High-Precision Secure Computation of Satellite Collision Probabilities

  • Brett Hemenway
  • Steve LuEmail author
  • Rafail Ostrovsky
  • William Welser IV
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9841)


The costs of designing, building, launching and maintaining satellites make satellite operators extremely motivated to protect their on-orbit assets. Unfortunately, privacy concerns present a serious barrier to coordination between different operators. One obstacle to improving safety arises because operators view the trajectories of their satellites as private, and refuse to share this private information with other operators. Without data-sharing, preventing collisions between satellites becomes a challenging task. A 2014 report from the RAND Corporation proposed using cryptographic tools from the domain of secure Multiparty Computation (MPC) to allow satellite operators to calculate collision probabilities (conjunction analyses) without sharing private information about the trajectories of their satellites.

In this work, we report on the design and implementation of a new MPC framework for high-precision arithmetic on real-valued variables in a two-party setting where, unlike previous works, there is no honest majority, and where the players are not assumed to be semi-honest. We show how to apply this new solution in the domain of securely computing conjunction analyses. Our solution integrates the integer-based Goldreich-Micali-Wigderson (GMW) protocol and Garbled Circuits (GC). We prove security of our protocol in the two party, semi-honest setting, assuming only the existence of one-way functions and Oblivious Transfer (the OT-hybrid model). The protocol allows a pair of satellite operators to compute the probability that their satellites will collide without sharing their underlying private orbital information. Techniques developed in this paper would potentially have a wide impact on general secure numerical analysis computations. We also show how to strengthen our construction with standard arithmetic message-authentication-codes (MACs) to enforce honest behavior beyond the semi-honest setting.

Computing a conjunction analysis requires numerically estimating a complex triple integral to a high degree of precision. The complexity of the calculation, and the possibility of numeric instability presents many challenges for MPC protocols which typically model calculations as simple (integer) arithmetic or binary circuits. Our secure numerical integration routines are extremely stable and efficient, and our secure conjunction analysis protocol takes only a few minutes to run on a commodity laptop.

The full version appears in [HLOW16].


Conjunction Analysis Secure Computation Satellite Operator Oblivious Transfer Multiplication Gate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by the DARPA. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation therein. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interptered as necessarily representing the official policies or endorsement, either expressed or implied, of DARPA, or the U.S. Government.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Brett Hemenway
    • 1
  • Steve Lu
    • 2
    Email author
  • Rafail Ostrovsky
    • 3
  • William Welser IV
    • 4
  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.Stealth Software Technologies, Inc.Los AngelesUSA
  3. 3.University of CaliforniaLos AngelesUSA
  4. 4.RAND CorporationSanta MonicaUSA

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