Efficient Privacy-Preserving mHealth Framework Using Crisscross AES and FCFS-NDPPP in Hybrid Cloud

According to the Cloud Security Alliance (CSA) in its security guidance report, cloud services are categorized into three distinct models based on the services they offer: Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS). IaaS, such as Amazon EC2, provides clients with core computing infrastructure such as networking capabilities, unstructured data storage, and processing units necessary for running any application [18]. It also supports all stages required for the development, testing, and deployment of internet-based applications. Examine multiple public cloud platforms and introduce CloudCmp systematic framework designed to evaluate and compare the costs and performance of various cloud providers. It focuses on key service attributes, including elastic computation, persistent storage, and network performance by analysing metrics that directly impact customer application efficiency [19].

To maintain fairness, accuracy, and consistency, CloudCmp operates within specific cost constraints while conducting these assessments. Upon applying the tool to several prominent cloud service providers, the researchers discovered significant differences in cost-effectiveness and service performance across vendors. As a result, CloudCmp serves as a valuable platform to help users identify the most appropriate cloud provider tailored to their specific application needs [20]. Key factors to consider when designing a secure network include non-repudiation, integrity, reliability, confidentiality, and availability. As outlined by the Open Systems Interconnection (OSI) model, encryption techniques are typically implemented at the application layer during data transmission to ensure secure communication [21].

Based on specific requirements, individuals can choose from various existing information security techniques. Security is an essential component that extends from the physical layer to higher levels of the information transmission system. To ensure comprehensive network information security, all layers above the physical (material) layer also contribute significantly. Depending on the developer’s security policies, authentication and identification processes may be implemented at one or more layers. At the physical layer, tasks such as fault detection, attack identification, and the deployment of intelligent countermeasures are crucial for maintaining network security [22].

Another critical concern is data availability. Any interruption in access to data can disrupt business operations or service delivery, potentially resulting in customer attrition, revenue loss, and reputational damage. This study also highlights the security implications of data inaccessibility, emphasizing the increased risks posed by mobile or distributed data particularly when information is exchanged between countries with conflicting regulatory standards. The research further explores network security concerns within virtualized environments, focusing on the Xen hypervisor is an open-source virtualization platform [23]. From a security standpoint, one of the key architectural challenges in cloud computing is securing communication among multiple VMs on the same host. To mitigate these risks, the authors propose a novel virtualized network architecture designed to better isolate and protect communication between VMs, thereby enhancing security in cloud-based infrastructures [24].

With the rise of mobile devices, patients now commonly access cloud-based services via smartphones support various authentication methods, including: Two-Factor Authentication (2FA); Three-Factor Authentication (3FA); Multi-Factor Authentication (MFA). These methods significantly strengthen personal data protection. Even with built-in multi-factor authentication, smartphones remain vulnerable, particularly when integrated with cloud platforms that may have security flaws. Implementing three-factor authentication may also hinder usability [25]. For ordinary patients, accessing their mobile devices for routine use becomes inconvenient, as authorization delays reduce user experience. Although smartphones and tablets have largely replaced traditional PCs and are often considered secure, still exposed to threats when used in security-sensitive environments such as healthcare, defense, and telecommuting. To address these vulnerabilities, multiple identification protocols have been designed to strengthen security, ensuring complete safety, client identity verification, and secure certification mechanisms [26].

As part of efforts to secure patient data stored in the cloud, a secure 2FA protocol was proposed. Due to persistent security vulnerabilities, researchers developed a secure message exchange mechanism based on watermarking. This technique enhances message integrity by embedding unique identifiers within the message, tolerating multimedia communication errors. Despite its merits, the watermarking-based method has a critical drawback: the absence of a timestamp during message transmission. This omission exposes the system to replay and processing-based attacks, undermining the security and authenticity of communications [27]. A fingerprint authentication technique was developed to enhance patient data security in the cloud. Fingerprint identification serves as a third authentication factor to improve privacy. The fingerprint recognition process involves converting RGB images to grayscale, adjusting and minimizing blur effects, and segmenting the image used for biometric-based verification. This processed fingerprint is embedded as a watermark in the patient's image. The study’s outcomes were validated using Galaxy S3 and BlackBerry Z smartphones, demonstrating that the proposed system performs effectively and is easy to use [28]. The method does not ensure secure image transmission. It remains vulnerable to session-based attacks. To address these issues, researchers developed a cloud-based authentication system using multiple biometric factors. For smartcard-based authorization, both palm vein patterns and fingerprint credentials are accepted. The smartcard stores the user’s biometric impressions and is matched against the patient’s records [29].

