The Effectiveness of Homomorphic Encryption in Protecting Data Privacy

Abstract

As the use of digital services grows, protecting the privacy and integrity of sensitive data, especially in fields like healthcare, finance, and secure surveying, has become a critical concern. Homomorphic encryption (HE) offers a solution by allowing computations to be performed on encrypted data without revealing the original information. This paper examines the principles of homomorphic encryption and its applications in privacy-preserving tasks, focusing on its use in cloud computing, healthcare, and cybersecurity. Various types of HE schemes, including Fully Homomorphic Encryption (FHE), Partially Homomorphic Encryption (PHE), and Somewhat Homomorphic Encryption (SHE), are reviewed to assess their performance, efficiency, and real-world use. The paper also discusses the challenges of implementing HE, such as computational overhead and key management, and suggests directions for future research to improve the scalability and usability of HE in real-time applications. Addressing these challenges will make homomorphic encryption an essential tool for secure, privacy-preserving data processing and sharing in modern digital systems.

Full text

International Journal of Research Publication and Reviews, Vol 5, no 11, pp 3235-3256 November 2024
International Journal of Research Publication and Reviews
Journal homepage: www.ijrpr.com ISSN 2582-7421
The Effectiveness of Homomorphic Encryption in Protecting Data
Privacy.
1Chris Gilbert, 2Mercy Abiola Gilbert
1Professor 2Instructor
1Department of Computer Science and Engineering/College of Engineering and Technology/William V.S. Tubman
University/chrisgilbertp@gmail.com/ cabilimi@tubmanu.edu.lr
2Department of Guidance and Counseling/College of Education/William V.S. Tubman University /mercyabiola92@gmail.com/moke@tubmanu.edu.lr
ABSTRACT
As the use of digital services grows, protecting the privacy and integrity of sensitive data, especially in fields like healthcare, finance, and secure surveying, has
become a critical concern. Homomorphic encryption (HE) offers a solution by allowing computations to be performed on encrypted data without revealing the
original information. This paper examines the principles of homomorphic encryption and its applications in privacy-preserving tasks, focusing on its use in cloud
computing, healthcare, and cybersecurity. Various types of HE schemes, including Fully Homomorphic Encryption (FHE), Partially Homomorphic Encryption
(PHE), and Somewhat Homomorphic Encryption (SHE), are reviewed to assess their performance, efficiency, and real-world use. The paper also discusses the
challenges of implementing HE, such as computational overhead and key management, and suggests directions for future research to improve the scalability and
usability of HE in real-time applications. Addressing these challenges will make homomorphic encryption an essential tool for secure, privacy-preserving data
processing and sharing in modern digital systems.
Keywords: Homomorphic encryption, data privacy, cryptography, cloud computing, healthcare security, fully homomorphic encryption, privacy-
preserving computing, secure data processing, big data, multiparty computation.
1. Introduction
Networked services are increasingly relied upon, making it essential to have effective methods for ensuring data privacy and integrity. In critical sectors
such as healthcare, finance, and secure surveying, the need for robust cryptographic solutions to protect sensitive data has become paramount. Terms like
“federated learning,” “fog/edge computing,” “security and privacy tokens,” “non-blocking censorship,” and “privacy-preserving analytics” have become
central to discussions about creating stronger privacy solutions. These technologies share a common goal: to enhance data security for real-time processing
demands at remote sites. They align closely with cryptographic solutions such as homomorphic encryption, which provides a framework for secure
outsourcing and computation (Aslett et al., 2015; Abilimi & Adu-Manu, 2013; Gilbert, Oluwatosin & Gilbert, 2024 ).
Homomorphic encryption allows computations to be performed on encrypted data, preserving data privacy, particularly in cloud computing and
distributed machine learning environments (Sen, 2013; Alloghani et al.,2019; Jia et al., 2021). This method is valuable when operations need to be carried
out on encrypted data without revealing the plaintext. However, homomorphic encryption is limited in terms of the operations it can support. Its four key
components—key generation, encryption, decryption, and evaluation algorithms—help maintain data security through cryptographic methods like chaotic
maps, lattices, and number theory(Alloghani et al.,2019). Despite its effectiveness, performing operations on encrypted data can be inefficient, leading to
increased time and space complexity. Homomorphic computations require tokens that verify correctness without accessing private keys ( Su et
al.,2024;Rupa et al.,2023; Jin et al, 2018). Therefore, ongoing research focuses on enhancing these encryption schemes to support a broader range of
operations while striking a balance between security and performance (Jafarigol et al., 2023; Abilimi & Yeboah, 2013; Gilbert, Auodo & Gilbert, 2024).
1.1. Background and Significance
Homomorphic encryption is a widely used cryptographic technique designed to preserve privacy. It has broad applications in protecting data, processing
queries, and ensuring secure data aggregation. While other modern public-key cryptographic methods, such as elliptic curve cryptography (Wylde et al.,
2022; Riek & Böhme, 2018; Cassim, 2015; Iezzi, 2020; Abilimi et al., 2015) and lattice-based encryption, are effective in safeguarding privacy, this
survey suggests that homomorphic encryption is particularly well-suited for preserving data privacy in big data analytics (Rupa et al.,2023; Jin et al,
2018). This is especially relevant in cases where additional layers of encryption, from logistics to software and data, may be required to protect sensitive
information stored in the cloud and on servers.

