Decentralized FHE Vector Database

The vector database is designed to store and manage FHE-encrypted vectors efficiently. Key features include:

Scalability:

The decentralized vector database is designed to efficiently manage and process large vol- umes of encrypted data. Its architecture supports scalability, making it suitable for applications with extensive datasets. This is achieved through distributed storage and computation, al- lowing the system to handle increasing data loads and query demands without compromising performance or security.

Query Optimization:

The database is engineered for efficient querying of encrypted data. It employs techniques such as Hierarchical Navigable Small Worlds (HNSW) to facilitate secure and precise vec- tor searches. This optimization ensures that search operations are performed swiftly, even with large datasets, by minimizing query times and maximizing retrieval accuracy within the encrypted domain. To demonstrate how this will work for a Distributed Database of CKKS Encrypted Vectors, we will provide an Algorithm and a diagram in Figure 2:

Step 1:

Build the HNSW Index

• Construct the HNSW index for the encrypted vectors distributed across multiple nodes.

• Each node builds a local HNSW index for the encrypted vectors it stores.

• Nodes communicate to share metadata about their local indices, such as the structure of the HNSW layers and representative points.

Step 2:

Query Initialization

• A query vector, encrypted using CKKS, is submitted to the distributed system.

• The query is first processed to identify the initial entry points for the search. These entry points can be either locally stored vectors or representative points from other nodes.

Step 3:

Distributed Search Coordination

• The search process is coordinated across multiple nodes to find the k-nearest neighbors.

• Coordinator Node: Designate a node as the coordinator for the query. This node manages the search process and aggregates results from other nodes.

Step 4:

Local Search

• Perform a local HNSW search on each node using the encrypted query vector.

• Each node starts the search from its local entry points and explores the HNSW graph to find approximate nearest neighbors.

• The search uses homomorphic computations to compare the query vector with the en- crypted vectors stored locally.

Step 5:

Communication and Aggregation

• Nodes communicate their local search results to the coordinator node.

• The results include distances and identifiers of the nearest neighbors found in each local search.

• Communication is performed securely to maintain the confidentiality of the encrypted vectors.

Step 6:

Global Aggregation and Finalization

• The coordinator node aggregates the local search results to determine the global k- nearest neighbours.

• It combines and sorts the results based on the homomorphically computed distances.

• The coordinator node may request additional local searches if needed to refine the re- sults.

Step 7:

Return Results

• The coordinator node decrypts the final k-nearest neighbors (if permissible) and returns the results to the querying entity.

• The results include the nearest neighbor vectors and their corresponding distances to the query vector.

Figure 2

Fully Homomorphic Encryption Integration for LLM Training

To further enhance security and privacy, our system allows Large Language Models (LLMs) to process encrypted inputs without ever decrypting them. This is achieved through the following methods: Secure LLM Training: Large Language Models (LLMs) are trained directly on encrypted data, ensuring the confidentiality of sensitive information throughout the training process. This method adheres to privacy and compliance standards, such as GDPR and HIPAA, by maintaining data encryption at all stages. Hence, it protects sensitive data from unauthorized access or exposure. Optimized Computation: The integration of CKKS with Zama-ai enables efficient arithmetic operations on encrypted data, crucial for the resource-intensive process of training LLMs. Techniques to manage noise and maintain computational accuracy ensure the feasibility of training sophisticated models on encrypted data.