Journal of Applied Mathematics

Volume 2014 (2014), Article ID 314180, 11 pages

http://dx.doi.org/10.1155/2014/314180

Research Article

An Agent-Based Auction Protocol on Mobile Devices

Yu-Fang Chung,¹ Tzer-Long Chen,² Tzer-Shyong Chen,³ Dai-Lun Chiang,³ and Yu-Ting Chen⁴

¹Department of Electrical Engineering, Tunghai University, No. 1727, Section 4, Taiwan Boulevard, Xitun District, Taichung 40704, Taiwan

²Department of Technological Product Design, Lingtung University, Taiwan

³Department of Information Management, Tunghai University, Taichung, Taiwan

⁴Department of Computer Science and Engineering, National Chiao Tung University, Taiwan

Received 14 October 2013; Revised 10 April 2014; Accepted 17 April 2014; Published 13 May 2014

Academic Editor: Li Weili

Copyright © 2014 Yu-Fang Chung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

This paper proposes an English auction protocol to preserve a secure, fair, and effective online auction environment, where the operations are integrated with mobile agent technology for bidders participating in online auctions. The protocol consists of four participants, namely, registration manager, agent house, auction house, and bidder.

1. Introduction

With the popularization of the World Wide Web and its prompt adaptability to trends, traditional auction systems and business transactions have gradually transferred themselves to network platform transactions. Not only does online auction solve general problems like market price discrepancy due to asymmetric information, it also makes up for the time, space, and location constraints faced by traditional auctions and provides for transactions being conducted in conditions much freer and more public, allowing information much more transparency, and thus much fairer, and equal trading opportunities for the interested [1]. Therefore, online English auctions have successfully come to replace the offline traditional auctions, appearing more powerful and capable than the offline ones.

With the rapid development of mobile phones, the demand for mobile commerce has increased as a consequence. Based on market demand considerations, mobile service providers have begun launching mobile commerce services. To meet auction security demands in an environment of heterogeneous networks, an auction mechanism must satisfy both mobile and constraint needs. Under the analysis of various auction mechanisms in the study, a safe, fair, and efficient online auction environment was established by mobility and autonomy features of employing mobile agent.

Today, online auction protocols are applied over the Internet, including open auction and sealed-bid auction. Open auction can be subdivided into English auction and Dutch auction [1]. English auction is to have all participant bidders place their bidding prices on the basis of the reserve price that is preliminarily set by a host. After everything is in place, the host starts the bidding process. The bidding price soars gradually, the item going to the participant at the highest price. In Dutch auctions, bidders place their bids for lower prices. The auction will be closed when a bidder is willing to pay the final price [2]. Bidders in English auction can observe the bidding behaviors of their competitors during the entire auction process, so as to immediately adjust the bidding hereafter. Such a protocol is highly competitive because its game rule forces the bidding price to rise up. Thus, an item fetches highest price [3] at auction. As a result, the expected return on the goods in English auction protocol is usually higher than that in other protocols. Most auction-based websites, such as eBay and Yahoo! auctions, run the auction following English auction protocol, which are applied to the application of mobile commerce in the paper.

For the auction model on a mobile-based environment, [4] proposed a mobile auction agent model (MoAAM); bidders participate in online auctions through mobile agents. The protocol employed modular exponentiation operations which require a large computation amount, bringing a gradual degradation of performance in key generation, bidding, and verification phases. In contrast, the study runs the proposed protocol under the difficulty of solving discrete logarithm problem, leading to the positive improvement of performance in key generation, bidding, and verification phases. In terms of computation reduction on mobile devices and the workload of the connected server, the proposed system makes online auction systems much more convenient. A system should be endowed with the following features to maintain a fair and secure auction [5].