A system was also developed for distributing ranked reports, leveraging an alternative encryption algorithm that allows hashtags to be securely shared with multiple users. To evaluate patient data, the Attribute-Based Encryption Method (ABEM) is applied. This method offers benefits such as reduced computation and a smaller index structure. It suffers from storage complexity. A key advantage of ABEM is that it only requires one key to decrypt patient records [30]. With the attribute set stored in an index tree, users can efficiently compute the decryption key. One strength of this method is that the encrypted medical document maintains a constant size. Its drawback lies in the length of the secret key. To enhance patient data security, proposed a method aimed at protecting the confidentiality of patient information. This approach utilizes an expansion operation to validate individual claims. Although this method requires minimal implementation effort, it consumes significantly more time compared to previous studies [31]. In this scheme, all patient data is processed for validation, but due to the extensive computation time, its efficiency is reduced. To address some of these issues, introduced a detection mechanism based on radio repetition rates. A major drawback of existing methods is the reliance on long decryption keys and lengthy storage periods [32]. To mitigate these issues, designed a cipher text protocol encryption with a fixed key size, minimizing storage complexity and decryption delays. The key size was standardized to 672 bits making it suitable for resource-constrained devices used for secure key storage and decryption. The main advantage of this method is the efficient storage of patient information, while its drawback is the long data transmission duration.

This study proposes a secure and efficient framework for managing mobile medical data in hybrid cloud environments by integrating planning, cloud computing, and encryption techniques shown in Figure 1. It uses a practical medical dataset containing sensitive patient information and deploys the system using Amazon Web Services (AWS) and Edge-based simulators. The proposed method enhances traditional AES through a modified Crisscross AES, which includes key iteration and row-column transpositions for improved security. The Network Data Privacy Preserving Protocol (NDPPP) employs a First-Come-First-Served (FCFS) scheduler and supports secure multi-user access using role-based data division and authentication tokens. SHA-256 ensures data integrity, while benchmarking tools measure latency and efficiency. The framework is evaluated for encryption strength, scheduler performance, and compliance with security standards in both standalone and hybrid setups. MATLAB, Python (PyCryptodome), and CloudSim are used to test the system's scalability, resilience, and real-time applicability.

1.jpg

Figure 1. Proposed system

4.1 Data acquisition from wearable and mobile devices

Wearable sensors (such as glucose and cardiac sensors) and applications for mobile health (mHealth applictions) continually track and record an individual's critical indicators are used in contemporary mobile medical facilities to collect information shown in Table 1. In addition to timestamp, setting, and gadget ID metadata, each entry of information contains physical parameters including heart rate (HR), blood pressure (BP), oxygen saturation (SpO₂), and glucose level (GL). The core of the health monitoring system is this uncooked, current information, which is produced often. The information is recorded in an organized manner as follows:

$D_x=\left\{H R, B P, S p O_2, G L, t, l o c, I D\right\}$                   (6)

where, $D_x$ represents the collected data from the $x^{t h}$ instance.

Table 1. Dataset description

4.2 Edge pre-processing for normalization and noise filtering

Preparing is an essential stage in the proposed architecture for integrity-assured and confidential mobile medical information to guarantee consistency of information, eliminate noise, and get it ready for scheduled and encryption. The edge processing unit may be installed on gateways or handheld devices, performs actual time pre-processing to guarantee data is accurate and uniform before transfer to the cloud. Each numeric property is first scaled for equitable encryption and scheduling processes using Z-score standardization. Each value X is changed using:

$Z=\frac{I-\mu}{\sigma}$                  (7)

where, $\mu$ is the mean and $\sigma$ is the standard deviation of the feature. This helps standardize data to a mean of 0 and standard deviation of 1. To eliminate transient sensor noise, a moving average filter is used, calculated as:

$I_t^{\prime}=\frac{1}{n} \sum_{x=t-n+1}^t I_x$                 (8)

This smoothens the signal, enhancing reliability before encryption and scheduling.