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As privacy concerns grow in today's digital world, the increasing collection and processing of confidential information pose significant risks.
Homomorphic encryption offers a practical solution for safeguarding both personal and enterprise data, particularly in query processing and secure data
aggregation (Archer et al., 2023; Yeboah, Opoku-Mensah & Abilimi, 2013a). This method enables queries to be performed on encrypted data without
exposing the actual content, ensuring strong privacy protection. The final results can be decrypted directly by the intended recipient, further ensuring
secure data interpretation (Opoku-Mensah, Abilimi & Boateng, 2013). Given its unique capabilities, homomorphic encryption has become a foundational
component in secure system architectures, and further technological advancements are needed to fully integrate it into distributed systems ( Opoku-
Mensah, Abilimi & Amoako, 2013).
1.2 Research Approach and methods
The research approach and methods in this paper focus on cryptographic systems, particularly their application in maintaining data privacy and security,
with an emphasis on homomorphic encryption (HE). The primary research methods are as follows( Othman et al.,2015; Ren et al.,2021).
Theoretical Framework: The study is based on cryptographic principles, specifically homomorphic encryption schemes, which allow encrypted data to
be processed without needing to decrypt it. The research considers both symmetric and asymmetric encryption, and investigates cryptographic techniques
like chaotic maps, lattices, and number theory.
Survey Methodology: The paper reviews various homomorphic encryption schemes, including Fully Homomorphic Encryption (FHE), Somewhat
Homomorphic Encryption (SHE), and Partially Homomorphic Encryption (PHE). It compares these schemes in terms of effectiveness, performance, and
limitations(Alloghani et al.,2019; Jia et al., 2021). Additionally, it examines cryptographic libraries and algorithms, such as the Ring Learning With Errors
(RLWE) and Paillier cryptosystem, to evaluate their computational efficiency in different fields like healthcare and cloud computing (Sinha eta al., 2023).
Analytical Methods: The research includes a detailed analysis of the performance overhead associated with homomorphic encryption. It focuses on the
computational complexity, efficiency, and arithmetic optimizations required, especially in distributed systems, cloud computing, and privacy-preserving
machine learning environments.
Experimental Simulations: Secure models are developed for privacy-preserving applications such as deep learning and multiparty computations using
homomorphic encryption libraries. The study tests these models in cloud-based environments to evaluate their efficiency (2016; Tao et al., 2019; Yeboah,
Opoku-Mensah & Abilimi, 2013b).
Application-Oriented Research: Finally, the research applies homomorphic encryption to real-world scenarios, particularly in cybersecurity, cloud
computing, healthcare, and secure data processing. The emphasis is on maintaining privacy in big data analytics while improving the efficiency of
encryption schemes (Cassim, 2015; Basharat et al., 2023).
Together, these methods aim to enhance the efficiency of encryption schemes while preserving data privacy across a range of digital environments.
2. Homomorphic Encryption
Homomorphic Encryption (HE) was first introduced by Gentry in 2009, marking a significant breakthrough in cryptographic technology. Since then, the
development and adoption of homomorphic encryption systems have progressed rapidly. Specifically, in the Ring Learning With Errors (RLWE) setting,
the number of public and private keys generated during encryption has increased dramatically(Alloghani et al.,2019;Su et al.,2024;Rupa et al.,2023; Jin
et al, 2018). This rise has spurred demand for homomorphic encryption schemes that offer greater computational efficiency, reduced arithmetic
complexity, and a smaller memory footprint. These challenges have become particularly relevant with the introduction of use cases like Smart Ubiquitous
and Safe AI (SUSA), which emphasizes security and privacy in Industry 4.0 environments. As a result, there has been a growing need for arithmetic
optimizations in RLWE schemes (Agrawal et al., 2020).
Homomorphic encryption schemes possess a unique homomorphic property, allowing operations to be performed on ciphertexts without decrypting
them(Alloghani et al.,2019; Jia et al., 2021; Jin et al, 2018). This means that after an operation is conducted on the encrypted data, the result can be
decrypted to reveal the encrypted outcome of that operation on the original plaintext. Since the inception of HE, public-key cryptography over various
algebraic structures has served as a core building block for these systems. A notable example is the Ring-LWE problem, which plays a crucial role in the
construction of secure homomorphic encryption schemes (Ren et al.,2021; Su et al.,2024;Rupa et al.,2023; Jin et al, 2018; Archer et al., 2023).

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Figure 1: Homomorphic encryption allows operations on encrypted data securely.
This diagram provides a simplified view of the landscape around Homomorphic Encryption, a type of encryption that allows for computations on
encrypted data without needing to decrypt it first:
i. Homomorphic Encryption is the main focus. It’s an advanced encryption method that’s particularly interesting because it allows data to be
worked on securely—without exposing sensitive information during processing.
ii. Development:
a. This area highlights how homomorphic encryption has gained traction since Craig Gentry's breakthrough in 2009, which first
proved that fully homomorphic encryption was possible.
b. Since then, there’s been a "Rapid Adoption" of this technology, as researchers and organizations recognize its potential to securely
handle data in areas like cloud computing, healthcare, and finance(Basharat et al., 2023).
iii. RLWE Setting (Ring Learning With Errors):

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a. This is a specific mathematical framework used within homomorphic encryption. It’s popular because it can offer more efficient
encryption.
b. KeyGenIncrease: As more people use this technology, the demand for generating keys has risen to enhance efficiency, represented
here as “More keys for efficiency.”
c. DemandIncrease: Alongside the rise in usage, there’s a growing need for optimization to make these operations faster and more
practical, hence the mention of “Need for optimization.”
d. Challenges: This highlights that optimizing RLWE settings is tough. The complexity of the mathematics behind RLWE creates
challenges in making it faster or more efficient.
e. Arithmetic Optimizations: To tackle these challenges, researchers are focusing on improving the arithmetic involved in these
encryption methods, looking for ways to make calculations faster and more manageable.
iv. Operations on Ciphertext:
a. A unique and powerful feature of homomorphic encryption is that it lets people perform calculations on encrypted data.
b. Unique Property: This section points out that with homomorphic encryption, you can "perform operations without decryption,"
which means data remains secure even while it’s being processed.
c. Operations on Ciphertext: Essentially, you can compute results on the encrypted data, and only after the processing is complete do
you need to decrypt to see the outcome(Alloghani et al.,2019;Othman et al.,2015; Ren et al.,2021)
2.1. Definition and Overview
Historically, data security has been maintained through cryptographic techniques like encryption, which protects sensitive data by transforming it into
ciphertext, ensuring only authorized parties can access it. However, traditional encryption methods are limited in situations where third parties must
perform services on behalf of users, such as analyzing medical data(Alloghani et al.,2019;Su et al.,2024;Rupa et al.,2023; Jin et al, 2018). In these cases,
third-party access to sensitive information can potentially compromise user privacy. Therefore, it is crucial to use secure computing technologies that
allow data processing without revealing privacy-sensitive information. Secure Multiparty Computing (SMC) protocols, including Homomorphic
Encryption (HE), provide a solution by enabling computations on encrypted data while maintaining confidentiality, even when using cloud services (Al-
Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek & Böhme, 2018; Cassim, 2015)
Jordan et al., 2022).
Data privacy consists of three essential components: confidentiality, integrity, and availability. Confidentiality restricts data access to authorized users or
entities, while integrity ensures that data remains accurate and has not been tampered with. Finally, availability guarantees that data is accessible when
needed (Sharma, 2013).
2.2. Types of Homomorphic Encryption Schemes
In public-key encryption systems, a key generation process creates a pair of keys—one public and one private. The public key is shared openly, typically
published in a public directory, while the encryption and decryption keys are related in a way that makes it computationally infeasible for anyone to
deduce one from the other. In additive homomorphic encryption systems, these keys are denoted as rA (for encryption) and rB (for decryption). This
paper focuses on a simplified version of the ElGamal encryption system, which supports additive homomorphism(Alloghani et al.,2019; Jia et al., 2021;
Othman et al.,2015; Ren et al.,2021). Similarly, other homomorphic encryption schemes use this framework to generate ciphertext efficiently. One
challenge in homomorphic encryption, however, is the large key sizes involved—particularly for polynomial encryption—resulting in inefficiencies and
longer processing times.
Although it is computationally difficult to evaluate a function fff of a hard problem hhh on a given input xxx, decryption remains feasible through
algebraic manipulation of the ciphertext. Homomorphic public-key encryption allows efficient generation of ciphertext for any result of fff, as the key
generation process ensures secure operations(Su et al.,2024;Rupa et al.,2023; Jin et al, 2018). This process must be carefully designed to ensure security,
as demonstrated by several homomorphic public-key encryption systems. In such systems, algebraic homomorphism-based encryption ensures that it is
impossible to compute a primitive element from either the output f(x)f(x)f(x) or the input xxx. Additive homomorphism, in particular, is one of the most
commonly studied properties in public key encryption systems (Suo et al., 2023).
Homomorphic encryption has the distinct advantage of performing complex operations on encrypted data without the need to decrypt it. It can generate
ciphertext for the final result while maintaining the security of the underlying data. Achieving this level of encryption requires running multiple
cryptographic processes (Sen, 2013; Ren et al.,2021; Su et al.,2024;Rupa et al.,2023; Jin et al, 2018). Cryptographic systems are generally divided into
two categories: symmetric and asymmetric. Symmetric encryption uses the same key for both encryption and decryption, while asymmetric encryption
relies on different keys for these tasks. Most symmetric encryption schemes, however, do not support homomorphic operations, unlike their asymmetric
counterparts.