(1)Anonymity: during the course of an auction, no one is able to recognize the other bidders’ identities.(2)Traceability: the winner’s real identity can be recognized at the end of the auction.(3)No framing: the identities of all bidders remain independent. No one can falsely claim to be any other bidder who participates in the auction.(4)Unforgeability: nobody is able to forge another one’s valid bidding price.(5)Nonrepudiation: the winning bidder is unable to deny the proposed bidding price after being announced.(6)Fairness: all bidding must be conducted in an open and fair manner.(7)Public verifiability: anyone can verify the identities and bidding prices of the participating bidders.(8)Unlinkability among various auction rounds: nobody will know the same bidder’s identity among different rounds of auction.(9)Linkability within a single auction round: the bidders can repeatedly place new bidding prices within a single auction round and can be recognized by other bidders.(10)Efficient bidding: in order to make the bidding efficient, computation complexity must be minimized.(11)One-time registration: the bidder only needs to register once and then he/she can participate in all auctions that are opened.(12)Easy revocation: the registration manager can easily revoke someone’s right to bid.

The rest of this paper is organized as follows. Section 2 contains a review of related work on English auction protocol, the related cryptosystem concepts, and how the mobile auction agent model actually works in practice. The proposed protocol is shown in Section 3. In Section 4, the analyses of security and efficiency would be performed to examine the proposed protocol. The final conclusion and recommendations for further studies are given in Section 5.

2. Related Work

2.1. English Auction Protocol

Regarding English auction protocol research, the concept of bulletin board for verification was firstly applied to an English auction protocol in [6], satisfying various security concerns in the auction and successfully reducing computation and server load during the auction. The method was based on the concept in [7, 8], where group signature technology was utilized in English auction protocol to offer bidders higher security. Under the consideration of security, the protocol in [6] would not publish any bidders’ information against the bidder privacy’s risk, leading to loss of anonymity, fairness, and unlinkability among auction rounds, etc., as required by the English auction protocol. Later, [5] made improvements on the method in [6], allowing bidders’ identities and information to be published, yet risking the unlinkability among auction rounds, for example, bidders’ identities could not be identified through released information of previous auction rounds. In 2003, [9] proposed a much simpler and more effective method for the anonymity in English auction. However, it was shown to be insecure enough for bidders’ privacy and rights by [10], as bidders were not allowed to verify whether the shared keys they possessed belonged to the same auctioneer during the auction. Subsequently, [11] utilized an alias for resolving the situation.

2.2. RSA Cryptosystem

RSA, developed by Rivest, Shamir, and Adleman, makes use of an expression with exponentials. It is the first algorithm known to be suitable for signing as well as encryption and is one of the first great advances in public-key cryptography. The RSA is one specific method of public-key cryptosystem utilizing two prime numbers as the key for encryption and decryption. The operations of RSA are listed below.

(1)Randomly select two large prime numbers and and calculate .(2)Compute the least common multiple of two large prime numbers .(3)Compute the public key , where satisfies .(4)Compute the secret key , where satisfies .(5)Publish but keep the secret key secretly. Since the security of RSA is based on calculating the prime factors and after publishing the large prime numbers and should be carefully selected so that their factorization becomes impossible.(6)The encryption and the decryption are presented as follows, where is the plaintext and is the ciphertext after the encryption.

 (Encryption)  . (Decryption) .

The difficulty in factorizing large prime numbers determines the reliability of RSA algorithm. In other words, the more difficulty the integer factorization presents, the more reliable the RSA algorithm is.

2.3. ElGamal Digital Signature

Putting digital signatures on a document aims to show the integrity and the nonrepudiation. Integrity refers to preventing the document from being tampered with in the transmission process, and the receiver can use the digital signature for verifying whether the document is tampered with or not. Since digital signature is calculated by the signer using his/her secret key, it could prevent the signer from denying the signature that he/she signed afterwards. This is considered to protect the receiver, as nonrepudiation. In numerous studies, many protocols were proposed for digital signatures, such as DSA, RSA, Schnorr, ElGamal [12], and ECDSS. The study applied the ElGamal algorithm to signature scheme, which is further introduced as follows.

