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Cloudedge data encryption in the internet of vehicles using Zeckendorf representation
Journal of Cloud Computing volume 12, Article number: 39 (2023)
Abstract
Cloudedge data security is a key issue in the internet of vehicles (IoV), as the potential for data breaches increases as more vehicles are connected. As vehicles become smarter and more connected, the risk of unauthorized access to the data generated by the vehicles also increases. Data encryption is a highly effective security measure that is widely used to protect the IoV from malicious actors. By encrypting data, it becomes virtually impossible for unauthorized individuals to access the information. This ensures that only the intended parties can access the data, allowing for secure communication between cloud and edge. Data encryption is a costeffective and reliable security measure that is essential for any organization that relies on the IoV. The IoV is characterized by the large volume of data that is exchanged between devices in cloud and edge. This necessitates the use of a strong encryption method, such as stream ciphering, which is particularly wellsuited to this type of environment. Stream ciphering provides the highest levels of security, making it the ideal choice for securing data transmission in the IoV. Many stream ciphering algorithms use bitwise exclusive or (XOR) to encrypt the data stream, so the core is the generation of a pseudorandom key stream. This paper proves that the probability of the number 1 appearing in the middle part of the Zeckendorf representation is constant, which can be used to generate pseudorandom key stream sequences. The pseudorandom sequence generated by the linear feedback shift register (LSFR) is periodic, and the key sequence will be duplicated. The logistic chaos (LC) sequence is too sensitive to the disturbance of initial value, and its stability is poor. In this paper, our proposed ZPKG (key generator based on Zeckendorf presentation) algorithm solves these two main problems in stream ciphering. The generated key sequence not only has strong randomness, but also is infinitely long, and it is robust to the minor disturbance of the initial value.
Graphical Abstract
Introduction
Internet of Vehicles (IoV) is an emerging technology that enables the connection of vehicles to the Internet, allowing them to communicate with other connected devices. This technology enables vehicles to be monitored and controlled remotely, allowing for advanced safety features such as automatic braking and lane departure warnings. It also allows for improved fuel efficiency and emissions management and the integration of other digital services such as navigation, entertainment, and more. IoV is a rapidly developing technology with the potential to revolutionize the automotive industry, making vehicles safer and more efficient. Big data analytics can be used to gain valuable insights from the data collected, allowing for better decisionmaking and predictive capabilities. With the everincreasing sophistication of technology, the sensors can detect a multitude of variables, from the vehicle’s speed and direction to the engine’s temperature and fuel level. Figure 1 gives examples of the data transmitted in the IoV, including advisory speed, flags, vehicle speed, driver input, raw position, lane level position, and so on. The data are often transmitted to cloud servers for Map Matching, Digital Twin Visualization, Human Behavior Modeling, Motion Planning, and Control, creating insights into the vehicle’s performance and making recommendations for better driving and maintenance. By combining the power of IoV and Big Data, businesses can make better decisions and create innovative solutions which can improve the lives of individuals and communities.
A typical model of IoV is comprised of three parties:

Cloud: The Cloud is considered reliable and trustworthy. Periodically, the RSU sends data packets to the Cloud. The data packets contain critical information such as car conditions, realtime traffic conditions, etc. The Cloud records the properties of each car and broadcast traffic statistics.

RSUs: RSUs (Road Side Units) are roadside units in the ETC system that are supported by Dedicated Short Range Communication (DSRC) technology. They interact with OBUs. RSUs are utilized for vehicle identification as well as computerized point deduction. RSUs are often put on the side of the road and unattended express lanes, which are responsible for the management of highways and vehicle yards.

