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Secure quantum steganography protocol for fog cloud Internet of Things Ahmed A. Abd ElLatif, Bassem AbdElAtty, M. Shamim Hossain, Senior Member Samir Elmougy and Ahmed Ghoniem
Abstract—The security of sensitive information is an urgent need in today’s communication, principally in cloud and Internet of Things (IoT) environments. Therefore, a welldesigned security mechanism should be carefully considered. This paper presents a new framework for secure information in fog cloud IoT. In the framework, the user in one location embeds his/her valuable data via the proposed quantum steganography protocol and uploads the covered data to the fog cloud. The intended receiver in another location accesses the data from the fog cloud and extracts the intended content via the proposed extraction approach. This paper also presents a novel quantum steganography protocol based on hash function and quantum entangled states. To the best of our knowledge, there is no prior quantum steganography protocol that authenticates an embedded secret message. In the suggested protocol, the hash function is utilized to authenticate embedded secret messages. The presented protocol is secure against wellknown attacks such as message, maninthemiddle, and nomessage attacks. In addition, it does not consume additional channels besides the proposed one to send a secret message or verify security. The proposed approach is nominated for use in fog and mobile edge computing. Index Terms—Quantum steganography, Authentication, Internet of Things, Fog computing, Cloud computing.
I. I NTRODUCTION The protection of sensitive data represents an urgent need for secure communications, especially in today’s innovative and modern information and communication technology, such as in fog cloud Internet of Things (IoT) [1], [7], [8]. Fog cloud IoT is a new paradigm and an incredible technology for equipping quickly deployable and scalable information technology solutions at conservative network bandwidth, reduced infrastructure costs, low latency, location awareness, and mobility support. It is a trusted and dependable solution to bring the services and resources of the cloud closer to users and thus assists in leveraging the available services A. A. Abd ElLatif is with Mathematics department, Computer Science Laboratory, Menoufia University, Shebin ElKoom, Egypt. email:
[email protected] B. AbdElAtty is with Mathematics department, Computer Science Laboratory, Menoufia University, Shebin ElKoom, Egypt. email:
[email protected] M. S. Hossain is with the Department of Software engineering, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia.Email:
[email protected] S. Elmougy is with with the Department of Computer Science, Mansoura University, Mansoura, Egypt; email:
[email protected] A. Ghoniem is with the Department of Software engineering, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia and also with Mathematics and Computer Science Department, Menoufia University, Shebin ElKoom 32721, Egypt. email:
[email protected] Manuscript received ; revised .
and resources in the edge networks. However, fog cloud IoT services lead to privacy and security issues and challenges [2]–[6], [9]. Transmitting secret data through unsecured and open channels, as in fog cloud IoT, is an issue that should be addressed. One of the solutions for dealing with the security concerns, especially the handling of secret data covertly in the Internetbased computing paradigm, is via quantum information processing (QIP). QIP has received considerable attention from scientists devoted to development and those interested in introducing novel quantum approaches for processing, storing, and transmitting quantum information. In recent years, some papers have focused on several key topics of QIP, such as quantum coding [10], quantum teleportation [11], [12], quantum cryptography [13], [14], and quantum steganography, among many others. The aim of quantum steganography is to transfer classical or quantum data covertly via open channels. Quantum steganography can classified into four categories according to the embedding methods used: quantum data hiding (QDH) [15], [16], quantum errorcorrecting code (QECC) [17], [18], quantum image steganography [19], [20], and quantum steganography protocols [21]–[25]. This paper focuses on quantum steganography protocols. In what follows, we shed light on the recently proposed quantum steganography protocols. In [17], GeaBanacloche presented a quantum protocol to hide a secret message as an error. In [18], Shaw et al. presented a quantum protocol that uses noisy quantum channels but consumes an extra Bell state for each transmitted fourbit secret message. On the basis of the BB84 protocol [13], Martin [21] presented a quantum protocol for steganography communications. In [22], Liao et al. presented a multiparty quantum steganography communication based on quantum secret sharing. In [23], Qu et al. proposed a protocol to send fourbit classical secret information with fewer keys required in each round than that of the embedding qubits of [18]. Qu et al. [24] presented a quantum protocol based on χtype entangled swapping to send eightbit classical secret information. Recently, Xu et al. [25] presented a quantum scheme based on Bell states to send fourbit secret information without any additional auxiliary quantum states. The security of quantum communication is guaranteed by the quantum nocloning theorem and the quantum uncertainty principle to prevent eavesdroppers from unconditional attacks. The techniques of attack in quantum communication are based only on the principles of quantum mechanics. Authentication is considered necessary as a defense against active attacks. Without the authentication step legitimate users can be easily