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Figure 2: Represents types and relationships of encryption schemes.
This diagram provides a high-level overview of the essential components in an encryption system and how they work together as follows:
i. Algorithms: This section represents the different encryption algorithms (like RSA or AES) used to secure data. Each algorithm has its own
properties that define how it works or what makes it unique. These algorithms are part of an encryption scheme, meaning they're the specific
"recipes" or methods used within a broader encryption setup.
ii. Security Level: Every encryption scheme has a security level that defines how strong or secure it is. The security level includes a name, a
description of its strength or purpose, and a score representing how secure it is. The encryption scheme relies on these security levels to protect
data, ensuring that the encryption is tough enough to withstand attacks.
iii. Operations: These are the different actions or processes that can be done within the encryption system, like encryption, decryption, or data
processing. Each operation has a type and indicates whether it supports homomorphic encryption (a type of encryption that allows data processing
without revealing the data itself). The encryption scheme uses these operations to handle data securely.
iv. Encryption Scheme:The encryption scheme is at the center of this model, bringing together all the components. It’s the overarching setup that
uses algorithms, ensures security levels, performs operations, and generates keys. Think of the encryption scheme as the “blu eprint” that defines
how all these parts work together to protect data.
v. Key Pair:The key pair consists of a public key and a private key. These keys are generated by the encryption scheme. The public key is shared
openly and can be used to encrypt data, while the private key is kept secret and is used to decrypt the data. The key pair is essential for secure
communication, ensuring that only the intended recipient can access the encrypted data.
3. Theoretical Implications for Data Privacy
Analytical Improvements: Traditional encryption schemes face significant challenges during the bootstrapping phase, which drastically slows down
computational efficiency and is highly intolerant of errors. This phase involves complex calculations, leading to high computational costs. For instance,
it is difficult to evaluate data similarity when multiplied by coefficients between 0 and 1, so standardization is used to enhance accuracy. A key
improvement is seen in the Isomorphism-LWE scheme, which offers larger moduli in polynomial rings compared to LWE, enabling a smaller ring

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dimension. Typically, the ring's degree of coefficients ranges between 1 and 4. One of the primary goals of this project was to create a secure computational
platform (Agrawal et al., 2020).
Sustainability is a crucial theoretical aspect of the proposed model. The approach offers multiple pathways to ensure the secure handling of data across
various encryption methods. After evaluating different encryption techniques, the most suitable method was selected based on its precision and efficiency.
This model not only enables secure data transfer across networks in theory but also provides practical solutions for facilitating communication between
networks in specialized fields (Patel et al., 2022).
Figure 3:Implications of encryption on data privacy efficiency.
This diagram provides a simplified way to understand the differences between two encryption approaches—Traditional Encryption and Isomorphism-
LWE—in terms of how they handle data privacy. The chart is divided into four key areas, each highlighting different priorities and trade-offs between
accuracy and efficiency:
Security Solutions (Top Left - Traditional Encryption, High Accuracy):This area focuses on security methods that use traditional encryption
techniques. These methods prioritize accuracy, ensuring that data remains secure and correctly encrypted. Point A and Point F: Represent solutions in
traditional encryption that emphasize high accuracy. They might be especially suitable for scenarios where data accuracy is critical, like financial
transactions or secure communication.
Complex Calculations (Top Right - Isomorphism-LWE, High Accuracy): This quadrant highlights more advanced, complex calculations that can be
done with Isomorphism-LWE, a newer encryption approach. Point C: Represents a solution within Isomorphism-LWE that excels at handling complex

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calculations with high accuracy. This could be useful in applications where secure data processing (like in machine learning on encrypted data) is essential,
even if it requires more computational power.
Computational Costs (Bottom Left - Traditional Encryption, High Efficiency): Here, the focus is on solutions that keep computational costs low,
making traditional encryption methods more efficient and quicker, though possibly at the expense of some accuracy. Point E: Represents an efficient
traditional encryption method that minimizes the resources needed to process data. It would be ideal for applications needing fast, lightweight encryption
without too much concern for ultra-high accuracy, like data logging or storage.
Data Transfer (Bottom Right - Isomorphism-LWE, High Efficiency): This area emphasizes efficient data transfer using Isomorphism-LWE, balancing
security with the ability to move data quickly. Point D and Point C (overlapping): Represent techniques within Isomorphism-LWE that support efficient
data transfer, suitable for real-time data exchanges or applications that need to keep data encrypted during transmission.
3.1. Confidentiality and Integrity Preservation
The growing use of smartphones and mobile devices presents a significant security threat to billions of users worldwide. Traditionally, security research
in mobile environments has focused primarily on testing the operating mechanisms of these devices, often overlooking the unique challenges posed by
smartphones. However, securing global privacy and data communication cannot be limited to just operating systems; the broader implications of potential
data breaches are too serious to ignore. Recent research has highlighted that current methods for ensuring data privacy through encryption are insufficient
to fully protect user data from tampering and other security threats (Tao et al., 2019; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek &
Böhme, 2018; Cassim, 2015; Xiong et al., 2020). This study undertakes a systematic review of the methodologies and processes involved in securing
communication systems in the smartphone environment, offering key conclusions, recommendations, and policy implications.
Homomorphic encryption methods, such as Fully Homomorphic Encryption (FHE), Somewhat Homomorphic Encryption (SHE), and Even
Homomorphic Encryption (EHE), have proven effective in safeguarding data services. FHE is particularly powerful, as it allows for an unlimited number
of operations on encrypted data, despite the high computational demands and large ciphertext sizes it generates. The Paillier cryptosystem, along with its
variants like symmetric key Paillier, offers a partial solution by mitigating some of the complexity in homomorphic encryption, but it introduces noise
with each operation, making it only somewhat homomorphic. To address this issue, additive homomorphic schemes like SHE and EHE have been
proposed, which limit the number of computations or operations on ciphertext, improving the overall efficiency of the encryption process (Patel et al.,
2022; Sen, 2013). These advancements aim to unlock the full potential of FHE by enabling infinite arithmetic operations on encrypted data.
Figure 4: Diagram illustrates encryption and security challenges in mobile devices.
This diagram gives a clear, step-by-step look at the current landscape of data privacy and encryption, especially as it relates to mobile devices and the
challenges of using advanced encryption methods.
i. Confidentiality and Integrity Preservation: This section is about protecting data on mobile devices, which face unique security risks.
• Security Threats from Mobile Devices: Highlights the challenges mobile devices face, like exposure to network threats or physical theft,
which can put sensitive data at risk.
• Unique Challenges in Smartphones: Points out that smartphones, with their constant connectivity and frequent software updates, require
special attention to keep data secure.
• Data Breaches Implications: Explores what can happen if mobile security fails—data breaches can lead to serious consequences, from
financial loss to compromised personal information.