OBUs: OBUs (Short for On Board Units) is a microwave device that communicates with RSUs through Dedicated Short Range Communication (DSRC) technology. The OBUs on the vehicle and the RSURoad Side Units on the side of the road interact with each other through microwaves in the ETC system. When the vehicle speeds through the RSU, the OBU, and the RSU interact with microwaves, much like our contactless card, but from a distance of a dozen meters and at a higher frequency of 5.8GHz. When it passes, it determines the authenticity, receives the model, computes the rate, and subtracts the toll.
Figure 2 depicts cloudedge communication scenarios, where OBUs and RSUs act as edge devices and they communicate with the cloud.
Cloudedge data security is a critical issue in IoV, as this technology introduces a range of new cybersecurity risks. Automated vehicles are connected to the cloud for critical services such as navigation, safety and security, and fleet management. However, this also means that the data and communication generated by these vehicles are vulnerable to cyberattacks. The data could be intercepted and manipulated, leading to potential safety issues, or the vehicle itself could be taken over by malicious actors. Data encryption is one of the most powerful tools available to address these security concerns, which offers an effective way to protect sensitive information from unauthorized access. By scrambling data and making it unreadable, encryption provides an extra layer of security to help ensure the privacy and integrity of data. The IoV has the feature of big data.
Before the largescale application of Quantum Cryptography, stream ciphering was the most suitable encryption method for “big data” [1]. For stream ciphers, pseudorandom sequence generation (PRNG) is very important. For normal applications, where good statistical properties and speed are important, consider O ‘Neill’s PCG collection, Vigna’s xoroshiro family, such as xoroshiro128 + (not the Japanese name btw, but “X or, rotate, shift, rotate “), and D. E. Shaw’s Random123 suite (including Philox and the wellnamed ARS, which is a simplified form of encrypting infinite zero sequences using AESCTR), though I’m not sure how much checking has been done with Random123 PRNG. To encrypt secure PRNG(CSPRNG) For encryption applications where unpredictability is important, consider using cryptographically secure PRNGS, for example, Bernstein’s ChaCha20, RF C7539. The alternative is Wu’s HC256 and Jenkins’ ISAAC64. The downside of these algorithms is that they’re too complicated. Linear Shift Register (LSFR) and Logistic chaos (LC) are the two popular PRNGs for stream ciphering. Logistic Chaos is a PRNG algorithm that utilizes chaotic dynamical systems to generate unpredictable numbers. LSFR is a PRNG algorithm that uses linear feedback to generate a sequence of pseudorandom numbers. Both algorithms have been used for various applications, including cryptographic applications, simulation, and game design. Both algorithms are capable of generating statistically random numbers, making them useful for applications that require a certain degree of randomness. However, the pseudorandom sequence generated by the linear feedback shift register (LSFR) is periodic, and the key sequence will be repeated. LC method, which is used most currently, however, has a synchronization problem. That is, it is too sensitive to the disturbance of initial parameters and has poor stability.
Fibonacci numbers have been known to mathematics for some 800 years and it seems rather surprising that this property of theirs did not receive attention until relatively recently. Indeed, nothing appeared in print concerning the Zeckendorf representation until the middle of the 20th century, with the publication of a paper by C.G. Lekkerkerker [2]. Zeckendorf did not publish his account until 1972 (see [3]) although he had proof of his theorem by 1939. Every positive integer can also be uniquely represented as a sum of the different powers of two, and it is natural to compare Zeckendorf representations with binary representations. This is pursued in [4], where there is a discussion of algorithms that, given two positive integers a and b in the Zeckendorf form, produce the Zeckendorf forms for a + b. Zeckendorf’s Theorem points out that natural numbers are the sum of one or more different Fibonacci numbers [5]. In other words, a positive integer n can be expressed as: \(N={F}_{k_1}+{F}_{k_2}+{F}_L+{F}_{k_r}\). For example: 17 = F_{1} + F_{4} + F_{7}, 20 = F_{3} + F_{5} + F_{7} . If all Fibonacci numbers in the above decomposition are mapped to a bit string composed of 0,1 according to their positions, that is, let the positions k_{1}, k_{2}, …, k_{r} of the sequence be 1, and the rest positions are 0, a new coding system represented by 0,1 can be obtained. This coding method, also known as ZeckendorfLekkerkerker coding, is the Ostrowski coding system [6, 7]. In recent years, The research in this field is focused on the discussion of mathematical properties. Among other results, Bugeaud [8] establishes, in a quantitative form, that any sufficiently large integer cannot simultaneously be divisible only by very small primes and have very few digits in its Zeckendorf representation. Idziaszek [9] investigates a relationship between the numeral system using Zeckendorf representations and the golden ratio numeral system. Alecci et al. [10] determine the Zeckendorf representation of the multiplicative inverse of a modulo F_{n}. Vukusic et al. [11] find an explicit upper bound for y^{a}, which only depends on the Hamming weight of y concerning the Zeckendorf representation. Other influential work includes [12]. The Zeckendorf representation has many advantages, such as nonuniqueness of coding, strong regularity of probability structure, periodicity of modules, and antiinterference, which may provide a new idea for the breakthrough of data encryption in IoV.