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eavesdropped on and the secret message revealed. In [26], Xin et al. presented a quantum authentication protocol with hash function, which uses four unitary transformations to directly encode classical bits (message + hash value) into a Bell state. Suppose Alice needs to send a message to Bob. When Bob receives the message, he does not know if it comes from Alice or Eve. Consequently, Bob wants a technique to authenticate the security of the transmitted message. Quantum authentication is used to verify the security of the transmitted message [27]. To the best of our knowledge, most quantum authentication protocols are quantum cryptography [26]–[35], quantum teleportation [36], and quantum network [37] protocols, and no quantum hiding protocol exists to authenticate embedded secret data. Therefore, it is necessary to study quantum steganography protocols based on authentication techniques to achieve high security for the embedded secret messages. Therefore, in this paper, a novel quantum steganography framework for secure messages in fog cloud IoT is proposed. The proposed approach is based on quantum entangled states, exclusive OR operation (XOR) , gray code, and hash function. Table I presents a simple comparison between some recent protocols and the presented one. In the proposed protocol, Alice computes the hash value of the secret message and then obtains the gray code for executing the XOR operation to the labels of initial states and the bit sequence as labels of final states. Afterward, Alice transforms the initial states into final states by applying two unitary operations on the two first particles of the initial states. Bob can get the bit sequence by executing the XOR operation to the decode operation of the gray code for the final states and the initial states. Bob can extract the encoded hash code and the secret message from the bit sequence and then get the hash value for the recovered message. By checking the hash value of the encoded hash code and the recovered message, Bob can ensure the security of the embedded secret information. Thus, any measurement on the transmitted qubits will be recovered by Bob. The remainder of this work is organized as follows. Section II discusses the framework of secure quantum steganography for fog cloud IoT. Section III offers preliminary work for the proposed approach. Section IV presents the proposed quantum steganography protocol. Section V is devoted to the performance analysis, including capacity, imperceptibility, and security analysis. Finally, Section VI provides the concluding remarks. II. F RAMEWORK OF SECURE QUANTUM STEGANOGRAPHY FOR FOG CLOUD I OT
2
mobile edge computing
fog
fog mobile edge computing
 C> Cover message
 C> Cover message
` `
Alice
Secret information  S>
Recovered secret information  S>
Bob
Fig. 1. Proposed framework for secure quantum steganography in fog cloud IoT
III. P RELIMINARY WORK A. Gray code Gray code is a signal coding method commonly used in digital conversions. It is defined as follows: gi = bi ⊕ bi+1 ,
(1)
where i = 0, 1, ..., q − 1 , and b = (bq bq−1 ...b1 b0 ) gq = bq
(2)
A simple example of gray code is shown in Table II. B. Unitary transformations and Bell states John Bell proved that, for a twoqubit quantum system, there are only four possible entangled states, which are called Bell states. They are as follows: ξ + i = √12 (00i + 11i) ψ + i = √12 (01i + 10i) ξ − i = √12 (00i − 11i) ψ − i = √12 (01i − 10i)
(3)
When a unitary transformation is applied on the first particle of the Bell state, the particle transforms into another state. The four unitary transformations, U0 , U1 , U2 , and U3 , can be written as follows:
Figure 1 shows the framework of the proposed secure quantum steganography in the scenario of fog and mobile edge computing. The user in one location embeds important and sensitive information via the proposed quantum steganography scheme and sends the covered secret information to the fog cloud. The staff in another location accesses the data from the fog cloud and recovers the content via the proposed extraction approach. The proposed quantum steganography system ensures the authentication and security for fog cloud IoT users.
1 0 = σI 0 1 0 1 U1 = 0ih1 + 1ih0 = = σX 1 0 1 0 U2 = 0ih0 − 1ih1 = = σZ 0 −1 0 1 U3 = 0ih1 − 1ih0 = = σZ σX = iσY −1 0 U0 = 0ih0 + 1ih1 =
(4)
Assume that Bob and Alice share a Bell state. Alice can transform the state into one of the four states as in Table III.