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• Research on Data Privacy: Indicates the ongoing work to understand and address these privacy concerns, with the goal of finding better
ways to secure mobile data.
ii. Encryption Methods: This section gives an overview of different encryption techniques, focusing on homomorphic encryption, which is
powerful because it allows data to be processed while still encrypted.
• Homomorphic Encryption Overview: Introduces homomorphic encryption, a method that lets you work with data without ever exposing
it. This is a big leap forward for data privacy.
• Fully Homomorphic Encryption (FHE): This type of encryption allows for unlimited calculations on encrypted data, though it requires
a lot of computing power.
• Somewhat Homomorphic Encryption (SHE) and Even Homomorphic Encryption (EHE): Describe simpler forms of homomorphic
encryption, which allow only a limited number of calculations but are more manageable in terms of resources.
• Paillier Cryptosystem and related methods: These represent encryption techniques that allow specific operations (like addition) on
encrypted data, useful for certain applications where full homomorphic encryption is not practical.
iii. Challenges & Solutions: This section deals with the obstacles and potential fixes in using homomorphic encryption.
• Insufficient Data Privacy: Points out that, even with advanced encryption, keeping data fully private can still be challenging.
• Noise Introduction in Operations: When performing calculations on encrypted data, "noise" (unwanted extra data) accumulates, limiting the
number of calculations possible. This noise needs to be managed to make encryption practical.
• Limiting Computations on Ciphertext: Suggests that simplifying the types of calculations allowed on encrypted data can help keep noise under
control and improve efficiency.
• Efficiency Improvement: Refers to the ongoing work to make homomorphic encryption faster and less resource-intensive, so it can be more
widely used.
iv. Recommendations & Implications: This final section summarizes findings and suggests steps to move forward.
• Key Conclusions from Study: Outlines what we’ve learned so far from studying data privacy and encryption techniques.
• Recommendations for Encryption: Provides practical advice on how to improve encryption strategies to make them more effective.
• Policy Implications: Emphasizes the need for strong policies to support data privacy, as technology alone isn’t enough.
• Unlocking Potential of FHE: Calls attention to the potential of Fully Homomorphic Encryption as a powerful tool for data privacy, despite
current challenges with efficiency.
4. Applications in Cybersecurity
Homomorphic encryption (HE) allows arbitrary functions and analyses to be performed on encrypted datasets without the need for decryption, ensuring
a high level of security. In HE-based systems, data owners first encrypt their datasets and then send the encrypted data to external storage or processing
entities(Alloghani et al.,2019;Ren et al.,2021; Su et al.,2024;Rupa et al.,2023; Jin et al, 2018). These entities do not have access to the secret keys used
for encryption, which prevents them from decrypting or gaining any meaningful insight into the encrypted datasets. Since the introduction of Fully
Homomorphic Encryption (FHE) in 2009, it has become possible to perform arbitrary operations on encrypted data. However, these systems can be
significantly slower than operations performed on plaintext, as they fail to account for the computational complexity associated with plaintext
operations(Rupa et al.,2023; Jin et al, 2018).
HE is designed to encrypt data using linear arithmetic, followed by encryption permutations, re-encryption, and function execution over the ciphertext.
HE schemes have been proposed as highly secure, scalable solutions, especially in cloud computing environments. Additionally, several homomorphic
encryption schemes have been developed that are secure against quantum computing threats(Rupa et al.,2023; Jin et al, 2018). For instance, in healthcare,
HE-based security schemes ensure the privacy and confidentiality of patient data by transforming it into ciphertext before processing. This allows
healthcare data owners to securely process and share encrypted data with external entities, such as storage servers and cloud service providers, without
exposing sensitive information (Chalasani et al.,2023; Sinha eta al., 2023; Jordan et al., 2022; Jafarigol et al., 2023; Archer et al., 2023).
Protecting personal data, particularly health data, is a recognized fundamental right. Patient medical records, which are highly sensitive, must be stored,
processed, and shared with the utmost security and privacy. Protecting these records not only shields individuals from identity theft and fraud, but also
plays a critical role in advancing healthcare research and combating diseases. Healthcare data is collected from numerous sources, including hospitals,
pharmacies, laboratories, insurance companies, and regulatory bodies, and is often referred to as healthcare datasets. As researchers increasingly rely on
these datasets for data modeling, analysis, and visualization, ensuring their privacy becomes a significant concern. Conventional healthcare datasets are
vulnerable to privacy breaches, security attacks, and mismanagement, and secure computation methods, such as HE, offer a practical solution to these
challenges(Chalasani et al.,2023; Sinha eta al., 2023).

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Figure 5: Homomorphic encryption enhances data security for healthcare.
This diagram shows how Homomorphic Encryption (HE)—a powerful encryption method—can be used to secure sensitive data, especially in areas like
healthcare, while addressing important privacy concerns:
a. Homomorphic Encryption Framework
• Data Encryption: Data owners (like individuals or organizations) start by encrypting their data, turning it into a secure, unreadable
format.
• Encrypted Data Transmission: Once encrypted, the data can be safely sent to outside services or cloud storage.
• External Processing Entity: These external entities (like cloud providers) store or process the encrypted data but cannot access its actual
contents, since they don’t have the decryption keys.
• Function Execution on Ciphertext: Even though the data is encrypted, calculations or analyses can still be performed on it, thanks to
homomorphic encryption, ensuring privacy without needing to decrypt the data.
b. Fully Homomorphic Encryption (FHE)
• Introduction of FHE: FHE is a special type of encryption that lets users perform any operation on encrypted data, just as if it were
decrypted.
• Arbitrary Operations on Encrypted Data: This feature allows for complex data processing without compromising data privacy.
• Slow Performance Comparison: A challenge with FHE is that it can be much slower than regular (plaintext) data operations, so making
it faster is a focus of ongoing research.
c. HE Schemes
• Hybrid Security Solutions: HE is often combined with other security measures, creating a layered approach that strengthens protection.
• Quantum Threat Resistance: Some HE schemes are designed to withstand the potential threats posed by future quantum computers,
making them more future-proof.
• Cloud Computing Applications: HE is particularly useful in cloud environments, where sensitive data needs to be processed by external
servers without exposing private information.
d. Healthcare Applications
• Patient Data Encryption: Patient information is encrypted before it is shared or processed, keeping it secure from unauthorized access.
• Secure Data Sharing: Encrypted patient data can be safely shared with other organizations, like hospitals or researchers, without
revealing any personal details.
• Preserving Patient Privacy: This method of sharing encrypted data allows healthcare providers to maintain patient confidentiality, which
is crucial for trust.
• Healthcare Data Collection: With HE, healthcare organizations can securely collect and analyze patient data, supporting valuable
research and improving healthcare outcomes without compromising privacy(Chalasani et al.,2023).
e. Privacy Concerns

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• Risks of Privacy Breaches: Despite strong encryption, privacy risks exist. Protecting sensitive data helps to mitigate these risks.
• Identity Theft Prevention: Encrypted data is much harder to misuse, reducing the risk of identity theft or fraud.
• Importance for Research: Protecting privacy is essential for research, as it encourages data sharing in a way that respects individuals’
confidentiality.
• Conventional Dataset Vulnerabilities: Traditional (unencrypted) datasets are prone to breaches and misuse, making HE a practical
solution for enhancing data security.
Figure 6: Homomorphic Encryption (HE) illustrated
This diagram illustrates how Homomorphic Encryption (HE) protects data in cybersecurity, especially in cloud computing and healthcare(Sharma et
al.,2023). It shows that data owners encrypt their data before sharing it with external services, ensuring that only they have the keys to decrypt it. Fully
Homomorphic Encryption (FHE) allows complex operations on encrypted data without exposing it, enabling secure data analysis in sensitive fields.
Additionally, some HE schemes are resistant to quantum threats, making them a future-proof choice for data privacy(Al-Harrasi, Shaikh & Al-Badi,
2023;Wylde et al., 2022; Riek & Böhme, 2018; Cassim, 2015). Overall, HE allows safe processing and storage of data without compromising privacy.