In what follows, based on the probability structure properties of the Zeckendorf representation, we propose a pseudorandom keystream generator (PKG), which can be used to encrypt cloudedge IoV data. The proposed PKG algorithm addresses the periodicity problem of linear feedback shift registers (LFSRs) as well as the synchronization problem of LC.
The following content is organized as follows: Related work section reviews the literature, The proposed algorithm section proposes our algorithm, Security analysis section carries out security analysis theoretically, Experiments and discussion section conducts experiments and discusses the results, and Conclusion section concludes.
Related work
Modern cryptography comprises symmetric encryption, asymmetric encryption, and hash functions, with symmetric encryption further split into block ciphers and stream ciphers. Block ciphers accept fixedsize plaintext as input, such as 64bit, 128bit, 256bit, and so on. Permutation and diffusion are also used. However, when large volumes of data with high realtime needs are sent, block encryption algorithms such as DES and AES fail to meet the requirements due to their strong correlation and high redundancy [13].
Stream ciphers are lightweight encryption algorithms that are ideal for big data. Stream ciphers are considerably faster to perform than block ciphers. Stream ciphers are classified into two types: those based on bytes and those based on pseudorandom number sequences, with the latter being more extensively employed in practice. RC4 is a bytebased stream ciphering method that uses the PRGA algorithm to create pseudorandom numbers and then uses the KSA encryption technique to accomplish particular encryption operations. RC4 is widely used in SSL/TLS protocol and WEP protocol as an IEEE802.11 WLAN standard [14]. The key of a stream ciphering technique based on a pseudorandom number sequence changes at random and every bit of data is encrypted with every bit of key (typically XOR /XOR operation), making cracking theoretically impossible (onetime encryption principle). Because the XOR technique is simple to implement in hardware, it allows for realtime encryption of highspeed large data. The statistical inspection institution has set stringent random criteria for the pseudorandom number sequence. Berger et al. [15] developed a new pseudorandom number generator that is resistant to common assaults and can increase internal diffusion properties greatly. In recent years, there are many pieces of research on big data encryption. For example, Hosseini [16] examines the fingerprint system, classifies different aspects of it, such as techniques for extracting features and matching procedures, and identifies various vulnerabilities. He then proposes three mitigation strategies, including software (big data and encryption/ decryption) and secure hardware techniques. Zhou et al. [17] present a chaotic secure communication strategy based on the synchronization of multiple complex dynamical networks with double layers. Djamaluddin et al. [18]’s goal is to verify a realtime data transport and analytics environment in terms of encryption and access control. Chen et al. [19] present a massive data encryption technique based on a deredundancy approach.
This study is not the first to propose research on stream ciphers utilizing Zeckendorf representation. Carry register feedback (FCSR) is critical in the hardware design of a stream cipher. Lin et al. [20] refined the FCRS circuit and developed a homogeneous Zeckendorf representationbased quark hash function that employs FCRS to produce random integers [21]. However, this type of study focuses on the hardware level rather than the software level production of stream cipher key streams; also, these studies have not thoroughly examined the properties of the Zeckendorf representation. The canonical Zeckendorf representation is only used in the random number generator to raise the disorder degree of the sequence; it has not been investigated for the construction of randomness.
The proposed algorithm
Requirements for stream ciphers of big data
RC4 stream cipher technology is a wordbased stream ciphering method with variable key length and a large number of permutation operations, making it more appropriate for software implementation. However, one out of every 256 keys in RC4 is a weak key susceptible to state table analysis attacks [22]. Furthermore, cryptanalysis can uncover a significant correlation between the key’s bytes, and if the same key sequence is repeated, the hacker can break the ciphertext. If the first three words of the key are discovered, iteration may be used to retrieve each word of the key used in RC4 [23]. Unlike RC4, which encrypts by byte, the LC and LFSR use a pseudorandom key stream to encrypt. Linear feedback shift registers (LFSRs) are excellent for hardware implementation due to their ease of algebraic analysis and high unpredictability (they can be successfully built by simple logic gates and registers). The primary drawback of LFSR is that it is periodic, which means that it can only be used to encrypt particular length sequences. Second, because its sequence is not a simple monotone sequence, it must be initiated [24]. The most often used stream ciphering technology is chaotic encryption. The difficulty with encryption is that it is excessively sensitive to the initial values of parameters due to its nonlinearity and synchronization [25]. To address the drawbacks of the LC and LFSR, a new pseudorandom key stream generation method with the following features must be investigated: First, the key stream sequence is sufficiently random. Second, the key stream sequence is lengthy enough to encrypt a large quantity of data. Third, the key stream sequence should not be very dependent on the starting value.