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TABLE I C OMPARISON BETWEEN THE PROPOSED PROTOCOL AND SOME RECENTLY PROPOSED PROTOCOLS . Items Authentication Steganography
Proposed protocol Hash Function Based on hidden rule
Scrambling
Using XOR operation and gray code Sequence of two pairs of entangled particles
Entangled particles
A1
B1
A2
B2
Xu et al. [25] Quantum covert channel based on hidden rule 
Xin et al. [26] Hash Function 
Using any quantum secure direct communication (QSDC)
Sequence of one pair of entangled particles

A
Hidden rule Unitary transformations
Based on two Bell states Transformation of the initial Bell states into final states
Based on Bell states Transformation of the initial states into final states
Security regardless of quantum properties
Authentication and initial Bell states
Initial Bell states
In practice, Alice applies into her particle one of the unitary transformations to get one of the four Bell states. Suppose Alice has two particles A1 and A2 that are maximally entangled with two particles B1 and B2 , respectively, in Bob’s side. There are 16 states of tensor products of any two Bell states as in S:
B
Used directly to encode the classical bits (message + its hash value) Authentication
Shared secret keys Bob
Alice Cover message secret message
 C〉
 C〉 Embedding procedure
 C'〉
Extracting procedure
Quantum channel
S or  S〉
S or  S〉
Cover message secret data
Fig. 2. Framework of a general quantum steganography protocol [38].
S = {ξ + i ⊗ ξ + i, ξ − i ⊗ ξ − i, ψ + i ⊗ ψ + i, ψ − i ⊗ ψ − i, ξ + i ⊗ ξ − i, ξ − i ⊗ ξ + i, ψ + i ⊗ ψ − i, ψ − i ⊗ ψ + i, ξ + i ⊗ ψ + i, ξ − i ⊗ ψ − i, ψ + i ⊗ ξ + i, ψ − i ⊗ ξ − i, ξ + i ⊗ ψ − i, ξ − i ⊗ ψ + i, ψ + i ⊗ ξ − i, ψ − i ⊗ ξ + i}
Set S consists of 16 elements, labeled as 0000, 0001, . . . , 1111, respectively. When applying two unitary transformations on the first particle of any initial state, the result must be an element in set S as a final state.
A. Initial preparation and sharing keys First, Alice and Bob negotiate the initial state Si0 , iterative key K, and id for the used hash function hid by utilizing any secure quantum channel, such as quantum secure direct communication (QSDC) schemes [39]–[42]. 1) K ∈ {−15, −14, ..., 14, 15} is used to iterate the initial state in the process of sending the message according to the following equation.: j Sij+1 = Si⊕k 0
IV. P ROPOSED QUANTUM STEGANOGRAPHY PROTOCOL
Any quantum steganography protocol consists of three parts [38], namely, sharing key, embedding procedure, and extracting procedure, as seen in Figure 2.
TABLE II S IMPLE EXAMPLE OF A GRAY Rank 0 1 2 3 4 5 6 7
Binary representation 0000 0001 0010 0011 0100 0101 0110 0111
(5)
where ⊕ means the modulo16 addition operation, j = 0, 1, 2,. . . , N (N is the number of agreeing positions), and i is the label of initial state i = 0, 1, 2,. . . ,15. For example, if the first initial state is S50 and K is 7, then 0 1 the next initial state is S5⊕7 = S12 and the next one is 1 = S32 and so on. S12⊕7 2) The id is a type of hash function, namely, hid . Table IV [43] shows the list of hash functions used in the proposed protocol. After negotiating the initial states and hash function, Alice chooses the positions of Bell states to embed the secret
CODE .