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4.1. Secure Data Processing
Partial Homomorphic Encryption (PHE) is often applied to algebraic operations like addition and multiplication. For instance, in supervised learning, the
sum is calculated through the linear transformation of data points with weight vectors. Because the encryption system operates linearly, the dot product
can be obtained by expanding the polynomials and linearly combining the results (Munjal & Bhatia, 2022). Threshold prediction can then be achieved
using element-wise operations, such as taking the absolute value of a prediction score for one class and comparing it with prediction scores from other
classes. In the healthcare sector, secure linear regression is commonly used since many machine learning and economic models are linear and require
training on the entire dataset(Basharat et al., 2023; Sinha eta al., 2023). Homomorphic encryption supports secure access to genomic and individual-level
data, allowing more researchers to access raw patient data while maintaining privacy and security ( Riek & Böhme, 2018; Cassim, 2015; Sidorov et al.,
2022).
Homomorphic Encryption (HE), initially proposed by Rivest, Adleman, and Dertouzos, enables operations to be performed directly on encrypted data,
which is not possible with traditional encryption systems. PHE allows for the computation of a single type of operation without the need to access the
secret key. This makes PHE a good fit for applications that require limited operations. RSA and ElGamal are among the simplest examples of PHE
systems, as they can handle only multiplication and addition, respectively. For more complex data processing tasks, Stochastic Partial Homomorphic
Encryption (SPHE) has been developed to minimize statistical errors and avoid the need for multiplication during computations.See the diagram below:
Figure 7: Explains secure data processing through encryption techniques.
4.2. Cloud Computing
Practical homomorphic encryption libraries have the potential to significantly boost cloud and edge computing applications (Fahina et al., 2022; Gilbert
& Gilbert, 2024e). This paper reviews the software and APIs of lattice-based homomorphic encryption libraries that are used in real-world scenarios,
such as running machine learning inferences, executing decentralized smart contracts via blockchains, performing mathematical operations on encrypted
RNA genomic data, facilitating multiparty quantitative finance calculations, and supporting secure face detection and recognition (Gilbert & Gilbert,
2024h). One of the main schemes used in these libraries is based on Ring Learning with Errors (RLWE), which is among the most popular public-key
cryptographic schemes for homomorphic encryption (Agrawal et al., 2020; Gilbert & Gilbert, 2024a).
To assess the effectiveness of homomorphic encryption in cloud computing, we developed a secure, efficient deep-learning model capable of performing
privacy-preserving inference tasks by integrating multiple homomorphic encryption libraries (Gilbert & Gilbert, 2024i; Sri Sathya et al., 2018).
Additionally, we aimed to address issues like overfitting in outsourced environments and demonstrate the versatility of the model by applying it to a
broad range of use cases. Homomorphic encryption facilitates encrypted data computation, enabling collaborative computing between multiple parties
without revealing the underlying data. This capability is critical for widespread adoption and further development, as the technology is essential in fields
such as healthcare, smart grids, and genomics, where stringent privacy requirements are non-negotiable(Sharma et al.,2023).

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Figure 8:Cloud computing enhanced by secure homomorphic encryption.
This diagram (Figure 8) provides an in-depth look at Homomorphic Encryption (HE)—a powerful tool for data security—and illustrates its applications,
challenges, and future potential across various fields.
At the heart of the diagram is an exploration of HE's foundational requirements for widespread adoption. To make HE practical, researchers are focusing
on improving computational efficiency, enabling collaboration, ensuring data privacy, and ultimately increasing adoption across industries. These
elements form the basis for understanding and advancing HE's capabilities(Tao et al., 2019; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek
& Böhme, 2018; Cassim, 2015).
One key area highlighted is the growing list of practical uses and the availability of libraries that support HE implementation. Libraries serve as essential
tools, making it easier for developers and researchers to apply HE in real-world scenarios. The diagram lists practical applications of HE, such as enabling
secure machine learning on encrypted data, supporting decentralized smart contracts for enhanced blockchain security, analyzing sensitive RNA genomic
data while keeping it encrypted, performing private financial calculations across multiple parties, and conducting face detection in a way that preserves
privacy(Tao et al., 2019; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022).
The diagram also introduces different key schemes and underlying technologies that support HE. Ring Learning with Errors (RLWE) is a specific
mathematical foundation within HE that strengthens its security, making it resilient to various threats. Additionally, as a form of public-key cryptography,
HE enables encrypted data operations without needing decryption, which broadens its applications across various sectors where data privacy is paramount.
The fields of application section underscores HE’s role in areas like cloud computing, where it enables secure data processing without revealing sensitive
information. In deep learning, HE allows privacy-preserving inference, enabling AI and machine learning models to make predictions on encrypted data.
Healthcare is another major field benefiting from HE, as it allows patient data to be securely analyzed and shared, protecting patient privacy in medical
research (Basharat et al., 2023; Sharma et al.,2023; Chalasani et al.,2023; Sinha eta al., 2023). In smart grids, HE ensures the privacy of energy data while
enabling efficient analysis. Genomics is another critical area where HE allows researchers to analyze genetic data securely, maintaining privacy in an
especially sensitive domain.
The diagram concludes with the concept of privacy-preserving inference, which is essential for using HE in artificial intelligence and machine learning.
This approach helps prevent overfitting, as models trained on encrypted data maintain privacy, which can lead to more generalized outcomes. Privacy-
preserving inference opens up versatile use cases for HE, from finance and healthcare to genomics, where data analysis needs to be both insightful and
private(;Wylde et al., 2022; Riek & Böhme, 2018; Cassim, 2015).
Overall, the diagram captures the far-reaching potential of Homomorphic Encryption to enable secure data processing in today’s privacy-conscious world.
It showcases how HE can transform sectors like cloud computing, healthcare, and machine learning by enabling data analysis without compromising
privacy, paving the way for a safer and more collaborative data-driven future.

