Encrypted Computation of Collision Probability for Secure Satellite Conjunction Analysis

TL;DR

The paper tackles the privacy challenges in computing satellite conjunction risk by introducing Encrypted $\mathcal{P}_c$, a protocol that embeds Monte Carlo estimation of collision probability into a three-party MPC/HE framework. By combining Monte Carlo methods with homomorphic encryption and secure computation, the approach allows two independent satellite operators and a cloud server to jointly compute $\mathcal{P}_c$ without revealing sensitive orbital data. Key contributions include the design of subprotocols that (i) securely derive the transformation to the conjunction plane, (ii) generate encrypted MC samples for the aggregate covariance, and (iii) perform secure comparisons to estimate $\mathcal{P}_c$, with discussion of potential protocols for secure comparison (e.g., DGK, Yao’s, sigmoid bootstrapping). The work aims to advance secure SSA and privacy-preserving data sharing among stakeholders, offering a practical pathway to safer, more cooperative space operations in a privatized orbital environment.

Abstract

The computation of collision probability ($\mathcal{P}_c$) is crucial for space environmentalism and sustainability by providing decision-making knowledge that can prevent collisions between anthropogenic space objects. However, the accuracy and precision of $\mathcal{P}_c$ computations is often compromised by limitations in computational resources and data availability. While significant improvements have been made in the computational aspects, the rising concerns regarding the privacy of collaborative data sharing can be a major limiting factor in the future conjunction analysis and risk assessment, especially as the space environment grows increasingly privatized, competitive, and fraught with conflicting strategic interests. This paper argues that the importance of privacy measures in space situational awareness (SSA) is underappreciated, and regulatory and compliance measures currently in place are not sufficient by themselves, presenting a significant gap. To address this gap, we introduce a novel encrypted architecture that leverages advanced cryptographic techniques, including homomorphic encryption (HE) and multi-party computation (MPC), to safeguard the privacy of entities computing space sustainability metrics, inter alia, $\mathcal{P}_c$. Our proposed protocol, Encrypted $\mathcal{P}_c$, integrates the Monte Carlo estimation algorithm with cryptographic solutions, enabling secure collision probability computation without exposing sensitive or proprietary information. This research advances secure conjunction analysis by developing a secure MPC protocol for $\mathcal{P}_c$ computation and highlights the need for innovative protocols to ensure a more secure and cooperative SSA landscape.

Figures (4)

• Figure 1: The mean absolute error (MAE) between the integral and the Monte Carlo approaches for computing $\mathcal{P}_c$.
• Figure 2: Monte Carlo Simulation to compute $\mathcal{P}_c$
• Figure 3: Architecture of Encrypted $\mathcal{P}_c$ protocol: a series of subprotocols $\pi_{i=1, \cdots, 3}$ make up the entire protocol $\Pi$, which is jointly run by three parties: orange (left) and maroon (right) satellite operators (Operator $1$ and $2$) each holding their secret keys $\mathsf{sk}_{2}^{1}$ and $\mathsf{sk}_{2}^{2}$, respectively, and the coordinator (cloud server) holding $\mathsf{sk}_1$ to assist the protocol. Public keys ($\mathsf{pk}_{1}$, $\mathsf{pk}_{1}^{1,2}$) are avaiable for all.
• Figure 4: Pictorial illustration of $\Pi:$ Encrypted $\mathcal{P}_c$ with its subroutines $\pi_{1, 2, 3}$.