The Proposed Protocol. In this section, we propose a chaotic maps-based mutual authentication and key-agreement protocol for wireless communications using smart cards that almost satisfies all the requirements of the existing authentication and key-agreement protocols for wireless communications and is immune to various known types of attacks. In addition, our protocol is simple and has a reasonable cost. The notations used in this section are listed in Table 1. Our protocol consists of three phases, i.e., (1) the registration phase; (2) the mutual authentication and session key- agreement phase; and (3) the password change phase.
The Proposed Protocol. In this paper, a new protocol, the Generalized Byzantine Agreement Protocol (GBAP) is proposed to solve the BA problem due to faulty component(s), which may send incorrect messages to influence the system to reach agreement in the virtual subnet. The notations and assumptions of the GBAP protocol for the virtual subnet network are shown below: ■ Let Pm be the total number of malicious faulty processors in a group. ■ Let Pd be the total number of dormant faulty processors in a group. ■ Let Cm be the total number of malicious faulty communication media in the virtual channels. ■ Let Cd be the total number of dormant faulty communication media in the virtual channels. ■ Let PGm be the maximum number of malicious faulty groups allowed. ■ Let PGd be the maximum number of dormant faulty groups allowed. ■ Let CGm be the maximum number of malicious faulty virtual channels allowed. ■ Let CGd be the maximum number of dormant faulty virtual channels allowed. ■ Let TFP is the total number of allowable faulty processors, TFP= Pm + Pd. ■ Let TFC is the total number of allowable faulty virtual channels, TFC= Cm + Cd. ■ Let ν is the number of processors in a group. ■ Let γ is the number of communication media in the virtual channel. ■ Let g be the group identifier where g>(g–1)/3+2(PGm+CGm)+PGd+CGd. ■ Let c be the connectivity of the virtual subnet network, where c is g–1 and c>2(PGm+CGm)+PGd+CGd. ■ Each processor can leave from the network or migrate into the network before executing GBAP. ■ In the BA problem, the source processor can transmit messages in the first round of message exchange phase. ■ Each processor always knows the total number of processors in the network. ■ The messages have encoded by Manchester code before communication [6]. Hence, the dormant faulty components can be detected. The procedure TRANSMISSION used to transmit messages in GBAP is based on the virtual subnet network characteristics [2] TRANSMISSION can provide a virtual channel to help each processor to transmit messages to each other. A detailed description of our proposed protocol based on the procedure TRANSMISSION is shown in Figure 2. Procedure TRANSMISSION
The Proposed Protocol. In this section, we shall introduce the proposed protocols RC and UAP to solve the BA problem with dual failure mode for the processors in a UNet. In UAP, RC is used to find out the c node-disjoint paths by the graphic information [3] to receive the messages from the sender processor, and the number of rounds of UAP operations is t +1 (t = ⎣(n-1)/3⎦). RC can provide a reliable channel to help the processors to transmit messages to each other, and using RC can make an un-fully connected network act just like a fully connected network without the common knowledge of the graphic information of the whole network structure. Moreover, the protocol RC encodes a transmitted message by using Manchester code before transmission. Therefore, the message(s) from dormant faulty processor can be detected by healthy processor. The definition of the protocol RC is shown in Figure 3. In a UNet, each processor only has the partial knowledge of its own graphic information. For example, in Figure 4(a ) and 4(b), P1 and P3 only have the information of the connection state of itself. Therefore, it is impossible for P1 to transmit a message to P3, and the reason is that P1 does not know the location of P3. In this study, the proposed RC can enable a sender processor to transmit a message to the destination processor without the location information of the destination processor. UAP can tolerate fm malicious faulty processors and fd dormant faulty processors, where n>⎣ (n-1)/3⎦+2fm+fd and c>2fm+fd. The definition of protocol UAP is shown in Figure 5. There are two phases in protocol UAP, which are the message exchange phase and the decision making phase. In the message exchange phase, each processor exchanges messages with others to get enough information through RC, which needs t +1 rounds of message exchange. If the received message is through the dormant faulty processors, then replace the value λ0 as the received message, if the received message is λi, then replace the value λi+1 as the received message (The value λi is used to report the absent value , where 0≦ i ≦t –1). In the protocol RC, the sender processor Pi (1≤ i ≤ n ) will transmit the value vi to the destination processor Pj (1≤ j ≤ n ) directly (if the sender processor has the connection with the destination processor). Moreover, the sender processor Pi will also transmit the value vi through the processor Py (1≤ y ≤ n ) which has connection with the sender processor Pi, then each intermediate processor Py (except t...