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5. Challenges and Limitations
The implementation of homomorphic encryption as a tool for privacy enforcement can significantly change how healthcare data are stored and processed.
These changes depend on the existing systems and information technology infrastructures in place. As a result, it is crucial to thoroughly assess how this
technology affects confidentiality, integrity, and availability of data, while also maintaining accountability and privacy, and allowing access to information
only when necessary (Dhasarathan et al., 2022; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek & Böhme, 2018; Cassim, 2015)).
Currently, there is a lack of digital platforms specifically designed to handle homomorphic data processing operations that ensure both the privacy of
healthcare data and their secure storage. To address this gap, mechanisms that protect data integrity and confidentiality during processing are essential
for healthcare data management in e-health environments(Basharat et al., 2023; Sharma et al.,2023; Chalasani et al.,2023; Sinha eta al., 2023). The most
promising solutions involve platforms that utilize homomorphic encryption, which has even been proposed for securely handling sensitive data, such as
COVID-19 information (Gilbert & Gilbert, 2024b; Sidorov et al., 2022).
Homomorphic encryption has demonstrated its effectiveness in solving data privacy issues and facilitating the secure use of stored data (Hamza et al.,
2022; Gilbert & Gilbert, 2024c). However, despite its promise, several challenges and limitations still impede its widespread adoption.
Figure 9: Illustrates Homomorphic Encryption's capabilities and applications.
This diagram provides an organized view of Homomorphic Encryption (HE)—an encryption technique that enables computations on encrypted data
without needing to decrypt it first. It shows key aspects such as foundational requirements, applications, supporting technologies, primary fields of use,
and potential future directions for HE.
The overview begins by introducing Homomorphic Encryption and identifying essential requirements for its effective implementation. These include
achieving computational efficiency to ensure operations on encrypted data are not excessively slow, maintaining data privacy so that sensitive information
remains secure, and fostering collaboration among stakeholders( Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek & Böhme, 2018; Cassim,
2015). Together, these elements contribute to broader adoption of HE across various industries, where security and privacy are critical concerns.
The diagram then details practical applications of Homomorphic Encryption, illustrating its versatility across different scenarios. For example, HE
supports secure machine learning by allowing algorithms to analyze encrypted data, which is essential for privacy-sensitive applications. In blockchain,
HE enables decentralized smart contracts, adding a layer of encryption that enhances security (Tao et al., 2019; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde
et al., 2022). It also facilitates sensitive data analysis, such as RNA genomic data, by allowing encrypted processing that keeps the data private. In finance,
HE supports private calculations, enabling organizations to perform financial analyses without revealing confidential information. Additionally, it allows
for privacy-preserving face detection, a feature that keeps biometric data secure.
Supporting technologies play a crucial role in making HE feasible and effective. Key schemes and mathematical foundations, such as Ring Learning with
Errors (RLWE), strengthen HE’s security, making it more resilient to potential threats. Public-key cryptography underpins HE, allowing encrypted
computations to be performed without decryption, which is fundamental for secure data processing across applications.

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HE has a range of valuable applications across several fields. In cloud computing, it provides a way to protect sensitive information stored and processed
in the cloud, maintaining privacy while allowing for data-driven insights. In deep learning and AI, HE enables privacy-preserving inference, allowing
models to work with encrypted data without compromising privacy. The healthcare field benefits significantly from HE, as it allows medical data to be
securely analyzed and shared without risking patient privacy(Chalasani et al.,2023; Sinha eta al., 2023). Smart grids leverage HE to maintain data security
while optimizing energy management. Genomics is another area where HE supports secure analysis of genetic information, preserving the confidentiality
of sensitive genetic data.
Looking to the future, the diagram highlights the potential of HE to advance privacy-preserving inference, a technique that enables AI models to analyze
encrypted data, which can help prevent overfitting and make models more reliable. This capability will allow HE to expand into even more versatile use
cases, reinforcing its role in enhancing data privacy across various industries(Riek & Böhme, 2018; Cassim, 2015)
In summary, this diagram captures the foundational components, applications, and future potential of Homomorphic Encryption. It showcases HE’s
ability to transform data privacy practices across diverse fields by enabling secure data processing, even in sensitive areas like healthcare, finance, and
artificial intelligence. As HE continues to evolve, it promises to play a vital role in securing data-driven insights while upholding the highest standards
of privacy.
5.1. Performance Overhead
Recent studies on practical homomorphic encryption have supported the development of faster and more streamlined schemes. NIST's Post-Quantum
Cryptography Standardization Project has introduced 17 candidate encryption schemes aimed at ensuring safe and accurate public-key cryptography.
Additionally, Deloitte's Cyber Quantities presents a new semi-hard problem that attempts to better replicate legacy encryption compression standards,
offering practical speed improvements (Ajayi, 2016). While web-based solutions are not initially considered, they may serve corporate objectives by
providing useful additions. Cloud-based encryption, however, can be influenced by several factors, such as cushion size and computational complexity,
especially if encryption methods or ciphertexts are known. Certain cryptographic tasks, like generating signatures for custom PowerPoint presentations,
cannot be efficiently managed with homomorphic encryption and commitment. More efficient commitment mechanisms are needed for some scenarios.
For example, the FullISING model has been proven unlearnable unless the structure maintains signature-controlled prime atoms. In this context,
unbounded homomorphic encryption schemes have been proposed using complex systems such as wind systems and atomic integer holds, which address
computational truth problems.
The study of homomorphic encryption began with Brakerski and Vaikuntanathan (2008), who proposed innovative methods to protect data from breaches.
They analyzed popular homomorphic encryption libraries, such as HElib and SEAL. HElib supports encryption and arithmetic operations, while SEAL
includes a variety of fully homomorphic encryption schemes and advanced cryptographic elements for encryption and decryption tasks. Additionally,
new mechanisms for handling discrete logarithms, such as NTRUEncrypt CPA schemes, have been developed to address challenges in expressiveness
and computational complexity. Homomorphic signatures—where both data and the corresponding signatures can undergo encrypted operations—have
also been proposed and are considered secure. However, these models still face constraints, such as limited operations, like the support offered by the
Toeplitz Cipher-Text-Policy Attribute-Based Signature (Archer et al., 2023; Gilbert & Gilbert, 2024d).
One major challenge with homomorphic encryption is the performance overhead. Both Partially Homomorphic Encryption (PHE) and Fully
Homomorphic Encryption (FHE) impose significant computational demands. While FHE allows for more complex operations, it is computationally more
expensive than PHE, which is insufficient for general secure computation because it can only support a limited number of operations. The overhead
results in longer operations, larger key sizes, and ciphertexts that slow down computations compared to traditional methods (Fraz Baig & Eskeland,
2021). Despite this, recent advancements have seen the emergence of homomorphic encryption schemes that support multiple arithmetic operations, such
as the Damgård–Jurik and Fan–Vercauteren schemes (Jafarigol et al., 2023; Gilbert & Gilbert, 2024f). Other notable cryptographic frameworks include
Saber and Crystals–Kyber, which are becoming more prominent in the field.

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Figure 10: Overview of homomorphic encryption performance and challenges.
Figure 10, offers a clear and structured look at the current landscape and future possibilities of Homomorphic Encryption (HE), a type of encryption that
allows data to remain secure even while being processed as below:
The first part, Homomorphic Encryption Overview, introduces the concept of HE and the challenges that come with it, especially around performance.
Because HE requires complex computations on encrypted data, it often leads to performance overhead, meaning it can be much slower than processing
unencrypted data. Researchers are looking at different candidate encryption schemes to improve this balance between security and efficiency. However,
each approach comes with its own challenges and limitations, such as the need for high processing power and specialized resources, which are key
considerations for making HE more practical.
The next section, Establishment of Encryption Schemes, traces the development of HE from early models to more advanced applications. Over time, HE
has evolved with the help of specialized libraries and mechanisms that make it easier to apply in real-world scenarios. The diagram also mentions
homomorphic signatures, a technique that allows someone to verify that calculations on encrypted data are correct without decrypting it. This feature is
important for ensuring trust in the results of encrypted computations. Despite these advances, computational demands—the need for significant processing
power—remain a major obstacle for widespread use.
Performance Considerations dives into one of the biggest challenges of HE: the added computational load, known as overhead, that comes with keeping
data encrypted during processing. The diagram highlights a comparison between Partially Homomorphic Encryption (PHE), which allows limited
operations on encrypted data, and Fully Homomorphic Encryption (FHE), which supports any type of computation. This comparison points to a trade-
off: PHE is faster but less flexible, while FHE allows for complete data processing but is more resource-intensive. Researchers are working on recent
advancements to make these processes faster and less demanding, moving HE closer to practical, everyday use.
Finally, Future Directions outlines where HE could go next. Web-based solutions could make HE more accessible by integrating it directly into online
services. Cloud-based encryption is another exciting possibility, allowing large-scale encrypted data processing in the cloud without compromising
privacy. As HE continues to improve, it may be tailored to custom use cases, serving specific industries like healthcare, finance, and artificial intelligence.
The diagram ends by pointing to emerging technologies that could drive HE forward, such as new computational methods or hardware designed to handle
encryption more efficiently(Basharat et al., 2023).
In totality, this diagram presents Homomorphic Encryption as a promising but challenging technology. It’s clear that HE has the potential to transform
how we process and protect sensitive data, with applications ranging from secure data sharing in the cloud to privacy-preserving AI. As researchers
continue to improve its performance and explore new applications, HE could become a key tool in our increasingly data-driven world.
5.2. Key Management
A successful homomorphic encryption algorithm consists of four key components: key generation, encryption, decryption, and evaluation algorithms that
enable operations within the encrypted domain without revealing intermediate results. While homomorphic encryption ensures secure and accurate
operations, it comes with high costs in terms of bandwidth, storage, and computational resources needed for managing these processes (Gilbert & Gilbert,
2024g; Yeboah, Odabi & Abilimi Odabi, 2016; Jafarigol et al., 2023). For instance, when calculating additions on encrypted confidential data in a PDF,
key generation, data encryption, and decryption algorithms are used. After the plaintext is encrypted using a set of keys {p, q, r}, the encrypted data E(P)