(1)Choose a large prime number , where has a large prime factor, and a primitive root , where .(2)The signer chooses one integer as his/her secret key satisfying .(3)After computing his/her public key using the following equation, the signer publishes it. Consider

(4)The signer randomly chooses an integer satisfying .(5)Compute the signature of plaintext . Consider

(6)The receiver verifies the legality after receiving the signature as follows:

If the equation holds, is the legal signature of the plaintext and vice versa.

The security of ElGamal depends on solving the difficulty of discrete logarithm problems and . An inappropriate selection of and would therefore result in the signature being forged.

2.4. Diffie-Hellman Key Exchange

Diffie-Hellman key exchange scheme allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communication channel [13]. The security is based on the difficulty of discrete logarithm problem (DLP). The operation of Diffie-Hellman key exchange is shown as follows.

(1) selects one integer as his/her secret key, which satisfies , where is a prime number. Then, uses the following equation for computing his/her public key and publishes :

(2) selects one integer as his/her secret key, which satisfies , where is a prime number. Then, uses the following equation for computing his/her public key and publishes :

(3)Both and have the published public key and their own secret keys to calculate the shared secret key as follows:

(4)The last step is the verification, as follows:

There are two disadvantages to Diffie-Hellman scheme. First, the session key could merely be used between the two parties. When there are users in a system, and one of them wants to communicate with any of the other users, the user will need to have session keys and the system will have to maintain session keys. Second, the identities of the presently communicated objects are unknown; i.e., and would not recognize each other’s actual identities.

2.5. Mobile Agent

2.5.1. Basic Concept of Mobile Agent

Recently, the application of mobile technology to network data transfer has received considerable attention. In information technology, the mobile agent is highly autonomous and is a mobile software that the users can capitalize to perform tasks in heterogeneous network environments. Since the mobile agent does not require constant online network connections, it also demonstrates significant improvement in the network performance.

The advantages of mobile agents include low network loads, high network latency resistance, encapsulation of protocols, asynchrony and autonomy, dynamical adaptation, and natural heterogeneity. The advantages of assigning tasks to mobile agents cannot be overemphasized. However, because it is entrusted with the user’s private key and agent code at the time of task assignment, the data transfer management regarding agents’ access management and control becomes particularly important.

Although this protocol can effectively solve data transmission insecurity, the efficiency can still be improved on. In Figure 1, the repetitious key storage in different agent codes not only results in the memory space consumption, it but also causes performance exhausted while computing keys.

Figure 1: Tree-based structure of key management and access control.

Therefore, [14] proposed two schemes in the application of mobile agent. The first method applied the tree-structure of Akl and Taylor into the agent management, integrating the keys of lower successive tiers as one. The server could thus use its own key and through mathematical computation obtain successive private keys that could restore confidential documents. This security is based on the difficulty of solving elliptic curve discrete logarithm problem. The second scheme, in its attempt to improve mobile agent’s computation efficiency, applied the cryptosystem based on the difficulty of discrete logarithm problem to reduce the public parameter size without compromising security. Their approach used the hierarchical structure for managing mobile agent’s access control to users’ keys, at the same time protecting data transmission when the access permission differed from user to user as shown in Figure 2.

Figure 2: Hierarchical structure of key management and access control.

During the task execution, the mobile agent roams between various hosts in a network. In the process to carry out message exchanges, it may also be required to connect with other mobile agents, which, thus, imposes security concerns arising out of insecure connections [15], malicious modifications by unauthorized external users, or even deliberate attacks by internal users. Therefore, mobile agent security is an important issue that needs to be overcome to effect into its successful application.

The mobile agent might face the following threats during the task execution.

(1)Unauthorized users access to the related information of servers:

(1.1)causing deliberate system paralysis and breakdown in a nonauthorization situation,(1.2) unauthorized access to data or resource from server by forging as authorized agents.

(2)Attacks on mobile agent by other agents:

(2.1)forging identity codes of other agents for authorization access to services and resources, thereby avoiding the responsibility and breaching other users’ trust on the legal mobile agent,(2.2)paralyzing the legal agent by sending repetitious messages.