The Proposed Protocol. The purpose of the BA protocol is to allow all correct nodes to reach a common agreement in a virtual subnet- based cloud computing environment. For this reason, nodes should exchange messages with all other nodes. Each correct node receives messages from other nodes during a number of rounds of message exchanges. Afterwards, all correct nodes have enough messages to make a decision value, called an agreement value or common value. Then, all correct nodes agree on the same value. The assumptions, notations and parameters of the proposed protocol OMA are shown as follows: • Each node in the network can be identified uniquely. • A node does not know the fault status of other nodes. • Let n be the total number of nodes in the network. • Let g be the number of groups in the network and g ≥ 4. • Let x be group identifier where 1 ≤ x ≤ g and g ≥ 4. • Let nx be the number of nodes in group Gpx, 0≤x≤g. If there are more than ⎡nx /2⎤ malicious faulty mobile nodes in Gpx, then Gpx will be named the malicious faulty group. • Let c be the connectivity of the virtual subnet, where c is g–1. • Let TFG be the total number of malicious faulty groups. • Let TFn be the total number of malicious faulty nodes. In the BA protocol, the first step is to count the number of required rounds of message exchange, which is determined by the total number of nodes at the beginning of protocol execution. Therefore, if the variety of faulty nodes malicious fault; this means Cs may arbitrarily send different message values (e.g., replicate command [9]) to different groups. Therefore, in order to solve the BA problem among correct nodes within this example, OMA requires θ (⎣(g– 1)/3⎦+1) rounds of message exchange. pre-execute counts of the number of rounds required before the message exchange phase in OMA. Then, three (⎣(g–1)/3⎦+1 = ⎣(7–1)/3⎦+1 = 3) rounds of message exchange are required. can be determined, then the number of rounds of message exchange can be reduced and then the fault tolerance capability is increased. The proposed OMA can solve the BA problem due to faulty node(s), which may send incorrect messages to influence the system to reach agreement in a virtual subnet- based cloud computing environment. By using the proposed OMA protocol, all correct nodes in the environment can reach a common agreement which requires θ rounds of message exchange, where θ = ⎣(g−1)/3⎦ + 1. The proposed OMA protocol is organized in two phases:
The Proposed Protocol. The proposed protocol Optimal Malicious Agreement Protocol (OMAP) can solve the BA problem due to faulty sensor nodes which may send wrong messages to influence the system to reach agreement in a synchronous CWSN. OMAP protocol consists two phases and needs σ rounds of message exchange to solve the BA problem.