4.3 Anonymization and secure tokenization at the edge

The solution incorporates token-based anonymity at the edge directly to safeguard the identities of patients because healthcare information is important. Before being stored or sent, a distinct hash-based token is used in place of each patient's ID to protect the confidentiality of data. A cryptographic hash function, such SHA-256, is used by the tokenization procedure and is defined as:

$Token_{I D}=Hash(PatientID \| Timestamp)$             (9)

This guarantees that the information cannot be connected to any particular person, even in the event that it is stolen. The solution complies with downstream Crisscross AES encryption requirements and NDPPP confidentiality laws by managing these pre-processing stages at the edge, minimizing cloud computing costs, lowering delay, and guaranteeing private.

4.4 Encryption layer - crisscross AES (ECAES)

The enhanced AES is applied in a grid fashion in the proposed crisscross AES method. AES, the proposed crisscross technique, is a ten-round, four-level combo. Three M-1s are included in the first level, three M-1s are included in the second round, and so on until the third level. All three levels are combined in the fourth round, which is then sent to the servers. In cloud computing, when the user accesses both IaaS and SaaS offerings, Figure 2 illustrates how ECAES is implemented. When it comes to user-related concerns, schedule, and safety are two of the cloud system's primary disadvantages. To solve this issue, a novel idea of combining FCFS of dominance components for scheduling purposes and Crisscross AES uses a crisscross conversion to reconstruct the normal AES state matrices. The change swaps components both row-wise and column-wise according to a hidden permutation variable π or a predetermined crisscross design. Unpredictability and resilience to cryptanalysis are increased as a result.

2.jpg

Figure 2. ECAES method

Let the AES state matrix be:

$S=\left[\begin{array}{llll}s_{00} & s_{01} & s_{02} & s_{03} \\ s_{10} & s_{11} & s_{12} & s_{13} \\ s_{20} & s_{21} & s_{22} & s_{23} \\ s_{30} & s_{31} & s_{32} & s_{33}\end{array}\right]$                 (10)

The Crisscross Transformation (CT) is applied as:

$S^{\prime}=C T(S)=\pi_{ {row }}\left(\pi_{{col }}(S)\right)$                  (11)

where, $\pi_{{row }}$: Row permutation function; $\pi_{c o l}$: Column permutation function. This reshuffles the AES state matrix before the usual AES rounds, enhancing diffusion.

Final ECAES: Combining standard AES operations with the crisscross transformation, the final Crisscross AES encryption can be expressed as:

$C=E_k(C T(M))$                  (12)

where, CT(M) Crisscross-transformed message matrix; $E_k$: Standard AES encryption on transformed data; C: Encrypted ciphertext ready for secure cloud storage. The ECAES layer secures sensitive mobile healthcare data before transmission to the hybrid cloud. It enhances standard AES by applying a crisscross transformation that permutes rows and columns of the AES state matrix, improving diffusion and confusion. To evaluate the efficiency of the proposed Crisscross AES, compared it against standard AES across key metrics such as encryption time, decryption time, memory consumption, and throughput. The experiments were conducted using a real-world healthcare dataset under a hybrid cloud simulation environment.

Table 2. Computational overhead comparison of standard AES vs. crisscross AES

Crisscross AES incurs a slight computational overhead (≈10–12% increase in encryption/decryption time and memory usage) due to dynamic key shuffling and matrix transposition shown in Table 2. This trade-off is justified as it achieves a ~28% increase in effective key entropy, thereby substantially improving resilience against cryptanalytic attacks. The marginal reduction in throughput (≈6%) is acceptable within healthcare applications, as the framework ensures end-to-end HIPAA/GDPR-compliant security with negligible impact on real-time data transmission.

