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.
Table 1. Notations used in the proposed protocol
The Proposed Protocol. This study proposes a new protocol TAP to solve the agreement problem of faulty TMs may send wrong messages to influence the system to achieve agreement in a CMCC. The proposed protocol TAP consists two phases, the message exchange phase and decision making phase. Moreover, TAP only needs two rounds of message exchanges to solve the agreement problem. In the first round of the message exchange phase, the source node ns multicasts its initial value vs through TMs by TTCB. And then, each node stores the received value in root of message-gathering tree (mg-tree) [9]. The mg-tree is a tree structure which is used to store the received messages. In the second round, each node ni acts as the sender, sending the value vs (received from source node ns) to other nodes by TTCB. However, the receiver can always detect the message(s) through dormant faulty components if the protocol TAP appropriately encodes a transmitted message by using Manchester code [7]. Hence, if the messages pass through any dormant faulty TMs, then λ will be stored in mg-tree of receiver. In decision making phase, in order to reduce the influence from the faulty components, a majority value is taken from all nodes in same cluster to set the majority value at level 2, Finally, the agreement among all nodes will be achieved. The proposed protocol TAP is presented in Figure 3. TAP protocol (for node ns with initial value vs) Message Exchange Phase Round 1: The source node sends its value (vs) to other nodes by TTCB; each receiver node obtains the value and stores the received value in the root of its mg-tree. If the cluster-disjoint path from source node to destination cluster passes through any dormant faulty transmission media, then λ is stored. Round 2: Each node transmits the values at the root in its mg-tree to each cluster’s nodes by TTCB. If the cluster-disjoint path from source node to destination cluster passes through any dormant faulty transmission media, then λ is stored. Each receiver node takes a majority on its received messages and stores the majority value in the corresponding vertices at level 2 of its mg-tree.
Step 1: (1) Take the majority value of Vi in mg-tree.
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:
(1) The underlying network is synchronous.
(2) Each node in the network can be identified uniquely.
(3) A node does not know the fault status of other components.
(4) Let n be the number of nodes in the underlying network.
(5) Let c be the number of clusters in the underlying network and c≥4.
(6) Let Ci be the cluster identifier where 1≤i ≤c and c≥4.
(7) Let ni be the number of nodes in cluster Ci, 0≤i≤c. If there are at least ni/2 malicious faulty nodes in Ci, then Ci is the malicious faulty cluster. If there are at least ni/2 dormant faulty nodes in Ci, then Ci is the dormant faulty cluster.
(8) Let FCm be the maximum number of malicious faulty clusters allowed.
(9) Let FCd be the maximum number of dormant faulty clusters allowed.
(10) Let FTm be the maximum number of malicious faulty TMs allowed.
(11) Let FTd be the maximum number of dormant faulty TMs allowed.
(12) Let TFC be the total number of allowable faulty clusters, TFC = FCm + FCd.
(13) Let con be the connectivity of the CWSN, where con>2(FCm + FTm)+ FCd + FTd. The purpose of the BA protocol is to make each fault-free node in the network reach common agreement. In order to reach a common agreement, each node should exchange messages with all other nodes. Then, each fault-free node collects enough messages to determine the decision value, i.e., the agreement value, each fault-free node’s agreement value should be identical. The CWSN discussed is a synchronous network, so no delay of nodes or TMs nee...
The Proposed Protocol. This section formally presents the proposed protocol based on the model developed in Section 2. Based on the definition of an AIC problem, every processor has its own initial value to perform the protocol to reach an interactive consistency. Based on the results of Xxx, Xxxx, Xxxx (Xxx et al., 1999), within two rounds of message exchanges, all fault-free processors can reach an agreement for all fault-free processors as if d dormant faulty links and m malicious faulty links exist in a n-processor fully connected network, in which m ≤ (n-d-3)/2. With a similar procedure, each processor performs the third round of message exchange. The proposed protocol can make all fault-free processors reach an agreement on the values they received in the first round. All fault-free processors can reach an agreement on common faults caused in the first round by comparing the common values received before and after the first round of message exchanges. Based on the same idea, the protocol can make all fault-free processors reach an agreement on a common set of faulty components if the components explore their faulty behavior in the second round of message exchanges. Therefore, all faulty components are detected and located by all fault-free processors and an interactive consistency is reached. The FDA problem is solved. Figure 1 illustrates the PFDA protocol, which can make all fault-free processors tolerate/detect/locate a common set of d dormant faulty links and m malicious faulty links which simultaneously exist in a n-processor fully connected network, where m ≤ (n-d-3)/2. PFDA reaches interactive consistency using two rounds of message exchanges and detects/locates a common list of faulty components using two additional rounds of message exchanges. We will demonstrate 1) the proposed method’s efficiency, and 2) the necessary and sufficient conditions for the number of rounds deemed necessary and faulty components allowed by PFDA. Protocol PFDA (For processor i with initial value vi,1≤ i ≤ n)
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 • 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:
1) the message exchange phase and 2) the decision making p...
The Proposed Protocol. The proposed solution has to satisfy the desired properties and avoid the unwanted ones. Thus, the proposed solution is a complete protocol that provides a mechanism to mitigate replaying attack, provides an encryption mechanism, enables anonymous connection, and provides mutual authentication process. The protocol has the following properties:
1. Has markers in each session in the form of session keys (each host has one session key with length up to 280 bits).
2. The session keys are generated by XOR computation of four random numbers (70 hex per random number). The session keys are used by both users to differentiate the messages in different sessions.
3. Has a mechanism to ensure that the random numbers that are received at the receiver side are correct. This mechanism is needed for both hosts to create the same session key. This is achieved by checking the MAC in each host. The MAC value that is sent by User B has the random numbers that is generated by User A and has been received by User B. If User A finds the difference in the MAC value (e.g., someone is altering the random numbers, or there is an error in the network so that User B cannot obtain the random numbers from User A), then User A will terminate the session. PIDA , PuB[XXX, nA1, nA2] PIDB, PuA[IDB, nB1, nB2], MACB To be continued ….
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 Malicious Agreement Protocol (MAP) 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. MAP 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 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...