(3)Attacks on mobile agent by other malicious servers:

(3.1)deceiving and threatening the mobile agent through the abuse of trusted third party servers’ identification codes,(3.2)ignoring the mobile agent’s requests deliberately,(3.3)deceiving negotiating mobile agents by tampering with their data field.

(4)Attacks on server by other malicious servers or mobile agents:

(4.1)deliberate delayed response to mobile agent’s request: such common attacks intend to cut off the requests or lower the mobile agent’s efficiency by making the mobile agent wait for responses, resulting in repeated requests and hence lowering the system efficiency. Abnormal or abrupt task termination of mobile agents results from deadlock state where other mobile agent continue to wait for responses,(4.2)deterring the mobile agents from task completion deliberately, resulting in a live-locked.

2.5.2. Mobile Auction Agent Model

Mobile auction agent model [4], called MoAAM, is designed to enable users to use their mobile devices to participate in online auctions. MoAAM consists of four agents, namely, personal agent, customer agent, auctioneer agent, and broker agent. How these agents communicate with each other in MoAAM through a web server is shown in Figure 3.

Figure 3: Communication in MoAAM.

Inside the mobile device, there is an interactive interface, called personal agent, which would connect with an agent house server via the wireless network. In a few words, a personal agent is a preset agent that operates on the mobile device and provides an interface to allow users to communicate with the agent house server. The customer agent, the auctioneer agent, and the broker agent all operate in the fixed network. The personal agent connects to the customer agent when a mobile network user wants to buy a specific product. Then, the person agent sends the description of desired products and price information to the customer agent. On the other hand, an auctioneer registers the information of products to the broker agent. After the broker agent receives the user’s request, an auction list, which meets the user’s needs, will be generated and sent back to the user. If the user decides to purchase the auction items from the received list, a bid agent will be created by the customer agent and be dispatched to an auction house server to participate in the bidding.

The architecture of MoAAM [4] is shown in Figure 4 and how it works is described as follows.

(1)Primary participants in the MoAAM:

(1.1)broker agent: it is responsible for pairing up bidders and auctioneers. Moreover, it generates auction item lists and provides bidding price information for the users,(1.2)bid agent: an individual user would use it for participating in auctions and placing the bids,(1.3)auctioneer agent: auctioneers use it as their representative for managing the items they are selling,(1.4)auction house server: a platform where online auctions take place.

(2)The running of customer agent. The customer agent provides an interface with three different functions for the user:

(2.1)query the broker agent: know what kind of auction items the broker agent so far has registered and the bidding prices for these items,(2.2)specify the bid agent: a user sends his/her request and bidding information to the bid agent generator. The generator will create a bid agent from a template,(2.3)control the bid agent: this function allows the user to communicate with the bid agent and control the behavior of a bid agent.

(3)The running of broker agent. First, the auctioneer needs to register his/her agent with the broker agent, and then the broker agent will store the auctioneer’s information in the database. When the customer agent sends a request for item information, the broker agent would reply with a list of recommended items to the customer agent.(4)The running of auction house. The auction house server offers a web interface to allow the auctioneers to execute the following functions:

(4.1)specify the auctioneer agent: an auctioneer sends his/her request and auction information to the auctioneer agent generator. The generator will create an auctioneer agent from a template. The newly created agent and auction information would be registered with the broker agent,(4.2)the management of the auctioneer agent: this interface allows the auctioneer to communicate with the auctioneer agent and control the auctioneer agent’s behavior.

(5)Mobile agent platform. The mobile agent platform is where the bid agent and the auctioneer agent would be sent to as the auction starts.

Figure 4: Architecture of MoAAM.

3. Proposed Protocol

The proposed system includes six phases of initialization, registration, generation of transaction public key, signature, auction bidding, and winner announcement. The whole process flow is shown in Figure 5. In the process, there are four main participants, which are registration manager (RM), agent house (AH), auction house (AUH), and bidder (B). What the participants do is described as follows.