4.5 Schedule layer-FCFS

Ensuring optimal system efficiency and allocating a large number of managed resources to programs are the primary goals of cloud task scheduling. The size of the assigned task is the first factor that contributes to the complexity of the scheduling problem. Performance analysis is based on studying jobs that arrive at random times and evaluating the maximum time a worker can wait for a required service. In the proposed cryptography and scheduling architecture, the cloud layer utilizes the FCFS scheduling technique to ensure that private and encrypted medical data is processed in the exact order of arrival. This non-preemptive scheduling method is ideal for time-sequenced medical data streams, where job fairness and temporal order are critical. FCFS is the simplest scheduling algorithm where: Tasks are executed in the order they arrive; No task is interrupted or reordered; this preserves data temporal integrity - crucial for time-dependent healthcare analysis.

Let: $n$ be the number of tasks/data packets, $A_x$ be the arrival time of the $x^{ {th }}$ task, $B_x$ be the burst (processing) time of the $x^{t h}$ task.

Completion Time (CT):

$C T_x=\left\{\begin{array}{c}A_1+B_1, \quad { if } \,\, x=1 \\ \max \left(C T_{x-1}, A_x\right)+B_x, \quad { if } \,\,x>1\end{array}\right.$                 (13)

Turnaround Time (TAT):

$T A T_x=C T_x-A_x$                  (14)

Waiting Time (WT):

$W T_x=T A T_x-B_x$                (15)

Average Waiting Time (AWT):

$A W T=\frac{1}{n} \sum_{x=1}^n W T_x$                   (16)

The FCFS method is employed by the Scheduler Layer in the proposed structure to manage encrypted mobile medical information as it enters the hybrid cloud. This non-preemptive strategy preserves the temporal sequence of time-sensitive health data by strictly organizing tasks based on their arrival time, ensuring that no information is unfairly delayed or reordered. Processor timings for each encrypted data packet treated as an individual job are calculated using burst time and arrival time. When integrated with the NDPPP protocol, the FCFS approach ensures efficient task handling across multiple locations with minimal waiting time and predictable scheduling also maintaining confidentiality and fairness.

4.6 NDPPP approach

The following outlines the complete process of the proposed system design: Encrypted data from the Data Owners (DOs) is stored in the cloud. The DOs generate encrypted keywords for their files and send them to the Administrative Servers (AS). To enhance communication security, the AS re-encrypts the keywords before forwarding them to the cloud. Data Users (DUs) generate a trapdoor, which is submitted to the AS. After verifying the DUs' identity, the AS forwards the request to the cloud and re-encrypts the data to ensure privacy. The cloud matches the owner’s keyword with the trapdoor and produces hierarchical results when a match is found. This hierarchical output reduces computational overhead. The DUs then receive the keys and the encrypted data. A secure connection between the DUs and the AS is used for hash exchanges, ensuring safe transmission. By substituting the plaintext into the received hash, the DUs calculate the symmetric key required to decrypt the files. The proposed system employs the Novel Data Privacy-Preserving Protocol (NDPPP) to secure information transmission from the cloud to the DUs. The architecture comprises four main components: the cloud, administrative servers, data owners, and data users, as illustrated in Figure 3.

3.jpg

Figure 3. NDPPP architecture

4.6.1 Patients initializing

To initialize the mechanism for secure private key transmission between itself and the DUs, the AS performs the following tasks. Let G₁ and G₂ be two cyclic groups of prime order p. The system constructed by the AS is defined as $S=\left(p, G_1, G_2, e(.,).\right)$, where $e: G_1 \times G_2 \rightarrow G_2$ is a bilinear map. The AS randomly selects $D, P \in G_1$ and $\alpha, \beta \in Z_p^*$. It then computes F = k.D,X = α.P,Y = β.D and K = e(D,P). Finally, the parameters D, F, I, J, K, and h (where h is a hash function h:{0,1}*→{0,1} are broadcast. The AS remains fully secure and keeps the parameters P, α and β confidential.

