition, the system parameters g and p, used for computing a session key, have to be embedded in the smart card for later use.
3.2. Login Phase
When Uiwants to log in to the system, Uifirst attaches
the smart card and inputs his password PWi∗. The smart card performs the following operations:
1. Generate a random number r. 2. Compute the pair (Hi, Si) as follows:
Hi = Kxiyi⊕ h(r ⊕ T ) (8) Si = θi⊕ h(PWi∗)⊕ r (9)
where T is the current timestamp.
3. Generate a random number a and compute the pair (ri, Ri) as follows:
ri = gamod p. (10)
Ri = h(θi⊕ ri) (11)
4. Encrypt (IDi, ri, UC(xi), vi, T) with Ri and
com-pute Cias follows:
Ci = θi⊕ h(IDi⊕ Kxiyi)⊕ h(PWi∗)⊕ Ri
= h(Ks)⊕ Ri (12)
5. Send the login message Mi= (Ci, ERi
(IDi, ri, UC(xi), vi, T), Hi, Si, T) to the server.
To achieve the requirements of key agreement and user anonymity, which are not provided in Pathan
et al.’s schemes [17,18], the smart card has to
compute the nonce ri and encrypt the user’s identity
and other parameters as Equations (10) and (12), respectively. Moreover, since the user has already bound the timestamp T into the login message according to Equation (8), rather than only transmitting the timestamp in the login message, the proposed scheme can resist a replay attack. Note that Pathan et
al.’s schemes [17,18] only transmit the timestamp in
the login message without bounding it into the login message.
3.3. Authentication Phase
Upon receiving the login request Mi, the server
performs the following operations:
1. Compute Ri= Ci⊕ h(Ks), and decrypt
ERi(IDi, ri, UC(xi), vi, T) with Ri.
2. Check the validity of IDi. If IDiis invalid, the server
rejects the login request.
3. Verify if the time interval (T− T ) ≤ T , where T is the current timestamp and T is the allowed time interval for transmission delay. If (T− T ) > T , the login request is considered out-of-date and is rejected.
4. Compute (vi⊕ h(Ks)), which is denoted as yi.
5. Compute the triple (Kyixi, t, r) as follows:
Kyixi = LR(yi)× UC(xi) (13)
t= h(IDi⊕ Kyixi) (14) r= Si⊕ T ⊕ h(Ks)⊕ t (15)
6. Verify if the following equation holds:
Kxiyi = Hi⊕ h(r) (16)
If not, the server rejects the login request. Otherwise, it proceeds to the next step.
7. Generate a random number b and compute rs as
follows:
rs= gbmod p. (17)
8. Construct the authenticated session key AKi:
AKi= rib= gabmod p. (18)
9. Send
ERi(Kyixi⊕ rs, ri+ 1, T)Ui.
After receiving the message ERi(Kyixi⊕ rs, ri+
1, T), Uiperforms following operations:
1. Decrypt the message, obtain Kyixi⊕ rs, and verify
whether (T− T)≤ T , where Tis the current timestamp. If so, Uiproceeds to the next step.
2. Check whether decrypted data contains the value
ri+ 1. If so, Uiuses Kxiyito compute rsas follows:
rs= (Kyixi⊕ rs)⊕ Kxiyi (19)
3. Generate the authenticated session key AKi as
follows:
AKi= rsa= gba= gabmod p. (20)
Then Uiuses AKito communicate with the server.
In this authentication phase, the server has to generate a nonce rs and compute a session key AKi
according to Equations (17) and (18), respectively. Furthermore, the user also needs to compute the session key as Equation (20). The session key computation mentioned above does not appear in Pathan et al.’s schemes [17,18] because their schemes did not provide key agreement.
3.4. Password-Changing Phase
When Uiwants to change his password PWito PWi,
he sends the triple (IDi, h(PWi), h(PWi)) to the server.
As in the registration phase, these private data should be submitted in person or via a secure channel. Upon receiving the password-changing message, the server takes the following steps:
1. Compute θias follows:
θi = θi⊕ h(PWi)⊕ h(PWi)
= h(IDi⊕ Kxiyi)⊕ h(PWi)⊕ h(Ks) (21)
2. Replace θiwith θiin the smart card.
As in the registration phase, the user has to transmit his password in hashed form in this phase to keep his password secret and withstand insider attacks. ©
4. Analysis of Our Scheme
In this section, we analyze our scheme and show that our scheme can resist several well-known attacks. In addition, we provide a comparative study with other authentication schemes.
4.1. Correctness
According to Equation (15), we first derive the equation as follows: r= Si⊕ T ⊕ h(Ks)⊕ t = θi⊕ h(PWi∗)⊕ r ⊕ T ⊕ h(Ks)⊕ t = h(IDi⊕ Kxiyi)⊕ h(PWi)⊕ h(Ks)⊕ h(PWi∗) ⊕ r ⊕ T ⊕ h(Ks)⊕ t = h(IDi⊕ Kxiyi)⊕ r ⊕ T ⊕ t = h(IDi⊕ Kxiyi)⊕ r ⊕ T ⊕ h(IDi⊕ Kyixi) = r ⊕ T (22)
Since the proposed scheme employs LU decomposi-tion, Kxiyi= Kyixi. That is, h(IDi⊕ Kxiyi)⊕ h(IDi⊕ Kyixi)= 0. Therefore, r= r ⊕ T .