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is generated. The decryption algorithm, outlined in Formula (2), allows users to retrieve the plaintext from the ciphertext, enabling secure computations
like summation.
In this research, we propose the Amplitude Encryption (HE) algorithm, which promises to enhance data security more efficiently and significantly reduce
the resources needed for cloud computing. Homomorphic encryption includes a variety of encryption algorithms that support operations in the encrypted
domain. These operations require only one decryption once all processes are completed. The ISEA encryption algorithm, specifically designed for
homomorphic encryption, uses 2048-bit keys and large data blocks to facilitate a secure and efficient encryption and decryption process. Additionally, it
supports RLT, a widely used homomorphic encryption algorithm that enables arithmetic operations to be performed while the data remains encrypted
(Kwame, Martey & Chris, 2017; Li, 2022; Gilbert & Gilbert, 2024i).
Figure 11: Visualizes homomorphic encryption processes and algorithms.
This figure (Figure 11) gives a comprehensive overview of Homomorphic Encryption (HE)—an advanced encryption method that allows secure data
processing without exposing the original information. Here’s a more accessible explanation of the key parts.
At the top, we see the specific encryption methods used in HE, referred to as Algorithm Specifics. The process starts with Amplitude Encryption, followed
by an initial encryption step called the ISEA (Initial Symmetric Encryption Algorithm), which lays the groundwork for securing the data. Then, the RLT
Algorithm is applied, adding extra layers of security to strengthen the encryption. The goal is to reach a point where Encrypted Data Operations can be
performed—this means that even though the data is encrypted, computations and analyses can still be done directly on it without the need for decryption.
The middle section, Resource Considerations, highlights the technical requirements needed to make HE work smoothly. First, there are Bandwidth
Requirements since encrypted data often takes up more space and requires more bandwidth to transfer. Then, we have Storage Needs because encrypted
data files are generally larger than unencrypted ones. HE also has significant Computational Resource demands, meaning it requires powerful processing
capabilities, especially for more complex operations. Lastly, Efficiency Metrics come into play to measure how well the HE system performs, helping to
ensure that it operates effectively without excessive delays or resource drain.
At the bottom of the diagram, we see the Homomorphic Encryption Process, which outlines how HE works step by step. The process starts with Key
Generation, where unique cryptographic keys are created to keep the data secure. Then, Data Encryption transforms the original data into an unreadable
format to protect it. After that, HE’s core feature—Operations on Encrypted Data—enables computations on the encrypted information without needing
to decrypt it, preserving privacy throughout. Finally, when the analysis or processing is complete, the data undergoes Decryption, where it’s turned back
into its original readable form, revealing the results of the computations only to authorized users.
Overall, this diagram illustrates the process, resource needs, and technical steps involved in Homomorphic Encryption. It highlights both the potential of
HE to enable secure, private data processing and the substantial infrastructure required to support it effectively. This approach is especially useful in
fields where privacy is paramount, as it allows data to be analyzed and used without ever exposing sensitive information.

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6. Improving Efficiency and Performance
The performance of a fully homomorphic encryption (FHE) scheme can be enhanced by several factors. First, the inherent data parallelism during training
plays a crucial role, particularly in highly parallelizable models like deep learning. In such models, the convergence rate is primarily determined by the
layer with the most parameters, meaning that the training time is more closely related to the iterations of this specific layer rather than the total number
of iterations across all layers. Consequently, the time spent on the most computationally demanding layers tends to dominate the overall convergence
speed. This implies that techniques aimed at reducing computational resources for these layers will significantly improve convergence rates (Gong et al.,
2023; Gilbert & Gilbert, 2024m).
Second, the offline and server-side training paradigm is another important factor. In this setup, the server runs the main training process, while numerous
clients provide their local data for updating the global model. Since the server operates as a cloud service, it might face various adversarial threats from
clients. The server cannot decrypt or fully trust any data it receives from clients. While client scheduling strategies, such as weighted federated learning,
can help mitigate these risks, the most secure approach for the server to maintain client privacy is by substituting non-homomorphic weights with
homomorphic encryption (HE) domain weights.
HE enables computations on encrypted data, generating an encrypted output that, when decrypted, matches the result of the same operation performed
on unencrypted data (Gilbert & Gilbert, 2024n; Jafarigol et al., 2023). In Figure 1b, the privacy levels of different methods are illustrated. The model
with the highest privacy and lowest convergence speed is represented by “p.” Each "p" layer detects encrypted true positives (TP) and false positives
(FP). The model retains complete data privacy but requires multiple observations (T PF P 1) to update parameters. Every time the client possesses partially
trained model parameters, there is a risk of data leakage. The most secure solution is to store these parameters between two HE transformations, as this
provides the highest level of privacy. The encrypted parameters do not reveal any information about the real parameters due to the semantic security
provided by HE (Hamza et al., 2022).
The a algorithm to improve efficiency and Performance
The approach to improve the efficiency and performance of a fully homomorphic encryption (FHE) scheme in a federated learning setup, focusing on
ways to optimize training while keeping client data private, as following:
i. Model Setup and Layer Parallelism: Begin by setting up the deep learning model with a focus on the layers that have the most parameters since
these layers will drive the overall training time. By configuring these layers for parallel processing, we can speed up training and take advantage of
the data parallelism inherent in many machine learning models.
ii. Secure Training with Federated Learning: In this setup, a central server coordinates the training process, while multiple clients (devices or users)
contribute their local data to improve the global model. To protect privacy, each client encrypts their data and model parameters using a
homomorphic encryption (HE) scheme before sending it to the server. The server then works with encrypted data throughout the training process
without needing to decrypt it, maintaining data security.
iii. Training Iterations and Parameter Updates: During each training round, clients perform local computations on their data using encrypted model
parameters and send the encrypted results to the server. The server aggregates these encrypted results without decrypting them, using homomorphic
operations to update the global model’s parameters. By prioritizing updates from clients with more relevant data (a technique called weighted
federated learning), the server can improve the model’s accuracy more efficiently.
iv. Ensuring Privacy and Preventing Data Leakage: To further protect privacy, the server stores encrypted model parameters between rounds of training.
These encrypted parameters do not reveal any underlying information about the data, thanks to the HE scheme’s built-in security. For additional
privacy, specific “privacy layers” within the model identify true positives and false positives based on encrypted data, enabling secure parameter
updates without risking data exposure.
v. Convergence and Final Model: After completing all training rounds, the server has a global model trained on encrypted data, ensuring that no
sensitive information was exposed during the process. If necessary, the model can be decrypted to evaluate performance. Once finalized, this trained
model can be shared with clients, retaining any required encryption to protect user privacy.By using parallel processing on key layers, leveraging
encrypted data throughout training, and focusing on privacy-preserving techniques, this approach allows for efficient and secure model training in
federated learning. This balance of performance and privacy helps build robust models without compromising sensitive client data.
7. Findings and Conclusions
7.1 Findings
Widespread Use of Homomorphic Encryption (HE)
Homomorphic encryption (HE) is widely used across various sectors, including healthcare, finance, and cloud computing, as it ensures data privacy by
enabling computations on encrypted data without revealing the plaintext (Basharat et al., 2023; Sharma et al.,2023; Chalasani et al.,2023; Sinha eta al.,