4.6.2 Patients authentication

To get a shared secret session key from the management servers, the AS and DUs in this division are carrying out the safe authenticating procedure. To get the public key of the management servers, we made the assumption in the present investigation that all DUs have gotten the AS certifications from the general directories. Let $I D_x$ represents to the unique identity like Aadhar number of the DUs, $p k_x$ denotes the public key, and denotes the account number of DUs $a_x$ selected from $Z_p^*$. DUs sends $\operatorname{DenC}_{P K_{a s}}\left(I D_x, p k_x, a_x\right)$ to the administration server. The administration server, in response to this query, dynamically chooses $\alpha_y \in Z_p^*$. At this point, it computes the values of Q and N as $Q=e(D, D)^{a_x} \quad$ and $\quad N=\left(\alpha_x+\right. \left.\beta . k . \alpha_x . h\left(I D_x \| p k_x\right)\right) . D$. The AS transfers the computed values of Q and N to the DUs in the public channel. Reception of values of Q and N from the administration server, the DUs can compute the similar values as $Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . F, Y\right)$ and $e(N, D)$. It validates whether the AS received values are trustworthy and correct by verifying whether $Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . F, Y\right)=e(N, D)$. The mathematical proof is clearly explained as follows:

$\begin{aligned} & Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . F, Y\right) \\ & =Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . k .D, \beta . D\right) \\ & =Q . e\left(k . \alpha_y . h\left(I D_x \| p k_x\right) . D, \beta . D\right) \\ & =Q . e(D, D)^{\beta . k . \alpha_y . h\left(I D_x \| p k_x\right)} \\ & =e(D, D)^{\alpha_y} . e(D, D)^{\beta . k . \alpha_y . h\left(I D_x \| p k_x\right)} \\ & =e(D, D)^{\alpha_x+\beta . k . \alpha_y . h\left(I D_x \| p k_x\right)}\end{aligned}$

$Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . F, Y\right)=e(N, D)$                 (17)

In the above scenario, the AS and DUs perform a secure authentication process to derive a common session key from the leadership servers. For this analysis, we assume that all DUs have obtained AS certificates from a global directory to acquire the public key of the leadership servers. Let ID_x denote the unique identification of a DU (e.g., Aadhar number), pk_x its public key, and $a_x \in Z_p^*$ its account number. The management service receives ${DenC}_{P K_{a s}}\left(I D_x, p k_x, a_x\right)$ from the DUs.

Upon receiving this query, the administration server dynamically selects $a_y \epsilon Z_p^*$. The server then computes $Q= e(D, D)^{a_x}$ and $N=\left(\alpha_x+\beta . k . \alpha_x . h\left(I D_x \| p k_x\right)\right) . D$. These values, Q and N , are broadcast by the AS over the public channel to the DUs. Once the DUs receive Q and N , compute the corresponding values $Q . e\left(\alpha_y . h\left(I D_x \| p k_x\right) . F, Y\right)$ and $e(N, D)$. To verify the correctness and integrity of the values received from the AS, the DUs check whether

The following section provides a detailed explanation of the mathematical proof underlying this verification.

After successful authentication, the DUs sends $I D_x, b_x, \operatorname{Denc}_{P K_a}\left(I D_x, a_x\right)$ to AS , where $b_y$ is a random number selected from $Z_p^*$. The AS decrypts $\operatorname{Denc}_{P K_x}\left(I D_x, a_x\right)$ using the DUs public key $P K_x$ and verifies that the identity contained in the message mathes the DU's registered identity.

Similarly, $b_x$ is also validated. Upon successful verification, the AS selects a new random number $s_y \in Z_p^*$, and sends ${Denc}_{P K_x}\left(s_x, a_x, b_x\right)$ key to decrypt the message and retrieve $s_x$ which serves as the secure private session key linking the DUs and the administration server. This session key $s_x$ is used to decrypt files retrieved from the cloud. Each file owner is assigned a unique secret key $s_x$ for file encryption. Using the same key transfer mechanism described earlier, the file owner and AS securely share the secret key $s_x$, ensuring confidentiality and integrity of the data during storage and transmission.