(1)Registration Manager (RM):

(1.1)it is a unit for bidders applying for the registration. All bidders only require registering once. After that, they can participate in multiple auctions and no more registration is needed,(1.2)to be in charge of storing bidders’ identity information and corresponding secret parameters,(1.3)to manage and maintain the bulletin board, which is called BBRM. On the bulletin board, two types of information would be published. One is the registration key and identity information of a bidder and another is a pseudonym that a bidder uses in a single auction round. The published information would be supplied to anyone for the identification verification, and only the RM has the authority to write and update the bulletin board.

(2)Agent House (AH):

(i)to be in charge of communicating with the broker agent and create bid agents,(ii)to manage and maintain a bulletin board, which is called . The bulletin board would provide the bidder’s transaction public key for the verification purpose, and only the AH has the authority to write and update the bulletin board.

(3)Auction House (AUH):

(3.1)to provide the auction place, to maintain the operations, and to host the auctions,(3.2)to manage and maintain a bulletin board, which is called . On this bulletin board, the published information would be the bidding information of bidders and the winning bidder’s information. All the published information can be used for verifying one’s identity, and only the AUH has the authority to write and update the bulletin board.

(4)Bidder ():

(i)it is the one who participates and places bids in the auction.

Figure 5: Flow chart of proposed system.

The system using modular exponentiation in the English auction protocol is presented as follows. The given system parameters are shown in Table 1.

Table 1: Parameters for modular exponentiation system.

p, q
Two big prime numbers, satisfying

g
A generator with order q in

A symmetric encryption method of message m with the key K;

(K is the shared key between Bi and AM)

H(x)
A one-way hash function, satisfying and

SKAH
AH’s private key

PKAH
AH’s public key

The ith bidder

A bidding price that is placed by Bi in the th round of auction

Bi ’s private key

Bi ’s registration key

, ,
Three secret parameters chosen by Bi

A pseudonym, RM creates only for Bi in the jth round of auction

A random number chosen by AH in the jth round of auction

The public information published by AH in the jth round of auction

A transaction public key, AH generates only for Bi in the jth round of auction

In the following are the auction processes.

3.1. Initialization

The RM and AH establish system parameters and the steps are as follows.

( 1) Registration Manager

Step 1.   Set up a read-only bulletin board () and post two kinds of information. One is the registration key and identity information of all bidders. Another is pseudonyms used by the bidders in the th round of auction. The RM is the only one who can write and update the bulletin board.

Step 2.  Declare , , , publicly.

( 2) Auction House

Step 1. Set up a read-only bulletin board () and publish the transaction public key and related information of all bidders on the bulletin board. AH is the only one authorized to write and update the bulletin board.

Step 2. Randomly select an integer as the private key to calculate the corresponding public key . The equation is as follows:

Step 3. Post on .

3.2. Registration

As a new bidder () joins in an auction; must apply for the registration with the RM at the very beginning. After the registration is completed, the RM would generate pseudonyms, which can only be used one time for in the th round of auction.

should first calculate all relevant parameters before registering with the RM. The registration process is shown as follows.

Step 1. randomly selects an integer as the private key and computes a corresponding registration key . The equation is given as follows:

Step 2. randomly selects an integer as a secret parameter.

Step 3.   randomly selects an integer and computes the verification information . The computation steps are given as follows:

Step 4.   sends the information and the identity information through a secure channel to the RM. After the RM receives the information transmitted by , the registration would proceed.

Step 5. The RM authenticates the validity of by the following equations:

If (12) holds, is valid. This proves and corresponding to each other. In contrast, RM would refuse to take the registration application from if the received information is forged.

Step 6. The RM keeps ’s identity information and the corresponding secret parameter in its own database.

Step 7. The RM posts ’s identity information and registration key on .

Step 8. Before the th round of auction starts, the RM would generate a pseudonym for every bidder . The order of all pseudonyms would be randomly arranged and posted on . The equation is shown as follows:

Step 9.   can use (13) for computing his/her own pseudonym and verify that his/her pseudonym matches with the one posted on . If dose not find his/her pseudonym on , he/she can appeal to the RM.

