Enhancing Privacy with Private Join and Compute

Enhancing Privacy with Private Join and Compute

Table of Contents:

1. Introduction
2. Problem Statement
3. Hypothetical Applications
4. Solution Strategy
5. Building the Extended Period Default
6. Combining Pure and Garble Bloom Filters
7. Experimental Costs and Results
8. Extending the Protocol
9. Conclusion

Introduction

In this article, we will discuss the concept of pure default and its applications. We will explore a problem called "inner join private join and compute" and look at ways to solve it. The goal is for a user to find the inner product of their dataset with a server's dataset, only for the values that are present in both datasets. Privacy and communication cost are key factors to consider in the solution.

Problem Statement

The problem We Are trying to solve is called "inner join private join and compute". It involves a user with multiple IDs and associated weights, and a server with a larger database containing more IDs and associated weights. The user needs to find the inner product of their dataset with the server's dataset, only for the values that are present in both datasets. Additionally, privacy and communication cost should be optimal.

Hypothetical Applications

There are several hypothetical applications where the concept of pure default can be utilized. Two examples are:

1. Exposure Notification: This application involves a user's dataset consisting of Bluetooth IDs and associated proximity values, and a server's dataset containing IDs of users infected with a particular disease and associated variance values. The inner join private join and compute can be used to determine the likelihood of the user being infected with the disease Based on proximity and variance values.
2. Ad Effectiveness Measurement: In this application, the user is a merchant with IDs and spend values, and the server is an ad tech company with user IDs who have seen a particular ad. The inner join private join and compute can be used to calculate the weighted conversion credit that should be given to the ad tech company based on spend values and time decayed ad effects.

Solution Strategy

To solve the problem of inner join private join and compute, we propose a secure multi-party computation protocol. The protocol involves using an extended period default, which allows the user to retrieve either the product of associated values or a default value, masked with a random mask. This ensures that the user cannot determine whether it received the product or the default value. The protocol also incorporates the use of bloom filters and garble bloom filters to handle keywords and associated values efficiently.

Building the Extended Period Default

To build the extended period default, we use a variant of private information retrieval protocol and modify it to retrieve a default value instead of garbage when the queried keyword is not present. We also introduce random masks to further hide the received values. This construction allows the user to retrieve either the product of associated values or a default value, depending on whether the keyword is present in the server's dataset.

Combining Pure and Garble Bloom Filters

To handle keywords and associated values efficiently, we combine pure queries and garble bloom filters. The server creates a garble bloom filter out of its key-value pairs, and the user sends encrypted indices to query the bloom filter. The server processes these queries and sends back masked values. By combining the results from pure queries and garble bloom filter queries, the user can retrieve the desired values while maintaining privacy.

Experimental Costs and Results

In our experiments, we measured the communication costs and total monetary costs of our implementation. The results showed that our protocol achieves low communication costs, especially when there is a large gap between the server's dataset size and the client's dataset size. The total monetary costs are competitive, with offloading a significant portion of the costs to the server. We also compared our protocol with existing works and found that it outperforms them in terms of communication costs.

Extending the Protocol

Our protocol can be extended to support other functions besides the inner join. It can also handle computations other than sums, as long as the function is supported by the underlying homomorphic encryption scheme. Additionally, optimizations such as Parallel queries and cuckoo hashing can be applied to further reduce costs and improve efficiency.

Conclusion

In conclusion, the concept of pure default and the solution strategy of inner join private join and compute provide a secure and privacy-preserving way to calculate the inner product of datasets. The use of extended period default, bloom filters, and garble bloom filters contributes to efficient and confidential computations. Our experiments Show promising results in terms of communication costs and total monetary costs. With further extensions and optimizations, this protocol can be applied to various real-world scenarios requiring privacy-preserving computations.

Highlights:

• Introduction to the concept of pure default and its applications
• Problem statement of inner join private join and compute
• Hypothetical applications in exposure notification and ad effectiveness measurement
• Solution strategy using secure multi-party computation protocol
• Building the extended period default for efficient retrieval of associated values
• Combining pure and garble bloom filters for improved privacy
• Experimental costs and results showing low communication costs
• Extensibility of the protocol to support various functions and computations
• Conclusion highlighting the benefits and potential applications of the protocol

FAQ:

1. What is pure default?

   • Pure default is a concept in which a user can retrieve either the product of associated values or a default value, while maintaining privacy.

2. What is the inner join private join and compute problem?

   • The inner join private join and compute problem involves finding the inner product of a user's dataset with a server's dataset, only for the values that are present in both datasets, while ensuring privacy and low communication costs.

3. How can the inner join private join and compute protocol be applied to exposure notification?

   • By utilizing inner join private join and compute, exposure notification systems can calculate the likelihood of a user being infected with a disease based on proximity values and variance weights, while preserving privacy.

4. How does the combining of pure and garble bloom filters enhance privacy?

   • Pure and garble bloom filters allow for efficient retrieval of associated values while hiding the specific items and intersection size, ensuring privacy in computations.

5. Is the inner join private join and compute protocol cost-effective?

   • Yes, the protocol achieves low communication costs and total monetary costs, particularly when there is a large difference in dataset sizes between the user and the server.