4.6.3 File upload

Let G be the product of two cyclic groups of prime order p . The bilinear pairing is denoted by $\hat{\mathrm{e}}$, where $\hat{\mathrm{E}}: G \times G=G_1$. Within this system structure, secret keys $K_{x, o}$ and $K_{x, a s}$ are randomly selected, with $K_{x, o}, K_{x, a s}$ from $Z_p^{+} \leftarrow(0,1)^*$ represents the secret key of the Data Owner (DO), while $K_{x, o}$ corresponds to the private key of the Administrative Server (AS). Both keys are used for file encryption. The secret hash function is denoted by $\mathrm{h}($.$) and its$ output lies in $Z_p^{+}$.

the ciphertext C. To enable Data User (DU) verification and keyword-based searching over the ciphertext C, the DO generates a keyword $\widetilde{w}_{x, d}$. The notation $\widetilde{w}_{x, d}$ specifically refers to the searchable keyword embedded for secure DU query and authentication over the encrypted data.

$\widetilde{w}_{x, d}=\left(g^{k_{x, o} . h\left(w_{x, d}\right)}, g^{k_{x, o}}\right)$                 (18)

where, $\widetilde{w}_{x, d}$ is the actual keyword which is used as the input to hash function. For simple description, the encrypted word is written in two different expressions as specified below:

$E_0=\left(g^{k_{x, o} . h\left(w_{x, d}\right)}\right)$                   (19)

$E_1=g^{k_{x, o}}$                  (20)

The computed values of $E_0, E_1$ which are represented in Eqs. (19) and (20) are given to the administration server.

4.6.4 Trapdoor generation

In this division, the DU submits his/her query using the word $W_{d^{\prime}}$ to the cloud. Whenever the DU needs to submit a query $W_{d^{\prime}}$ the DU will be computing the trapdoor as:

$T_{w_{d^{\prime}}}=\left(g^{h\left(w_{d^{\prime}}\right) . r_u}, g^{r_u}\right)$                (21)

The DU doesn't have to acquire the keys from the data owner for computing the trapdoor. Here, $r_u$ denotes the DUs randomly generated number, denotes the search keyword and h denotes hash. To avoid the $W_{d^{\prime}}$ impersonation attack, we have established a new protocol for trapdoor generation,

$T_{d u}=\left(g^{h\left(w_{d^{\prime}}\right)}\right)$                 (22)

where, the DU hashes the whole trapdoor before sending it to the AS.

4.6.5 Re-encryption of the administrative servers

The equation that follows will be used by the AS to re-encrypt the trapdoor:

$T_{a s}=\left(g^{h\left(T_{d u}\right) . K_{a s} . r_{a s}}, g^{r_{a s}}\right)$                  (23)

where, $K_{a s}$ represents the AS private key, $r_{a s}$ represents the AS randomly chosen number. This type of trapdoor computation is simple and secure when related to the existing methods. For easy understanding and representation, the trapdoor has been divided into two as showed below:

$T_1=g^{h\left(T_{d u}\right) . K_{a s} . r_{a s}}$               (24)

This can be represented as:

$T_{a s}=\left(T_1, T_2\right)$                 (25)

AS functions as an authentication authority for both Dus and Dos. The information owners send the encrypted keyword $\widetilde{w}_{x, d}$ along with ciphertext components $E_0$ and $E_1$ to the Administrative Server (AS). Upon receiving them, the AS reencrypts $E_0$ using its private key $K_{a s}$, thereby generating a new ciphertext component $E_2$, which is defined as follows:

$E_2=\left(E_0 . g\right)^{K a s}$                (26)

Finally, $\tilde{r}_{x, d}=\left(E_2, E_1\right)$. The AS submits the $\tilde{r}_{x, d}$ towards the cloud. The AS will be doing some simple alterations in the encrypted keyword.

4.6.6 Cloud matching

The encrypted files and their corresponding keywords, generated by the Data Owner (DO), are stored in the cloud. The Administrative Server's (AS) secret key is also maintained in the cloud in encrypted form, expressed as $S_{a s}= g^{K_{a s}}$. When a search query is submitted by DU, the cloud verifies the DO's encrypted keyword. It checks whether the encrypted keyword provided by the DO matches the trapdoor generated for the DU's query, as shown in the following equation.