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2023). It has proven to be highly effective in privacy-preserving computations for distributed systems and machine learning applications (Yeboah &
Abilimi, 2013).
Privacy-Preserving Applications
HE is essential for secure data aggregation, query processing, and computations that maintain confidentiality. This technology supports privacy-preserving
analytics in critical industries such as healthcare, where it safeguards sensitive data like medical records and enables secure collaboration without exposing
raw information.
Challenges in Efficiency
Despite its promise, homomorphic encryption faces significant efficiency challenges. Homomorphic operations can substantially increase time and space
complexity, and the performance overhead of fully homomorphic encryption (FHE) remains a significant obstacle to widespread adoption. While FHE
allows for an unlimited number of operations on encrypted data, it comes with high computational demands and slower performance.
Types of Homomorphic Encryption
There are various types of HE schemes, such as Fully Homomorphic Encryption (FHE), Partially Homomorphic Encryption (PHE), and Somewhat
Homomorphic Encryption (SHE), each offering different levels of functionality and computational efficiency. Asymmetric key encryption schemes, like
ElGamal, are often used, with additive homomorphism being one of the most commonly studied properties.
Real-World Applications
Homomorphic encryption is widely applied in real-world cybersecurity, particularly in cloud computing. It enables external entities to process sensitive
data securely without needing to decrypt it (Gilbert & Gilbert, 2024j). In healthcare, HE plays a pivotal role in protecting patient data during secure
computations and facilitating data sharing across platforms without compromising privacy(Basharat et al., 2023; Sharma et al.,2023; Chalasani et al.,2023;
Sinha eta al., 2023).
Security and Cryptography
HE relies on strong cryptographic foundations, such as lattice-based encryption and number theory, to provide a secure framework that ensures the
confidentiality, integrity, and availability of data. These cryptographic tools are critical for maintaining data security, particularly in cloud-based and
distributed environments.
Privacy and Healthcare Data
There is growing interest in using HE to protect healthcare datasets, given the sensitive nature of health-related information. Breaches of privacy in this
area can have severe consequences, including identity theft and fraud, underscoring the importance of secure computation techniques like HE.
Cloud Computing and Multiparty Computation
HE facilitates secure, privacy-preserving computations in cloud computing and multiparty environments, making it ideal for fostering collaboration
without sacrificing data security. This makes HE well-suited for decentralized applications such as secure face recognition, genomic data processing, and
smart contracts.
7.2 Conclusions
Homomorphic Encryption as a Critical Privacy Tool
Homomorphic encryption (HE) has become a crucial technology for maintaining privacy across various applications, including healthcare and cloud
computing. Its ability to perform computations on encrypted data without needing to decrypt it makes HE ideal for secure data processing, especially in
situations involving sensitive information (Gilbert & Gilbert, 2024k; Basharat et al., 2023; Sharma et al.,2023; Chalasani et al.,2023; Sinha eta al., 2023).
Need for Efficiency Improvements
Although HE holds great promise, its widespread adoption is limited by performance challenges, particularly the high computational demands of fully
homomorphic encryption (FHE). Future research should prioritize optimizing these schemes to reduce the computational burden and improve scalability.
Application in Critical Sectors
HE is particularly valuable in sectors like healthcare, where data privacy is a major concern. By enabling secure computations on encrypted health data,
HE protects patient information while allowing researchers and healthcare professionals to carry out critical analyses without compromising privacy.
Future Research Directions
To realize its full potential, future research in HE must focus on overcoming current limitations, such as performance inefficiencies, complex key
management, and the challenges of integrating HE into cloud-based systems. The development of more efficient cryptographic libraries and real-world
applications will be essential for broader adoption of HE technologies.
Balancing Privacy and Performance

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A balance between privacy and performance is essential for the practical implementation of HE. Optimizations in arithmetic and computational
frameworks are needed to make HE a feasible solution for real-time applications, particularly in environments handling large volumes of data.
Impact on Secure Data Communication
HE’s ability to enable secure data processing without exposing sensitive information positions it as a key player in the future of privacy-preserving
communication, especially in distributed and cloud-based systems. This makes HE a fundamental component for secure data communication in various
industries.
8. Future Research Directions
The extensive survey of homomorphic privacy enforcement models highlights the importance of preserving health data privacy, particularly in response
to the COVID-19 pandemic. With the rapid expansion of digital health data, the volume of information generated daily has grown exponentially. A
decade ago, 2.5 exabytes of health data were generated per day, and by 2020, that number had surged to over 44 zettabytes. This 20-fold increase in
digital health data poses significant challenges for data management and security (Sri Sathya et al., 2018). To handle such vast amounts of data, strategies
like authorized storage environments, bandwidth optimization, and live database swapping for hiding personally identifiable information (PII) are
becoming common. However, the lack of adequate data privacy measures could lead to serious issues in the future, such as identity theft or other forms
of cybercrime (2016; Tao et al., 2019; Al-Harrasi, Shaikh & Al-Badi, 2023;Wylde et al., 2022; Riek & Böhme, 2018; Cassim, 2015). In the European
Union (EU), failure to properly secure patient health information could impact policy-making, management, and economic decision-making on a large
scale.
Technological advancements have driven healthcare toward digitization, with an expected 2.5 exabytes of data generated in 2020 alone (Ahmed et al.,
2023; Agrawal & Prabakaran, 2020; Al Kez et al., 2022). As healthcare services move toward precision-based diagnoses, sharing medical data among
patients, healthcare professionals (HCPs), organizations, and researchers becomes increasingly risky due to the potential exposure of PII (Basharat et al.,
2023; Sharma et al.,2023; Chalasani et al.,2023; Sinha eta al., 2023). To mitigate these risks, privacy-preserving (PP) techniques, such as advanced
cryptography-based systems, are crucial to ensuring the security of health data. This study proposes strategies to safeguard private health data, making it
inaccessible to unauthorized servers while ensuring its secure management by national healthcare service providers through the use of secure currencies
and cryptographic measures (Dhasarathan et al., 2022; Scheibner et al., 2021; Gilbert & Gilbert, 2024l).
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