# Homomorphic Encryption

## <mark style="color:green;">**Decentralized Model Training with Homomorphic Encryption**</mark>



<figure><img src="https://3382609217-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FJHAcIqOUNM2gXyHb9rrl%2Fuploads%2FHgLL17lUo23oQLi9SDF8%2Fimage.png?alt=media&#x26;token=8a0f628b-8dbd-4f19-b1e6-1e9a87b17fab" alt=""><figcaption><p>Decentralized Model Training</p></figcaption></figure>

This image depicts a decentralized model training utilizing homomorphic encryption to ensure privacy during AI training. Here's how the process works:

Data owners, each with their unique secret keys, encrypt their local gradients, which are partial computations derived from their data. These encrypted gradients are then sent to an aggregator. The role of the aggregator is crucial—they sum up all the encrypted gradients from the data owners. It's important to note that this aggregation happens while the gradients are still encrypted, preserving the privacy of individual data contributions.

Once the aggregator has combined all the encrypted gradients, they send the aggregated encrypted gradient, along with a public key, to the trainer. The trainer uses this public key to decrypt the aggregated gradient and update the model's parameters. This decryption step does not reveal individual data or gradients but only the combined information, ensuring that the trainer cannot reverse-engineer or access the original data.

Homomorphic encryption is the underlying magic that makes this process secure. It's a form of encryption that allows computations to be carried out on ciphertexts, generating an encrypted result that, when decrypted, matches the result of operations performed on the plaintexts. This means that data can be encrypted and processed without ever being exposed in its raw form, ensuring that personal or sensitive information remains confidential throughout the training process.

This method strikes a balance between leveraging valuable data for AI development and upholding stringent privacy standards, thus facilitating a collaborative AI training environment where data owners can contribute to model improvement without compromising data security.

## <mark style="color:green;">**Homomorphic Encryption**</mark>

A cloud computing security solution based on fully homomorphic encryption

The process of homomorphic encryption:

<figure><img src="https://lh7-us.googleusercontent.com/l5vbVmKir-Ty1MYjJrY7w9hI8dl3w38_bZIJq4x95gwuGf01wdS5qB8DcPZhcwx9uLwSUj9gf4qopZY3V2Smi2Y8PlDLEHuITuk2BtxybWWkE6hCgfo47OFZvULmCo1XhrfRYySJ7_WvE0BN4EjsCqs" alt=""><figcaption><p>Process of HE</p></figcaption></figure>



<figure><img src="https://lh7-us.googleusercontent.com/C0Q-zW1Dr6CEVVTJcIQ3LhLspnPxbyXHHkaUZPhGlxBHHABblVrUTC-TI4uM__RTgWQpyJ-u55enz3Ql63PXNwMOhjzPXJPTvdc7lO9Snd5bxgN-wYC56c7WWpATQ74ijHTA3ivTCX7uB2U6UH1U2WU" alt=""><figcaption><p>Continued</p></figcaption></figure>

Craig Gentry constructs a homomorphism encryption scheme including 4 methods. They are the key generation algorithm, encryption algorithm, decryption algorithm, and additional Evaluation algorithm. Fully homomorphic encryption includes two basic homomorphism types. They are the multiply homomorphic encryption algorithm and additively homomorphic encryption algorithm. The multiplication and addition with Homomorphic properties. Homomorphic encryption algorithm supports only addition homomorphism and multiplication homomorphism before 2009\[4]. Fully homomorphic encryption is to find an encryption algorithm, which can be any number of addition algorithm and multiplication algorithm in the encrypted data. For simply, this paper uses a symmetrical fully encryption homomorphic algorithm proposed by Craig Gentry.

<figure><img src="https://lh7-us.googleusercontent.com/HF_tB--JaRIF5JW1WopWtkJ2JEqATI2jjALdBv8egrShGsDLxJvec4COLUtx_wBn3QNddN6vC86ax8uDT1TcJ7kQhKetr94jG4vOa1Ncg1mofp71f_Zd3edLTprfxMCPVNjPRRSwpOzQ13uQYM8O79g" alt=""><figcaption></figcaption></figure>

Privacy Protection: User transmit and save their data to the cloud by encrypted. Both ensure the security of data in the process of transmission and ensure safe storage of data. Although the cloud computing service providers handle it, they can’t easily obtain the information of plaintext.