Gray number 0000 0001 0011 0010 0110 0111 0101 0100
TABLE III B ELL STATES AND THE CORRESPONDING UNITARY TRANSFORMATIONS ξ + i ξ − i ψ + i ψ − i
U0 ξ + i ξ − i ψ + i ψ − i
U1 ψ + i ψ − i ξ + i ξ − i
U2 ξ − i ξ + i ψ − i ψ + i
U3 ψ − i ψ + i ξ − i ξ + i
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message, as shown in Figure 3 and illustrated in the following steps: 1) Alice owns a sequence of entangled states of Ψ+ iAB Bell state, and then sends each B particle to Bob through a quantum channel, while keeping A particle for herself. 2) After Bob gets the particles of sequence B, Alice can randomly apply unitary transformation U2 to her particles to transfer the Bell state Ψ+ iAB to Bell state Ψ− iAB . Next, she can apply three other unitary transformations U0 , U1 ,and U3 to the remainder particles and then transmit the sequence to Bob. 3) Using measurements of the Bell states, Bob simply gets the positions of Bell state Ψ− i that will be used to embed the secret message, while other positions, (ξ + i, ξ − i, and Ψ+ i), are used for the cover message. Alice
Bob
Alice
Bob
Alice
Bob
Ψۄ
Ψۄ
Alice and Bob share a sequence of Alice randomly applies U2 on her particles to entangled particles in state Ψ + ۄtransfer the Bell state Ψ+ to Ψ and apply three other unitary transformations on the remainder of her particles prior to sending the sequence to Bob.
Bob simply gets the positions of the Bell states Ψۄ
Fig. 3. Selected positions of the embedded secret message
B. Proposed quantum steganography protocol 1) Embedding Procedure: Quantum steganography is used to embed or hide a classical/quantum information under the cover of a normal quantum channel. In this section, we will explain how to embed a classical message under the cover of a quantum channel. In the proposed protocol, the embedding technique is based on the hidden rule between the Bell states and the unitary transformations. To embed the secret message, we use four sequences of particles of maximally entangled states labeled as A1 , A2 , B1 , and B2 . The sequences of particles A1 and A2 belong to Alice, and the other two sequences belong to Bob. The particles in sequences A1 and A2 are in the maximally entangled state with the particles in sequences B1 and B2 , respectively. The embedding and extracting procedures of the suggested protocol are given in Figure 4. TABLE IV S IMPLE EXAMPLES OF HASH FUNCTIONS [43]. Id 1 2 3 4 5 6 7 8 9
Type SDBM Hash Function JS Hash Function PJW Hash Function RS Hash Function ELF Hash Function BKDR Hash Function DJB Hash Function DEK Hash Function AP Hash Function
The embedding procedures are described as follows: 1) Alice and Bob share four sequences of particles, which are maximally entangled states labeled as A1 , A2 , B1 , and B2 . The sequences A1 and A2 belong to Alice, and the other two sequences belong to Bob. The Bell states of two entangled sequences in the agreeing positions are in the specific initial states according to the first initial state Si0 and K. 2) Alice computes the hash value for the secret message hid (secret message) = bn+1 bn+2 . . . bn+m , and then converts the secret message to bit string b = b1 b2 . . . bi . . . bn , where bi is a onebit message bi ∈ {0, 1} for i = 1, 2, . . . , n + m. 3) Alice applies the XOR operation to the bit sequence SB = b1 b2 . . . bi . . . bn bn+1 bn+2 . . . bn+m and the labels of initial states (Si0 , Si1 . . . Sij , Sij+1 . . . SiN −1 , SiN ) and gets the gray code for the result as labels of final states (Sf0 , Sf1 . . . Sfj , Sfj+1 . . . SfN −1 , SfN ). In other words, labels of Sf = gray code (XOR (SB, labels of Si )). Note that i and f are in {0000, 0001, . . . , 1111}. 4) Alice gets the gray code for executing the XOR operation to the bit sequence SB = b1 b2 . . . bi . . . bn bn+1 bn+2 . . . bn+m and the labels of initial states (Si0 , Si1 . . . Sij , Sij+1 . . . SiN −1 , SiN ) as labels of final states (Sf0 , Sf1 . . . Sfj , Sfj+1 . . . SfN −1 , SfN ). In other words, labels of Sf = gray code (XOR (SB, labels of Si )). Note that i and f are in {0000, 0001, . . . , 1111}. 5) Alice applies two unitary transformations to each of her own particles in the agreeing positions to transfer the initial states Si0 , Si1 , ..., Sij , Sij+1 , ..., SiN −1 , SiN into final states Sf0 , Sf1 , ..., Sfj , Sfj+1 , ..., SfN −1 , SfN according to Table III. She also applies two unitary transformations to each of her own remainder particles according to the cover message and then sends the results of the particles 0 0 (sequences A1 , A2 ) to Bob. 2) Extracting Procedure: The extracting procedures are described as follows: 1) Using quantum measurement, Bob simply gets the labels of the final states in the agreeing positions of secret message Sf0 , Sf1 , ..., Sfj , Sfj+1 , ...,SfN −1 , SfN , as well as the unitary transformations Alice applied on her particles of remainder positions, to obtain the cover message. 2) Bob executes the XOR operation to the result of the decode operation of the gray code for the labels of final states Sf0 , Sf1 , ..., Sfj , Sfj+1 , ..., SfN −1 , SfN and the labels of initial states Si0 , Si1 , ..., Sij , Sij+1 , ..., SiN −1 , SiN ,which comes from the negotiated first initial state 0 0 0 Si0 and key K to get the bit sequence SB = b1 b2 . . . 0 0 0 0 bi . . . bn bn+1 . . . bn+m . 0 0 3) Bob simply gets the hash code bn+1 . . . bn+m from the 0 bit sequence SB . 0 0 0 4) Bob converts the bit string b = b1 . . . bn to a message string and computes the hash value for the recovered message.