$\begin{aligned} & \hat{e}\left(E_2, T_2\right)=\hat{e}\left(\left(g^{K_{x, o} . h\left(w_{x, d}\right)} . g\right)^{K_{a s}}, g^{r_{a s}}\right) \\ & =\hat{e}(g, g)^{\left(K_{x, o} . h\left(w_{x, d}\right)+1\right) . K_{a s} . r_{a s}} \\ & =\hat{e}(g, g)^{K_{x, o} . h\left(w_{x, d}\right) . K_{a s} . r_{a s}} . \hat{e}(g, g)^{K_{a s} . r_{a s}} \\ & =\hat{e}\left(g^{K_{x, o}}, g^{\left.h\left(T_{d u}\right) . K_{a s} . r_{a s}\right) . \hat{e}(g, g)^{K_{a s} . r_{a s}}}\right.\end{aligned}$

$\hat{e}\left(E_2, T_2\right)=\hat{e}\left(E_2, T_2\right) . \hat{e}\left(S_{a s}, T_2\right)$                 (27)

The requirement is satisfied if the condition $h\left(w_{x, d}\right)= h\left(T_{d u}\right)$, holds true. In this case, the Dus can successfully retrieve the ordered results, as the hash of the DO keyword $h\left(w_{x, d}\right)$ mathes the hash of the DU's trapdoor keyword $h\left(T_{d u}\right)$.

4.7 Algorithm: Secure healthcare data encryption and scheduling in hybrid cloud

Input: $D=\left\{d_1, d_2, \ldots, d_n\right\}$ : Set of mobile healthcare data records; K: Secret encryption key; $A=\left\{a_1, a_2, \ldots, a_n\right\}$ : Arrival times of data packets; $B=\left\{b_1, b_2, \ldots, b_n\right\}$ : Burst times (processing times) of each data record

Output: $C=\left\{c_1, c_2, \ldots, c_n\right\}:$ Encrypted healthcare data; $Scheduled_C$ : Securely scheduled and stored data packets in hybrid cloud

Steps:

a. Initialization: Set $x=1$; initialize arrays $C T[x], T A T[x], W T[x]$ to zero Define encryption key K

b. Preprocessing and normalization

For each $d_x \in D:$

Normalize using Z-score:

$d_x^{\prime}=\frac{d_x-\mu}{\sigma}$

where, μ: mean and σ: standard deviation

c. Crisscross AES encryption

For each $d_x^{\prime} \in D$:

Apply Crisscross Transformation:

$C T\left(d_x^{\prime}\right)=\pi_{ {row }}\left(\pi_{ {col }}\left(d_x^{\prime}\right)\right)$

Encrypt:

$c_x=E_K\left(C T\left(d_x^{\prime}\right)\right)$

where, $E_K$ is the AES encryption with key K

d. FCFS scheduling (NDPPP-enabled)

Sort data C by arrival time $a_x$

For x = 1 to n

$C T_x=\left\{\begin{array}{c}a_1+b_1, \quad { if }\,\, x=1 \\ max \left(C T_{x-1}, a_x\right)+b_x, \quad { if } \,\, x>1\end{array}\right.$

$T A T_x=C T_x-a_x$

$W T_x=T A T_x-b_x$

e. NDPPP protocol application

Apply NDPPP to ensure secure multi-user storage with privacy tags and data partitioning.

f. Storage in hybrid cloud

Send scheduled encrypted data $c_x$ to hybrid cloud (public/private partition) Maintain audit log and hash digest for integrity.

The proposed algorithm ensures secure and efficient handling of mobile healthcare data within a hybrid cloud environment by integrating ECAES, FCFS scheduling, and the NDPPP protocol. Initially, incoming healthcare data undergoes pre-processing through Z-score normalization to standardize the input. The Crisscross AES encryption enhances existing AES by introducing row-column permutations, significantly improving diffusion and data security. Once encrypted, the data is passed to the FCFS scheduler organizes tasks based on their arrival time, ensuring fairness and maintaining the temporal order of sensitive health records. NDPPP framework is applied to manage multi-user privacy, enforce access control, and securely store the scheduled and encrypted data across public and private sections of the hybrid cloud. This approach guarantees confidentiality, integrity, and efficient task handling, making it suitable for time-sensitive and privacy-critical healthcare applications.