3.3. Generation of Transaction Public Key

In the th round of auction, can obtain the auction information through the AH who could ask the broker agent to supply the information about currently open auctions. The broker agent would prepare an auction house list that matches the needs of and send the list back to the AH for to review. When decides which auction he/she wants to participate in, would have to apply for a transaction public key (), which is managed by the AH. The AH would generate with ’s pseudonym on for the bidder. The steps are given as follows.

Step 1. The AH randomly selects an integer and computes the public information . Then, the AH would post on . The equation is shown as follows:

Step 2. The AH would use and its own private key for generating a parameter and for each and post the generated information on BBAH. The equation is shown as follows:

3.4. Signature

Before starts to participate in the auction, must verify given by the AH on BBAH. If the key is valid, would calculate the corresponding signature with the bidding price and related information. Subsequently, can start participating in the bidding. The steps are stated as follows.

Step 1.   uses the AH’s public key for computing a parameter , as follows:

Step 2.   combines his/her private key and parameter to generate , as follows:

and must verify that they are matched with the information posted on BBAH; if not, can appeal to AH.

Step 3.   randomly selects an integer and decides a bidding price . Afterwards, a corresponding signature is created, shown as follows:

Step 4.   uses the AH’s public key for computing the shared key , shown as follows:

Step 5.   used for encrypting the bid and the signature to obtain the ciphertext .

3.5. Auction Bidding

Before the auction starts, needs to obtain a bid agent from the AH. After a bid agent is acquired, , then, is allowed to bid. The auction bidding process is stated as follows.

Step 1.   should first send out the data tuple to the AH and apply for a bid agent.

Step 2.  After the AH receives the data from , the AH must compute the shared key to decrypt the ciphertext and authenticate the validity of . The equations for verification are shown as follows:

If (22) holds, this proves that is valid, and vice versa. The AH can reject the bidding request from if the received information is false.

Step 3.  The AH uses the bidding information for creating a new bid agent for , and then the AH would send this agent to the selected AUH to represent participating in the auction.

Steps 1, 2, and 3 can be skipped if the bid is placed more than once. Only the bidding information would be verified.

Step 4.  When the bid agent arrives at the AUH, it has to be verified that is the same as on BBAH. If not, the AUH can reject ’s application.

Step 5.  The AUH verifies the bidding information using (22). If (22) holds, it means that is valid.

Step 6.  The AUH posts the bidding information on . Anyone can use (22) for verifying the bidding information of .

3.6. Winner Announcement

When the th round of auction ends, the one who places the highest bidding price would be announced as the winner. Then, the AUH would take the winner’s to reconfirm the winner’s information and with the AH and RM. Afterwards, the result would be published on and can be obtained by anyone to verify. The steps are stated as follows.

Step 1. The AUH takes the winner’s to the AH and asks for the pseudonym used by the winner.

Step 2. The AH returns the information back to the AUH.

Step 3. The AUH can use (16) for confirming the relationship between and .

Step 4. The AUH takes the winner’s to the RM and asks for the winner’s .

Step 5. The RM returns the information back to the AUH.

Step 6. The AUH can use (13) for confirming the relationship between and .

Step 7. The AUH will post the winner’s information, and , on . The winner’s information on can be obtained by anyone to verify again according to (13) and (16).

4. Security and Efficiency Analysis

The proposed cryptosystem applied the ElGamal algorithm, it having two advantages: not keeping secret parameters, as all system parameters can be public, and different ciphertexts formed from the same plaintext at distinct time by one same user. The ElGamal parameters are generally used in each phase of this system. The security is established on the difficulty of solving discrete logarithm problem, for example, giving , , and ; the attempt of guessing or deciphering is computationally infeasible. Regarding the above-mentioned security features, the proposed protocol is discussed as follows.

( 1) Anonymity. Except RM and AH working together to reveal the identity during the auction, nobody can find out who the bidder is. The anonymity of bidders can be analyzed from the perspectives of RM, AH, and AUH.

