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High-Precision Secure Computation of Satellite Collision Probabilities

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Book cover Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

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].

B. Hemenway—Work done while consulting for RAND Corporation.

R. Ostrovsky—Work done while consulting for Stealth Software Technologies, Inc.

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Notes

  1. 1.

    An alternative approach using Garbled RAM [LO13, GHL+14] avoids the problem of converting the calculation to a circuit. Practical implementations of GRAM is an interesting area to be explored.

  2. 2.

    These covariance matrices are usually assumed to be diagonal, i.e., the variances along the three principal axes are independent. This assumption does not significantly affect the computation.

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Acknowledgements

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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Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, USA

    Brett Hemenway

  2. Stealth Software Technologies, Inc., Los Angeles, USA

    Steve Lu

  3. University of California, Los Angeles, USA

    Rafail Ostrovsky

  4. RAND Corporation, Santa Monica, USA

    William Welser IV

Authors
  1. Brett Hemenway
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  2. Steve Lu
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  3. Rafail Ostrovsky
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  4. William Welser IV
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Corresponding author

Correspondence to Steve Lu .

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Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Hemenway, B., Lu, S., Ostrovsky, R., Welser IV, W. (2016). High-Precision Secure Computation of Satellite Collision Probabilities. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_9

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