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Sender
Receiver
labels of initial states
Alice
Alice
Secret message
Bob
Secret message
labels of initial states
Hash value
Execute hash function
Recovered message
labels of initial states
QM
Execute hash function
No
attacked
attacked Hash value
Bit string
Check
10100001
Yes
0101 0001 0100 1101
Sequence of bits
Check
Yes
secure
Hash value= hash code
secure
Hash value= hash code
Hash code
Bit string 0101 0001 0100 1101
Hash code 10100001
0101 0001 0100 1101 1010 0001 (bit string + hash value)
QM
010101010101 010101010101
Bit string
Execute hash function No
labels of initial states
Bob Execute hash function
Hash value 10100001
010101010101 010101010101
Bit string (bit string + hash code)
0101 0001 0100 1101 1010 0001
Sequence of bits
⊕
(bit string + hash code)
⊕ 0000 0100 0001 1000 1111 0100
XOR
0000 0100 0001 1000 1111 0100
Gray code
Decode Gray code
XOR Gray code
labels of final states
0000 0110 0001 0100 1000 1110
0000 0110 0001 0100 1000 1110
As labels of final states
Decode Gray code
As labels of final states in the agreeing positions
For each 4bit determine two unitary transformations
labels of final states For each 4bit determine two unitary transformations according to Table 3 Apply second unitary in the agreeing positions
Final states in the agreeing positions
Apply first unitary in the agreeing positions
entanglement
Apply second unitary in the agreeing positions
A2
Sending the sequence A1 to Bob A1
Final states in the agreeing positions
S0000 S0110 S0001 S0100 S1000 S1110
U 2U 0 , U 3U 3 , U 0U 2 , U 2U 2 , U 2U1 , U 3U 2 Apply first unitary in the agreeing positions Sending the sequence A1 to Bob A1
entanglement entanglement
B1 B2
Sending the sequence A2 to Bob
B1
Quantum channel A2
entanglement
B2
Sending the sequence A2 to Bob
Quantum channel
Fig. 5. Illustrated example of the proposed protocol Fig. 4. Procedures of the proposed protocol
5) By checking the hash code obtained from the bit sequence and the hash value obtained from the recovered message, Bob can validate the embedded secret message. Any measurement or forgery on the transferred qubits will be detected by Bob. Thus, Bob will either accept the secret information or reject it. C. Illustrated example for the proposed protocol Let us now illustrate a simple example for the proposed protocol (see Figure 5 ) and explain the three parts of the quantum steganography system, namely, sharing keys, embedding procedure, and extracting procedure to send the secret message. The secret message, for example, says ”QM.” Sharing keys: Suppose that the negotiated initial state is S0101 , K is 0, and the id hashing is 1 (the SDBM hash function returns integers in the range of 0255 and converts the value to binary form eightbit). According to the value of K and the initial state S0101 , Alice can get the initial states S0101 S0101 S0101 S0101 S0101 S0101 according to Eq. (5). Then, Bob and Alice can share the positions of embedding the secret message. Now, Alice needs to transmit the string ”QM” to Bob. Embedding Procedure: The hash value of the secret message ”QM” is 1010 0001 and the bit string of the secret message and hash value (bit string + hash value) is 0101 0001 0100 1101 1010 0001. The result of executing the XOR operation for the bit sequence and the labels of initial states S0101 S0101 S0101 S0101 S0101 S0101 0101 0101 0101 0101 0101 0101 is 0000 0100 0001 1000 1111 0100, and the result of the gray code is 0000 0110 0001 0100 1000 1110 as
labels of final states [S0000 S0110 S0001 S0100 S1000 S1110 ]. According to Table III, Alice performs the following unitary transformations [U2 U0 , U3 U3 , U0 U2 , U2 U2 , U2 U1 , U3 U2 ] into the sequences of her pair particles in the agreeing positions to get the final states [S0000 S0110 S0001 S0100 S1000 S1110 ], respectively, and sends the sequences of particles to Bob. Extracting Procedure: Utilizing quantum measurements of particles in the agreeing positions, Bob simply obtains the final states [S0000 S0110 S0001 S0100 S1000 S1110 ] and the cover message from the remaining positions. The labels of the final states are 0000 0110 0001 0100 1000 1110, respectively. The decode operation of gray code for the labels of final states is 0000 0100 0001 1000 1111 0100. By executing the XOR operation to the result of the decode operation of gray code and the labels of initial states S0101 S0101 S0101 S0101 S0101 S0101 as 0101 0101 0101 0101 0101 0101, Bob obtains the bit sequence 0101 0001 0100 1101 1010 0001. The hash code is 10100001 from the bit sequence, and the recovered message for 0101 0001 0100 1101 is ”QM.” By checking the hash code obtained from the bit sequence 10100001 and the hash value for the recovered message 10100001, Bob accepts the recovered message. V. P ERFORMANCE ANALYSES A. Capacity The embedding capacity for quantum steganography protocols is the number of embedded qubits (bits) in a single qubit. The maximum embedding capacity of the quantum steganography protocols in [15]–[17], [21], [22] is one bit (qubit) by transferring one qubit. In [23], the actual capacity is two bits by