(1)
Randomness
XOR is commonly used in stream ciphers. If numerous data are encrypted with the same key string in this situation, the data may be decoded without knowing the key sequence. The following are the reasons: suppose P_{1} and P_{2} are two strings of plaintext data, K is the key used to encrypt the data. The ciphertext: E_{1} = P_{1} ⨁ K, E_{2} = P_{2} ⨁ K, ⨁ denotes XOR operation. Because E_{1} ⨁ E_{2} = P_{1} ⨁ K ⨁ P_{2} ⨁ K = P_{1} ⨁ P_{2} ⨁ (K ⨁ K) = P_{1} ⨁ P_{2}, XOR P_{2} on both sides, we obtain E_{1} ⨁ E_{2} ⨁ P_{2} = P_{1} ⨁ P_{2} ⨁ P_{2} = P_{1}. The ciphertext is cracked.
The Golomb randomness hypothesis [26] defines the basic characteristics that a sequence needs to have if it is considered random enough. Include:

C1: In a periodic segment, the difference between the numbers of 1 s and 0 s is no more than 1.

C2: In a periodic segment, if the length of runs accounts for the total number of runs, here it is assumed that there are at least two lengths of runs.

C3: Autocorrelation function:
$$R\left(\Delta \right)=\sum \limits_{i=1}^L{l}_i{l}_{i+\Delta}=\left\{\begin{array}{l}L/2,\Delta =0\\ {}L/4,0<\Delta <L\end{array}\right.$$(1)L denotes the length of the sequence, Δ denotes the interval.


(2)
Infinity
Because the LSFR pseudorandom sequence is periodic, key duplication will occur if the plaintext length exceeds the period of the key sequence. As a result, given a large key space, the key stream sequence must be both random and aperiodic. In theory, this needs an infinitely long key sequence.

(3)
Stability
The LC method is extremely sensitive to the initial value, and it is precisely because of this sensitivity that it produces randomness, which is also the origin of the term “chaotic,” that is, the phenomenon in which the dynamic system appears random but is not random; however, a minor change can result in different encryption results, implying that chaotic systems are highly uncontrollable.
To some extent, the key sequence must be sensitive to the starting value. If it is not sensitive, all sequences will be the same or equivalent, and the intended unpredictability will be lost. The key sequence, however, will be easily broken if the initial value sensitivity is too high.
Algorithm principle
Assuming that there are m ones in the Zeckendorf representation sequence, the coding sequence is marked as: Z_{L, m}, according to Filipponi and Wolfowicz’s discovery in 1987 [27], the number of possible sequences is
N_{L, m}(k) indicates the number of all Zeckendorf representation sequences with kth bit being 1. Filipponi et al. proved that:
and
Based on the following assumptions [28]
It can be inferred from (4) that i > m − 1.
Theorem 1 If m < k < L − m + 1, N_{L, m}(k) = N_{L, m}(m) is a constant.
Proof From (4), we have
From (5), we have
Then,
Therefore,
Similarly, using (7) and (9), we can get
Algorithm implementation
Based on the characteristics of the Zeckendorf representation structure, a pseudorandom key stream generation algorithm is designed.
Suppose there is a pair of keys (e_{1}, e_{2}), which are calculated as follows:
where μ_{n}, μ_{m} are two prime numbers of the same order of magnitude. There is a pseudorandom sequence of integers
Its initial value satisfies:
Each of M and Ν is
μ_{n}, μ_{m} are prime numbers that satisfy N_{h + 1} ≠ M_{h + 1} 。 H is determined by the message length. Then
Next, perform OR operation on the middle part (the part with constant probability) to get C_{i} of length t:
where,
and
Concatenate C_{i}, we obtain C of length Ht.
C is the desired pseudorandom key stream. We call this pseudorandom key stream generation algorithm “ZPKG” (key generator based on Zeckendorf presentation).
Security analysis
Randomness analysis
Let F_{r} be the maximum Fibonacci number no larger than N_{i}, then the shortest Zeckendorf sequence is S_{L}(N_{i}) with length L = n − 1. We can prove
where \(\Phi =\frac{1+\sqrt{5}}{2}\) denotes the Golden ratio.
When L goes to infinity, \({\Pr}_{L,{U}_L}\left({U}_L\right)\) converges. In this case, L > 25. Then, the kth number of Z_{L}(N_{i}) and Z_{L}(M_{i}) is
Among them,
Similarly,
From (24) and (26), it can be known when L > 25 Golomb’s first randomness hypothesis is satisfied. Golomb’s second randomness hypothesis is difficult to prove directly. We can verify whether Pr(00), Pr(01), Pr(10) and Pr(11) are satisfied. As per the definition of Zeckendorf representation, there is no 11 pair. Therefore, we compute
and
Perform logical OR operation to get all pairs.
Golomb’s second randomness hypothesis is thus satisfied.
Infinity analysis
When H → + ∞, N and M goes to infinity.
In this way, the pseudorandom key stream that is obtained by OR operation with the middle part of the Zeckendorf representation of the integer pair tends to be infinitely long, that is
That is, the sequence length of C is infinite.
Stability analysis
According to the definition of each item of N and M
Where e_{1} = (a_{n}, c_{n}, μ_{n}), e_{2} = (a_{m}, b_{m}, μ_{m}) are the initial parameters. We make a small change in the initial parameter, for example, make c_{n} be c_{n} = c_{n} + 1, then
If encode it as Zeckendorf representation again, then
The new sequence only changes from 0 to 1 at F_{1}, while the position of the sequence segment that generates the pseudorandom key stream is: [m, L − m + 1] . That is to say, the generated pseudorandom key stream will not change.
Experiments and discussion
Statistical properties test
Using the FIPS140–2 [29] standard to test the random performance of the output keystream sequence. The four main tests are as follows:

(1)
Monobit test: The number M of “1” in the output 20,000bit stream sequence satisfies 9725 < M < 10275.

(2)
Poker test: Divide 20,000bit stream sequences into 5000 continuous 4bit blocks, and the following conditions are required f(i) is the number of decimal values i of 4bit blocks, where 0 < i < 15, the test value \(X=\frac{16}{5000}{\sum}_{i=0}^{15}{f}^2(i)5000\), passes the standard 2.16 < X < 46.17.

(3)
Run test: The number of continuous “1” or “0” in the 20,000bit stream sequence is required to meet the standard in Table 1.

(4)
Long run test: It is required that the length of continuous “1” in the 20,000bit stream sequence cannot exceed 26.
To test the randomness of the keystream sequence generated by the algorithm, each of the four main tests was performed k = 200 times, each time using a different initial key. The results are shown in Figs. 3 and 4.
Scrambling effect

(1)
First check the relevance of the key. The key autocorrelation function obtained by randomly generating a 2048bit key stream is shown in Fig. 5a. The autocorrelation function of the ciphertext obtained by encrypting the same plaintext “vehiclerelated data...trafficrelated data” using these keys is shown in Fig. 5b.
It can be seen that the correlation function of the key and the ciphertext has no repetition period, has characteristics similar to white noise, and has good autocorrelation.

(2)
Information entropy is one of the measurement indicators of uncertainty. The ciphertext (2048bit) information entropy is shown in Table 2.
According to information theory, when the probability of occurrence of each symbol of the sequence (in binary terms, 0 or 1) is equal, the information entropy reaches the maximum value. Here, the maximum information entropy of the 2048bit sequence is log2048 = 11. It can be seen that the information entropy of the three algorithms is close to 11, approaching the theoretical upper limit. The information entropy of the ZPKG algorithm is greater than that of the LSFR and LC, indicating that the ciphertext generated by it has a higher degree of disorder and a better scrambling effect.
Sensitivity test

(1)
Check whether it conforms to the avalanche principle and the mutual correlation characteristics. Randomly change the key by 1 bit, and the obtained 2 KB ciphertext changes by 1.023 KB and the change amount is 49 95%, which shows that the encryption method has a strong avalanche effect. The crosscorrelation functions of the obtained two sets of ciphertexts are shown in Fig. 6. A value close to zero indicates that a small change in the key will cause a complete change in the ciphertext.