(1.1) For the AUH, it is only authorized to obtain the bidding information, and , is the signature for , where is a key for the verification. Thus, the AUH is just allowed to use for verifying the signature and comparing to the one posted on . Still, who the bidder is will never be known.(1.2)For the AH, it merely knows the relationship between and ; thus, it does not have enough information to recognize who the bidder is.(1.3)For the RM, it cannot derive from to obtain the corresponding , even if the RM has the bidder’s identity information.

( 2) Traceability. Anyone can get and from and use (13) and (16) for verifying the winning bidder’s identity.

( 3) No Framing. Unless attackers get ’s , ’s signature cannot be forged. Even if attackers get and intend to derive from , it will be difficult for him/her to obtain , because of the security based on the DLP.

( 4) Unforgeability. Attackers will be unable to calculate the transaction public key by using the equation (in modular exponentiation system) or or to forge any valid bidding information . The reason can be explained in three aspects.

(4.1)Attackers cannot obtain ’s , , and .(4.2)Attackers have to spend a great deal of time on resolving the DLP, even if or is captured.(4.3)Because is different in each round of auction, the bidder’s pseudonym and transaction public key would be different in each round of auction.

( 5) Nonrepudiation. A signature is hidden inside the bidding information and it has the characteristic of no framing. Therefore, the winning bidder of the auction round cannot deny his/her signature.

( 6) Fairness. All bidders use pseudonyms to join in the auction. The AUH will post the valid bidding information . If does not find his/her bidding information, he/she could appeal to the AUH. Like this, the AUH can fairly handle all bidders’ information.

( 7) Public Verifiability. Anyone can confirm the validity of the bidder, the validity of a bid, and the winning bidder’s real identities.

( 8) Unlinkability among Various Auction Rounds. In each auction, the pseudonym generated by the RM and the transaction public key generated by the AH are different. Except the RM and AH sharing these keys with each other, no one will know the relationship about among various auction rounds.

( 9) Linkability within a Single Auction Round. Within a single round of the auction, holds the same to place a bid in the auction. It is traceable to know how many times the bidder places the bid and who places the bid.

( 10) Efficiency of Bidding. The efficiency of bidding shall be explained later.

( 11) One-Time Registration. A bidder uses a pseudonym for participating in the auction. Hence, only needs to register once with the RM.

( 12) Easy Revocation. It is easy for the RM to revoke a bidder’s identification and secret parameters from the database. Once the information is removed from the database, the bidder loses the right to participate in the auction.

The following is the performance comparison between [4] and the proposed protocol. The notation used is defined as shown as Tables 2 and 3.

Table 2: Definition of the notation.

The time cost for modulus multiplication operation

The time cost for modulus exponentiation operation

The time cost for one-way hash function operation

Table 3: Analysis of computation complexity

Phase
[4]
The proposed system

Registration

Generation of transaction public key

Signature

Auction bidding

Winner announcement

As seen in the comparison table, the computation amount of this system is much lower than [4], especially in the generation phase of transaction public key.

Due to modulus addition and subtraction operation amount being low, they can be omitted.

The analysis of computation complexity related to these two systems is described below following the above information.

As seen in the comparison table, the computation amount of this system is much lower than [4], especially in the generation phase of transaction public key.

5. Conclusion

This paper puts forward an agent-based English auction protocol to allow bidders to obtain information and participate in auctions through an agent. Based upon the proposal, it clearly satisfies all of the security requirements for online auction protocols, such as anonymity, traceability, fairness, and so on. Because the mobile devices are identified with inherently weaker computation capability, this protocol is employed on the mobile agent to achieve lower computation amount and to reduce the time cost consumed by verification and computation. This is a means to make the online auction on mobile devices become more efficient and convenient. As wireless networks continue to become extensively used, the proposed system for wireless data exchange has just met the minimum for the security purpose. In the future, the key point would be focused on enhancing the auction-related data protection.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This work was supported partially by National Science Council, Taiwan, under Grant NSC 102-2221-E-029-008.

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