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consuming one Bell state and transferring one qubit. In [24], [25], the actual capacity is four bit by transferring two qubits and consuming two Bell states. The capacity for the proposed protocol is four bits per two Bell states. If the number of shared particles between the two participants is large, then the number of embedded bits increases depending on the increase in the number of agreeing positions. The embedding efficiency of the quantum steganography protocol is given by the number of embedded secret bits over the number of transferred qubits. From this point of view, the embedding efficiency can be increased by increasing the selected embedding positions. By utilizing the hash function in the authentication process, Bob will be able to detect any measurement or forgery on the transferred particles. Thus, Alice can select a large number of embedding positions. Furthermore, we can conclude that the proposed protocol has good capacity compared with other competing quantum steganography protocols. B. Imperceptibility analysis Imperceptibility analysis is conducted to ensure the embedded secret message is hardly detected and prevent damage from eavesdroppers. Quantum steganography protocols have imperceptibility advantages derived from the quantum nocloning theorem and the quantum uncertainty principle compared with traditional steganography protocols. The imperceptibility of the proposed protocol lies completely on the initial states and the selected positions of the embedded secret message. Let Eve be an eavesdropper who fails to get the final states only by measuring the transferred qubits in the two sequences A1 and A2 because all particles are in a maximum entangled state and the four qubits cannot be accessed by Eve simultaneously. No leakage data occur in the final states, so the imperceptibility of the suggested protocol can be ensured. C. Security analysis Security analysis is a critical assessment standard for any quantum protocol. The main aim of security analysis is to prevent the secret information from being eavesdropped on or being attacked. The security of the suggested quantum steganography protocol is not only ensured by the quantum nocloning theorem and the quantum uncertainty principle to prevent the unconditional attack of eavesdroppers, but also in the initial states, gray code, the used hash function, and the selected positions of particles carrying the secret message. Herein, we explain the security analysis in detail. 1) Maninthemiddle attack: Eve plays the role of Alice (Bob) to communicate with Bob (Alice) and extract the embedded information. Eve cannot know the initial states Si , selected positions, or selected hash function hid to send a fake sequence of entangled particles prepared by herself to send to Bob. First, Alice and Bob negotiate the first initial state Si0 , iterative key K, and id hid utilizing any secure QSDC scheme, and then Alice chooses the positions of the Bell states to carry the secret message. From this point of view, the initial states are prepared according to Si0 and K, which are negotiated by any secure QSDC scheme. This section shows how the
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proposed protocol defends versus a maninthemiddle attack. Hence, we discuss the following possible cases. Case 1: has no knowledge of the selected positions and the keys transmitted by the QSDC scheme, and so she cannot get any thing about the embedded secret data. Thus, Eve fails to attack the proposed protocol. Case 2: Eve succeeds in guessing the selected positions of Bell states that carry the secret message. Eve does not get any useful information about the initial states of the selected positions. It turns out that one initial state has 16 possibilities. Owing to the key K, the total initial states have 2N possibilities, where N is the total number of embedded bits. Then, Eve can predict the initial state with probability p = 21N . To prove this, consider the following examples: 1) Assume that Alice needs to embeds the string ”Q” that has a binary equivalent of 10100001. Two initial states are required to transmit this secret message. Given the change of initial states, Eve can predict one initial state 1 . Therefore, the probability with probability p = 214 = 16 1 1 1 of predicting the initial states is p = 16 × 16 = 256 = 1 . 