Collision Risk Analysis for LEO Satellites with Confidential Orbital Data

TL;DR

This contribution proposes a solution based on fully homomorphic encryption (FHE) that enables secure and private collision risk analysis and thus enables secure and private collision risk analysis.

Abstract

The growing number of satellites in low Earth orbit (LEO) has increased concerns about the risk of satellite collisions, which can ultimately result in the irretrievable loss of satellites and a growing amount of space debris. To mitigate this risk, accurate collision risk analysis is essential. However, this requires access to sensitive orbital data, which satellite operators are often unwilling to share due to privacy concerns. This contribution proposes a solution based on fully homomorphic encryption (FHE) and thus enables secure and private collision risk analysis. In contrast to existing methods, this approach ensures that collision risk analysis can be performed on sensitive orbital data without revealing it to other parties. To display the challenges and opportunities of FHE in this context, an implementation of the CKKS scheme is adapted and analyzed for its capacity to satisfy the theoretical requirements of precision and run time.

Figures (3)

• Figure 1: Representation of satellite $s_1$ as sphere with combined radius $r=r_1+r_2$ and satellite $s_2$ as point particle with combined covariance matrix. Additionally, the encounter plane normal to the relative velocity as well as the projection of $s_1$ and $s_2$ onto the plane are displayed. Inspired by CloseApproach.
• Figure 2: Illustration of the Trapezoidal rule, the Simpson's rule and the Gaussian quadrature of order 3 (red) for the function $y\mapsto f(y)=ye^{-\frac{1}{2}y^2}$ (blue). The marked points are used to calculate the approximation.
• Figure 3: Visualization of addition and mulitplication in somewhat homomophic schemes as well as the bootstrapping technique for noise reduction.

Theorems & Definitions (1)

• Remark 1