Using Equation (22), we verify Equation (16) as follows:
Kxiyi = Hi⊕ h(r)
= Kxiyi⊕ h(r ⊕ T ) ⊕ h(r ⊕ T )
= Kxiyi (23)
4.2. Security Analysis
We now analyze the security properties of our scheme. We first introduce a few terms used in this paper [28].
Definition 1. The discrete logarithm problem (DLP) is defined as follows: given a prime p, a generator g
of Z∗p, and an element β∈ Zp∗, find the integer α, 0≤
α≤ p − 2, such that gα≡ β (mod p).
Definition 2. The Diffie–Hellman problem (DHP) is defined as follows: given a prime p, a generator g
of Z∗p, and elements gc(mod p) and gs(modp), find
gcs ( mod p).
The security of the proposed scheme is based on the difficulty of DLP and DHP, which are believed infeasible to solve in polynomial time. We will show
that our scheme can resist replay attack, forgery attack, insider attack, reflection attack, and parallel session attack. We will also analyze the following security properties: anonymity, mutual authentication, forward secrecy, and known-key security.
Theorem 1. The proposed scheme can resist a replay attack.
Proof. Assume an adversary eavesdrops the login
message sent by Uiand uses it to impersonate Uiwhen
logging into the system in a later session. However, the replay of Ui’s previous login message will be
detected by the server since the user has already bound the timestamp T into the login message according to Equation (8), and the server will verify the validity of the timestamp T used by Ui. Therefore, the adversary
cannot replay the login message. However, there seems to be one potential security threat common to most existing timestamp-based user authentication schemes. That is, an adversary could impersonate a legitimate user by replaying that user’s previous login message within the allowed time interval T . This threat can be solved by the additional requirement that T is not reused by Uiwithin T .
Theorem 2. The proposed scheme can resist a forgery attack.
Proof. If the adversary wants to
imperson-ate Ui, he has to create a valid login message
(Ci∗, ER∗i(IDi, ri∗, UC(xi), vi, T∗), Hi∗, Si∗, T∗), where
T∗ is the current timestamp. First he has to choose a random number r∗ and compute the pair (Hi∗, Si∗)as follows:
Hi∗ = Kxiyi⊕ h(r∗⊕ T∗) (24) S∗i = θi⊕ h(PWi)⊕ r∗ (25)
Because having no idea about Kxiyi, θi, and PWi, the
adversary cannot forge a valid login message and hence cannot launch a forgery attack.
Theorem 3. The proposed scheme can resist an insider attack.
Proof. In our proposed scheme, when Ui wants
to resigter with a server for remote-access services, he has to submit (IDi, h(PWi)) instead of (IDi, PWi),
as in Pathan et al.’s schemes [17,18]. Due to the employment of the one-way hash function h, it is considered practically impossible for the server to derive the user’s password PWifrom the hashed value
[29]. That is, even the server does not know PWi.
Obviously, the proposed scheme can prevent the insider attack.
Theorem 4. The proposed scheme can resist a reflection attack.
Proof. A reflection attack is one in which, when a
user sends a login message to a server, the adversary eavesdrops the message and sends it (or a modified version of the message) back to the user. In the proposed scheme, the adversary cannot fool the server since he has to know the server’s secret key Ks in
computing Ri, which is used to decrypt the ciphertext
ERi(IDi, ri, UC(xi), vi, T) sent by Ui. Therefore, it
is ensured that our scheme can withstand the reflect attack.
Theorem 5. The proposed scheme can resist a parallel-session attack.
Proof. In the proposed scheme, an adversary
cannot impersonate a legitimate user by creating a valid login message in another on-going run from the honest run since the server’s response message
ERi(Kyixi⊕ rs, ri+ 1, T) is encrypted with Ri, which
is unknown to the adversary. Therefore, the proposed scheme can resist the parallel-session attack.
Theorem 6. The proposed scheme can provide user anonymity.
Proof. If an adversary eavesdrops the login
message, he cannot extract the user’s identity from the ciphertext ERi(IDi, ri, UC(xi), vi, T) since it is
encrypted with Ri, which is unknown to the adversary.
In addition, due to the use of the nonce and the timestamp in the login phase, the login messages submitted to the server are different in the login sessions. Hence, it is difficult for the adversary to discover a user’s identity. Clearly, the proposed scheme can provide user anonymity.
Theorem 7. The proposed scheme can provide mutual authentication.
Proof. The proposed scheme uses the Diffie–
Hellman key exchange algorithm to achieve mutual authentication between the server and a user. Ui and
the server securely exchange ri and rs in the login
and authentication phases, respectively. As a result, the authenticated session key is established as follows:
AKi= rbi = r
a s = g
ab
mod p (26)
Therefore, Uiand the server can use the authenticated
session key AKiin subsequent communications. Theorem 8. The proposed scheme can provide perfect forward secrecy.