28 2) Assume that Alice needs to embeds the string ”QM” that has a binary equivalent of 01010001 01001101. Four initial states are required to transmit this secret message. Thus, Eve can predict the initial states with probability 1 1 1 1 1 p = 16 × 16 × 16 × 16 = 654336 = 2116 . Therefore, it is very difficult for Eve to guess the initial states for the positions of the Bell states carrying the secret message. Eve has no knowledge about about the embedded secret message and the attack fails [she cannot communicate with Alice (Bob) as Bob (Alice)]. In addition, Bob will reveal the presence of Eve and abort the communication by using the hash function. Hence, the suggested scheme is secure against a maninthemiddle attack. 2) Message attack: Eve can only access the qubit transferred from Alice to Bob for each Bell state. Eve can get nothing about the secret information because she does not have the initial states and the selected positions of states carrying the secret message. If Eve performs any unitary transformation to any particle in the selected positions, Bob deduces the attack when he executes the hash function. Hence, the proposed scheme is secure against a message attack. 3) Measurement attack: Eve aims to obtain any thing about the secret information from the two sequences A1 and A2 that Alice sends to Bob. However, Eve cannot deduce the final states by measuring the transferred qubits because all qubits are in a maximum entangled state and Eve is unable to access the four qubits jointly. Thus, Eve has no information about the secret message. Any measurement on any particle in the two sequences A1 and A2 performed by Eve leads to corresponding changes of particles in the two sequences B1 and B2 because of the entanglement property of Bell states. This condition leads to changes in the final states and in the 0 0 0 0 0 0 extracted bit sequence SB = b1 b2 . . . bn bn+1 . . . bn+m (secret message + hash code). By checking the hash code 0 0 obtained from the bit sequence bn+1 . . . bn+m and the obtained hash value from the recovered message, Bob can detect any measurement on the transmitted particles. Eve likewise has no
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information about the initial states and the selected positions of qubits carrying the secret message. Therefore, the measurement attack has no effect on this quantum steganography protocol. 4) Nomessage attack: Eve generates a sequence of particles and transmits it to Bob. Her main goal is to make Bob believe that the classical bits embedded in this sequence comes from Alice. Eve does not have the initial states, hash function, or the selected positions of states carrying the secret message in order to send two fake sequences of particles. When Bob receives these particles, he cannot determine if it comes from Alice or an eavesdropper. After receiving all particles of the two sequences A1 and A2 , Bob extracts the message from a bit string and its embedding hash value from the labels of the final states in the selected positions. In addition, he deduces the attack by checking the hash code obtained from the bit sequence with the hash value obtained from the recovered message. Thus, the suggested protocol is secure against a nomessage attack. VI. C ONCLUSION This paper proposes a new framework for secure quantum steganography in fog cloud IoT. A new secure quantum steganography protocol based on quantum entangled states, XOR operation, gray code, and hash function is also proposed. The suggested protocol does not use any extra quantum communications and/or quantum states besides the proposed protocol to transmit the secret message or verify it. The hash function is used to confirm the security of the proposed protocol. The performance and security analyses demonstrate that the suggested quantum steganography scheme is secure against most wellknown attacks. ACKNOWLEDGMENT The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through Research Group Project RGP229. Corresponding author: M.Shamim Hossain (
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