Securing Control in Cyber-Physical Systems

In today's world, protecting information is very important, especially in systems that combine physical devices and computers. These systems can be targeted by attacks that could cause serious damage. Encrypted Control is a method that allows controllers to manage these systems while keeping the data secure. By using special types of encryption, controllers work directly with encrypted data without needing to decrypt it, which helps maintain privacy throughout the process.

This paper discusses a way to encrypt controllers for linear dynamic systems. This method allows for multiple operations on encrypted data without needing to reset the encryption. In simpler terms, it enables controllers to perform many calculations on data while still keeping that data safe from outsiders.

#Challenges in Encrypted Control

When using encrypted control, several challenges arise, particularly related to how data is handled. Many control parameters are real numbers, which need to be converted into integers for encryption. This conversion process can lead to problems, as the size of the data can grow quickly and exceed the limits of the encryption system.

Another issue involves the accumulation of Errors in the data. When operations are performed multiple times, errors can build up, affecting the performance of the control system. Previous methods used additional techniques to manage these errors, but such techniques can be impractical for real-time applications.

#Our Approach

We propose a new way to encrypt linear dynamic controllers. Our method allows for multiple calculations on the encrypted data without needing to reset the encryption. This is possible because we use a special kind of encryption based on polynomial rings that injects errors in a way that can be controlled.

The core idea is that only certain parts of the errors, specifically the constant terms, are important for the performance of the controller. These parts can be managed through stability in the control loop, meaning that even if other parts of the errors become large, they won't necessarily affect the system's performance.

#Key Components

#Encryption Method

The encryption method we use involves creating polynomials that represent the data. This allows the controller to perform operations on encrypted data without needing to decrypt it first. Our method also includes a Packing Algorithm that combines multiple pieces of data into a single polynomial. This reduces the number of operations needed and improves how efficiently memory is used.

#Packing Algorithm

The packing algorithm is a fundamental part of our approach. By storing multiple messages in one polynomial, we can perform operations on many pieces of data at once. This not only speeds up the calculations but also makes better use of memory resources.

When data is processed through this algorithm, it remains encrypted throughout the process. This means that even while being manipulated for control purposes, the data stays secure from any potential threats.

#Impact of Errors

Errors are a significant concern in any control system, especially when encryption is involved. In our approach, we show that the growth of these errors can be kept within safe limits through the stability of the control system.

We find that as long as the parameters are chosen correctly, the performance of the encrypted controller can remain consistent, regardless of how many calculations are performed. This means it is possible to manage the control processes effectively without the need for re-encryption.

#Simulation Results

To demonstrate the effectiveness of our method, we conducted simulations using a model of an aircraft. The model was designed around specific flight conditions and tested various settings for the encrypted controller.

The results showed that the performance of our encrypted control method remained within acceptable limits throughout the tests. The coupling of our packing algorithm with the Ring-LWE-based encryption allowed for efficient performance without compromising security.

#Conclusion

We have introduced a new method for encrypting linear dynamic controllers using a specific type of encryption that supports multiple calculations without the need for resetting encryption. This allows controllers to maintain privacy and security while performing their necessary functions in cyber-physical systems.

By focusing on the stability of the control system and utilizing innovative techniques like a packing algorithm, we addressed key challenges in encrypted control effectively. Our results suggest that this method is practical for real-time applications and can significantly enhance the security of critical systems.