Proof. Perfect forward secrecy means that the
disclosure of the long-term secret key material (e.g., server’s secret key Ksand user’s password PWi) does
not compromise the secrecy of the agreed keys in earlier runs. In the proposed scheme, perfect forward secrecy is ensured since the Diffie–Hellman key exchange algorithm is used to establish the authenticated session key gab. Even if the adversary knows the server’s secret key Ks, he is only able to obtain ga and gb from
earlier runs. However, based on the difficulty of the discrete logarithm problem and the Diffie–Hellman problem, it is computationally infeasible to compute the authenticated session key gab from ga and gb.
Thus, our proposed scheme provides perfect forward secrecy.
Theorem 9. The proposed scheme can provide known-key security.
Proof. Known-key security means that the
com-promise of a session key will not lead to further compromise of other secret keys or session keys. Even if a session key gab is revealed to an adversary, he still cannot derive other session keys since they are generated from the random numbers ga and gb based on Diffie–Hellman key exchange algorithm. Hence, the proposed scheme can achieve known-key security.
4.3. Functionality
We summarize the functionality of our proposed scheme in this subsection. The crucial criteria in a user authentication scheme are listed below:
C1. Freely chosen password: a user can choose his
password freely in the registration phase.
C2. Mutual authentication: the server and a user can
authenticate each other.
C3. User anonymity: a user’s identity is protected
when he logs into the system. No one knows the user’s identity except the server.
C4. Session key agreement: while mutual
authenti-cation is established between the server and a user, they can agree on a session key for use in subsequent communications.
C5. Secure password change: after the registration, a
user can change his password freely. ©
Table II. Comparison of authentication schemes.
C1 C2 C3 C4 C5
Our scheme Yes Yes Yes Yes Yes
Pathan et al. [18] Yes Yes No No No
Hu et al. [8] Yes Yes Yes Yes Yes
Pathan and Hong [17] Yes Yes No No Yes∗
Chien and Chen [2] Yes Yes∗ Yes Yes No
Das et al. [5] Yes No Yes∗ No No
Juang [9] Yes Yes No Yes No
Chien et al. [4] Yes Yes No No No
C1: freely chosen password; C2: mutual authentication; C3: user anonymity; C4: session key agreement; C5: secure password change. ∗Authors claimed such a security property but the property actually failed.
Table III. Evaluation parameters. Symbol Definition
TH Time for performing a one-way hash function
TM Time for performing a vector multiplication operation
TXOR Time for performing an XOR operation
TEXP Time for performing an exponentiation operation
TENC Time for performing a symmetric encryption operation
TDEC Time for performing a symmetric decryption operation
We summarized the functionality of related authen-tication and key distribution protocols in Table II.
4.4. Efficiency Analysis
Now we examine the performance of our proposed scheme. The evaluation parameters are defined in Table III. The time requirement of the proposed scheme is summarized in Table IV. We use the computational overhead as the metrics to evaluate the performance of the proposed scheme. In our scheme, only one hashing operation is required for a user to register and get his smart card. In the login phase, three hashing operations, nine exclusive-or operations, one exponentiation operation, and one symmetric encryption operation are needed for a user. For authentication, two exclusive-or operations, one symmetric decryption operation, and one exponentiation operation are needed for a user. We can see from Table IV that the exponentiation
operations are required by the server and the user due to the requirements of key agreement and perfect forward secrecy. These operations might be expensive for smart cards nowadays. However, with an increasing demand for information security as today’s security systems still have plenty of room for improvement, it is expected that the complicated computations will be widely adopted as a necessary security measure and hardware security enhancement for smart cards will become prevalent in the near future.
5. Conclusions
In this paper, we present a bilateral user authentication scheme based on LU decomposition. The scheme can withstand well-known attacks and possesses many merits, including freely changeable passwords, mutual authentication, user anonymity, and session key agreement. In addition, the proposed scheme is secure against replay attacks, forgery attacks, insider attacks, reflection attacks, and parallel session attacks. Moreover, compared with other authentication schemes, our scheme achieves more functionalities.
Acknowledgement
This work was supported by the National Science Council, Taiwan, Republic of China, under grant NSC Table IV. Performance of the proposed scheme.
Phase The server A user
Registration 1TM+ 2TH+ 4TXOR 1TH
Login — 3TH+ 9TXOR+ 1TEXP+ 1TENC
Authentication 1TM+ 2TH+ 8TXOR+ 2TEXP+ 1TENC+ 1TDEC 2TXOR+ 1TDEC+ 1TEXP Total 2TM+ 4TH+ 12TXOR+ 2TEXP+ 1TENC+ 1TDEC 4TH+ 11TXOR+ 2TEXP+ 1TENC+ 1TDEC
96-2752-E-009-005-PAE, NSC 96-2219-E-009-012, NSC 96-2219-E-009-006, NSC 96-2219-E-009-008, and NSC-96-3114-P-001-002-Y.
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