Data Processing: A fully homomorphic encryption mechanism enables users or the trusted third party to process ciphertext data directly, instead of the original data. Users can obtain arithmetic results to decrypt to get good data. For example, in the medical information system, electronic medical records are in the ciphertext stored in the cloud server. When the health department deals with potential safety problems, they must know some areas of certain disease locations and age distribution. They can give encrypted electronic medical record data to professional data processing services. Then they can get the correct data after decryption.

The Ciphertext Retrieval: Fully homomorphic encryption technology based on the ciphertext retrieval method can search directly on the ciphertext data. It not only ensures query privacy and improves the efficiency of retrieval but the retrieval data can be added and multiplied without changing the corresponding plaintext. Three generations of network defense technologies have appeared in the past. In the first generation, tools were designed to prevent or avoid intrusions. These tools usually manifested themselves as access control policies or tokens, cryptographic systems, and so forth. However, an intruder could always penetrate a secure system because there is always a weak link in the security provisioning process. The second generation detected intrusions promptly to exercise remedial actions. These techniques included firewalls, intrusion detection systems (IDSes), PKI services, reputation systems, and so on. The third generation provides more intelligent responses to intrusions.



## <mark style="color:green;">**Privacy in Data Utilization**</mark>

The utilization of data, particularly in training machine learning models, is a double-edged sword. While it offers the promise of significant advancements in technology and society, it also poses substantial risks to individual privacy and data security. Personal data, ranging from medical records to financial information, is invaluable for training models that can predict diseases, optimize financial services, or enhance customer experiences. However, the exposure of such sensitive information without adequate protection can lead to grave privacy violations and security breaches.

### <mark style="color:green;">**Homomorphic Encryption and Machine Learning**</mark>

Integrating homomorphic encryption into machine learning processes is not without its challenges. The computational complexity and processing time associated with HE have historically been significant barriers to its widespread adoption. However, ongoing advancements in algorithms and hardware acceleration techniques are steadily overcoming these hurdles, making HE more feasible for practical applications.

In the context of machine learning, HE allows for the development of models that can learn from data they never "see" in the unencrypted form. This opens up new paradigms for privacy-preserving machine learning, where data owners can contribute to collective learning efforts without relinquishing control over their data. Furthermore, it enables the creation of secure multi-party computation frameworks where multiple entities can collaboratively train models without exposing their proprietary or sensitive data to each other.

### <mark style="color:green;">**Broader Implications for Artificial Intelligence**</mark>

The integration of encryption techniques like homomorphic encryption into data utilization processes has broader implications for the future of artificial intelligence. As AI systems become increasingly integrated into everyday life, ensuring their development and operation do not compromise privacy is essential. Privacy-preserving techniques allow for the expansion of AI applications into areas where privacy concerns might otherwise limit their use.

Moreover, the ability to securely leverage vast amounts of data without compromising privacy could accelerate the development of more sophisticated and accurate AI models. This, in turn, could lead to breakthroughs in personalized medicine, financial security, and personalized consumer services, among other areas.

### <mark style="color:green;">**The Future of Privacy in Data Utilization**</mark>

Looking forward, the field of privacy-preserving data utilization is ripe for innovation. Advances in encryption technologies like fully homomorphic encryption, secure multi-party computation, and differential privacy are paving the way for a new era of secure and private data analysis. These technologies promise to enhance the capabilities of machine learning models while safeguarding the privacy of the data they learn from.

As machine learning and AI continue to evolve, the importance of privacy-preserving techniques will only grow. The development of efficient, scalable encryption methods will be crucial in enabling the widespread adoption of privacy-preserving machine learning. Meanwhile, collaboration between technologists, policymakers, and ethicists is essential to ensure these technologies are used responsibly and for the public good.