The Proposed Protocol. The proposed protocol, Dual Fault Detection Consensus (DFDC), can solve the consensus problem and FDA problem with dual failure mode in an FCN. The assumptions and parameters of our protocol to solve the FDA problem in an FCN are as follows: ■ Each processor in the network can be identified as unique. ■ Let N be the set of all processors in the network and ∣N∣= n. ■ The processors of the underlying network are assumed to be fault-free. ■ The fallible component of the underlying network is communication media only. ■ Let m be the maximum number of malicious faulty communication media allowed. ■ Let d be the maximum number of dormant faulty communication media allowed. ■ Let c be the lower bound of connectivity of the FCN, where c= n-1, and m ≤ (n-c-2)/2. That is, DFDC can tolerate d dormant faults and m malicious faults simultaneously in the network, where m ≤ (n-d-3)/2, if the processors always work accurately and communication media are fallible. DFDC needs two rounds of message exchange to reach the consensus, and only one additional round (the third round of message exchange) is needed to detect and locate the faulty components. There are three phases in DFDC, which are the message exchange phase, the decision making phase, and the fault detection phase. In the message exchange phase, the processors exchange messages to get enough information. In the first round, each processor Pi transmits its initial value vi through the communication media, where 1≤ i ≤ n, and receives the initial value vj from every processor Pj, for 1≤ j ≤ n. Then, the processor Pi constructs the vector Vi = [v1, v2,…, vj,…, vn]. If a dormant communication medium, say ik, is found, then vk in the vector Vi is replaced with λ, where 1≤ k ≤ n. In the second round, each processor Pi transmits a vector Vi to the other processors, where 1≤ i ≤ n, and then it receives the vectors transmitted by all the other processors and constructs MATi, (Setting the vector Vj in column j, for 1≤ j ≤ n.) If a dormant communication medium, say ik, is found, then Vk = [λ, …, λ, …, λ ], where 1≤ k ≤ n. In the third round, each processor Pi transmits MATi to all the other processors and then receives the matrices transmitted by the other processors to construct FDMATi (Setting the matrix MATj in j-th layer of FDMATi, for 1 ≤ j ≤ n.). If a dormant communication medium, say ik, is found, then all the values of the k-th layer of FDMATi is set to be λ, where 1≤ k ≤ n . In the decision making phase, each pr...
The Proposed Protocol. In this section, we describe a one round authenticated group key agreement protocol which uses one more key pair as well as the long term public and private keys of typical IBE system.
The Proposed Protocol. This part describes the proposed scheme in detail. The proposed scheme consists of four phases: multi-environment setup phase, the user regis- tration phase, the authentication key agreement phase, and the biometrics and password update phase, respectively. Symbols used in the proposed scheme are defined in Table 1 as follows: Table 1. Symbols Symbol Definition U ,IDU ,PWU user, the identity of user, the password of user, respectively Sj,IDSj thejthserverthe identity of thejthserver, respectively RC registration center B the biometrics sample of user τ predetermined threshold for biometrics authentication d(·) symmetric parametric function (x, Tk (x)) , k the public key and secret key of RC, respectively EK(·),DK(·) secure symmetric encryption/decryption algorithm with secret keyK a.b random integer number SK session key h(·) secure one-way hash function ⊕,|| XOR operationconcatenation operationrespectively
The Proposed Protocol. In this paper, a new protocol, the Optimal Generalized Byzantine Agreement (OGBA), is proposed to solve the BA problem when resulting from faulty component(s) which may send incorrect messages to prevent the system from reaching agreement in the CWSN. Basically, the messages received from non-faulty components will be the same with each other node. Based on the same messages, every node can make the same agreement value easily. Thus, the protocol OGBA should help the correct node remove all the influences of the faulty components in the messages receiving from all other nodes. Essentially, the dormant faults of TMs/nodes are easily identified and removed. The influence of TMs with malicious fault can be removed at each round of message exchange by taking a majority of the messages received. At the final step, the influences caused by malicious nodes can be removed by using a special data structure and a vote function. The notations and assumptions of the OGBA protocol for the CWSN are shown below:
The Proposed Protocol. 4.1. Dual semirings action The idea of this action is two dual idempotent semirings to act over a matrix semiring. Let S be a set and let D = S,⊕• ,⊗• , ⊥, T and D d = S,⊕• ,⊗• , ⊥, T be two complete dual semifields (here we denote the minimum element by ⊥ and maximal element by T ) and S = S,⊕,⊗, ⊥, T . We consider matrix semirings, defined over S , D and D d . Let these be respectively M n×n (S ) , M n×n (D) and M n×n (Dd ) . Additionally, we consider polynomials of matrices over two dual semifields. Then if N ∈ M n×n (Dd ) , X ∈ M n×n (S ) ,the action is: (( p(M ), q(N)), X ) p(M ) ∘ X ∘ q(N) . M ∈ M n×n (D), In general case, the protocol consists of the following: two users agree on a public channel about the dual semifields and three matrices M ∈ M n×n (D), N ∈ M n×n (Dd ) , X ∈ M n×n (S ) .