(2)
The generalized avalanche effect is not only the change of the ciphertext caused by the change of the key but also the change of the ciphertext caused by the change of the bits of the plaintext. Extend the experiment in Fig. 6, flip 1 bit of the plaintext, exchange 2 bits of any plaintext, change 3 bits of the key, change 10 bits of the key, and see the bitflipping ratio of the ciphertext. All experiments were repeated 10 times, and the average value of the results was taken, as shown in Table 3. It can be seen that the ciphertext bit flip ratio is close to 0.5, which meets the strict avalanche criterion (Strict Avalanche Criterion, SAC).
Algorithm performance
The simulation environment of this experiment is: Windows Server 2008 R2 Enterprise operating system, the processor is Intel(R) Xeon(R) CPU E74860 v4 @ 2.27GHz, RAM 4.0 GB.
In the experimental simulation process, the simulation generates a key stream from 0 to 1 million bits and observes the time consumption of LSFR, LC, and this scheme (ZPKG). The results are shown in Fig. 7. As the length of the required key stream increases, and the execution time of the algorithm also increases. The timeconsuming increase of the LC algorithm with the key stream length is the largest, followed by ZPKG, and LFSR is the smallest. In terms of basic time consuming, the basic time consuming of the ZPKG algorithm is the most, followed by LC, and LFSR is the least. This reflects that the initial preparation time of the ZPKG algorithm is the longest, but as the length of the keystream increases, the time consumption of the ZPKG algorithm increases linearly, and the performance is slightly lower than that of LFSR, but slightly higher than that of LC.
Conclusion
This paper presents a novel stream ciphering algorithm that is suited for cloudedge communication in IoV. The unpredictability of the keystream is the foundation of stream ciphering. The probability of digit 1 occurring in the center section of the Zeckendorf representation is proven to be constant, which may be utilized to construct a pseudorandom keystream sequence. The pseudorandom sequence created by the linear feedback shift register (LSFR) is periodic and always repeated. The starting value of the sequence generated by chaotic encryption is too sensitive to disturbance, making it easy to be cracked. These two issues are addressed by the proposed algorithm: ZPKG. The keystream generated by ZPKG is not only very random but also endlessly lengthy, with a moderate parameters sensitivity. The experimental results support the above advantages.
Future research directions include:

(1)
The ASIC design of this algorithm. In terms of hardware resource utilization and operating speed, this technique is nearly identical to the linear feedback shift register (LFSR). LFSR has the disadvantage of being periodic, therefore it can only be used for the encryption of particular length sequences. The sequences created by ZPKG, on the other hand, are not only random, but also aperiodic, and can yield limitless keystreams. Therefore, ZPKG might be investigated as a replacement for LFSR as a PRBS (pseudorandom binary sequence) generator, which is often used in telecommunication to produce white noise.

(2)
Quickly generate the Fibonacci numbers. Fibonacci numbers are required for the Zeckendorf encoding process. The computational complexity (o(logn)) of generating Fibonacci numbers is still high, resulting in slow encoding.
Availability of data and materials
The plaintext data used for encryption testing is randomly generated. Relevant experimental results can be requested by email to the corresponding author.
Abbreviations
 IoV:

Internet of Vehicles
 RSU:

Road Side Unit
 OBU:

Short for On Board Unit
 DSRC:

Dedicated ShortRange Communication
 ZPKG:

Pseudorandom Keystream Generator with Zeckendorf representation
 LFSR:

Linear feedback shift register
 LC:

Logistic Chaos
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Acknowledgments
The authors acknowledge Tianqi Cai for language polishing.
Funding
This work was supported in part by the National Natural Science Foundation of China under Grant 61832014.
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Yun Wu: data curation, investigation, visualization, and writing. Liangshun Wu: software, validation, methodology, and formal analysis. Hengjin Cai: conceptualization, ideas, funding acquisition, project administration, resources allocation, and supervision. All authors reviewed the manuscript. The author(s) read and approved the final manuscript.
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Wu, Y., Wu, L. & Cai, H. Cloudedge data encryption in the internet of vehicles using Zeckendorf representation. J Cloud Comp 12, 39 (2023). https://doi.org/10.1186/s13677023004177
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DOI: https://doi.org/10.1186/s13677023004177