Advertisement

Secure Multi-party Computation for Cloud-Based Control

  • Andreea B. AlexandruEmail author
  • George J. Pappas
Chapter

Abstract

In this chapter, we will explore the cloud-outsourced privacy-preserving computation of a controller on encrypted measurements from a (possibly distributed) system, taking into account the challenges introduced by the dynamical nature of the data. The privacy notion used in this work is that of cryptographic multi-party privacy, i.e., the computation of a functionality should not reveal anything more than what can be inferred only from the inputs and outputs of the functionality. The main theoretical concept used towards this goal is Homomorphic Encryption, which allows the evaluation of sums and products on encrypted data, and, when combined with other cryptographic techniques, such as Secret Sharing, results in a powerful tool for solving a wide range of secure multi-party problems. We will rigorously define these concepts and discuss how multi-party privacy can be enforced in the implementation of a Model Predictive Controller, which encompasses computing stabilizing control actions by solving an optimization problem on encrypted data.

References

  1. 1.
    Alexandru AB, Gatsis K, Shoukry Y, Seshia SA, Tabuada P, Pappas GJ (2018) Cloud-based quadratic optimization with partially homomorphic encryption. arXiv preprint arXiv:1809.02267
  2. 2.
    Alexandru AB, Morari M, Pappas GJ (2018) Cloud-based MPC with encrypted data. In: IEEE conference on decision and control (CDC), pp 5014–5019Google Scholar
  3. 3.
    Alexandru AB, Pappas GJ (2019) Encrypted LQG using Labeled Homomorphic Encryption. In: 10th ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS), pp 129–140Google Scholar
  4. 4.
    Ali M, Khan SU, Vasilakos AV (2015) Security in cloud computing: opportunities and challenges. Inf Sci 305:357–383MathSciNetCrossRefGoogle Scholar
  5. 5.
    Archer D, Chen L, Cheon JH, Gilad-Bachrach R, Hallman RA, Huang Z, Jiang X, Kumaresan R, Malin BA, Sofia H, Song Y, Wang S (2017) Applications of homomorphic encryption. Technical report, Microsoft ResearchGoogle Scholar
  6. 6.
    Aslett LJ, Esperança PM, Holmes CC (2015) A review of homomorphic encryption and software tools for encrypted statistical machine learning. arXiv preprint arXiv:1508.06574
  7. 7.
    Barbosa M, Catalano D, Fiore D (2017) Labeled homomorphic encryption. In: European Symposium on Research in Computer Security, pp 146–166. Springer, ChamGoogle Scholar
  8. 8.
    Beimel A (2011) Secret-sharing schemes: a survey. In: International conference on coding and cryptology, pp 11–46. Springer, BerlinGoogle Scholar
  9. 9.
    Bellare M, Hoang VT, Rogaway P (2012) Foundations of garbled circuits. In: Conference on computer and communications security, pp 784–796. ACMGoogle Scholar
  10. 10.
    Bellovin SM (2011) Frank Miller: inventor of the one-time pad. Cryptologia 35(3):203–222CrossRefGoogle Scholar
  11. 11.
    Borrelli F, Bemporad A, Morari M (2017) Predictive control for linear and hybrid systems. Cambridge University PressGoogle Scholar
  12. 12.
    Bost R, Popa RA, Tu S, Goldwasser S (2015) Machine learning classification over encrypted data. In: Network & distributed system security symposium (NDSS)Google Scholar
  13. 13.
    Botta A, De Donato W, Persico V, Pescapé A (2016) Integration of cloud computing and internet of things: a survey. Future Gener Comput Syst 56:684–700CrossRefGoogle Scholar
  14. 14.
    Catalano D, Fiore D (2015) Boosting linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data. Cryptology ePrint Archive, Report 2014/813. https://eprint.iacr.org/2014/813
  15. 15.
    Catalano D, Fiore D (2015) Using linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data. In: 22nd ACM SIGSAC conference on computer and communications security, pp 1518–1529. ACMGoogle Scholar
  16. 16.
    Chase M, Gilad-Bachrach R, Laine K, Lauter K, Rindal P (2017) Private collaborative neural network learning. Technical report, Cryptology ePrint Archive, Report 2017/762 . https://eprint.iacr.org/2017/762
  17. 17.
    Chen H, Gilad-Bachrach R, Han K, Huang Z, Jalali A, Laine K, Lauter K (2018) Logistic regression over encrypted data from fully homomorphic encryption. BMC Med Genomics 11(4):81CrossRefGoogle Scholar
  18. 18.
    Couteau G (2016) Efficient secure comparison protocols. Cryptology ePrint Archive, Report 2016/544. http://eprint.iacr.org/2016/544
  19. 19.
    Cramer R, Damgård I, Nielsen JB (2012) Secure multiparty computation and secret sharing-an information theoretic approach. Book draftGoogle Scholar
  20. 20.
    Cramer R, Damgård IB, Nielsen JB (2015) Secure multiparty computation. Cambridge University PressGoogle Scholar
  21. 21.
    Damgård I, Geisler M, Krøigaard M (2007) Efficient and secure comparison for on-line auctions. In: Australasian conference on information security and privacy, pp 416–430. Springer, BerlinGoogle Scholar
  22. 22.
    Damgård I, Geisler M, Krøigaard M (2009) A correction to "Efficient and secure comparison for on-line auctions". Int J Appl Cryptogr 1(4):323–324MathSciNetCrossRefGoogle Scholar
  23. 23.
    Damgård I, Orlandi C (2010) Multiparty computation for dishonest majority: from passive to active security at low cost. In: Annual cryptology conference, pp 558–576. SpringerGoogle Scholar
  24. 24.
    Damgård IB, Jurik M (2001) A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: International workshop on public key cryptography, pp 119–136. Springer, BerlinGoogle Scholar
  25. 25.
    Dwork C (2008) Differential privacy: a survey of results. In: International conference on theory and applications of models of computation, pp 1–19. Springer, BerlinGoogle Scholar
  26. 26.
    Dwork C, Kenthapadi K, McSherry F, Mironov I, Naor M Our data, ourselves: privacy via distributed noise generation. In: Annual international conference on the theory and applications of cryptographic techniques, pp 486–503. Springer (2006)Google Scholar
  27. 27.
    Dwork C, Roth A et al (2014) The algorithmic foundations of differential privacy. Found Trends® Theor Comput Sci 9(3–4), 211–407Google Scholar
  28. 28.
    Farokhi F, Shames I, Batterham N (2017) Secure and private control using semi-homomorphic encryption. Control Eng Pract 67:13–20CrossRefGoogle Scholar
  29. 29.
    Gentry C (2009) A fully homomorphic encryption scheme. Ph.D. thesis, Department of Computer Science, Stanford University. http://www.crypto.stanford.edu/craig
  30. 30.
    Gentry C, Boneh D (2009) A fully homomorphic encryption scheme, vol 20, no 09. Stanford University StanfordGoogle Scholar
  31. 31.
    Goldreich O (2003) Foundations of cryptography: basic tools, vol 1. Cambridge University Press, New YorkzbMATHGoogle Scholar
  32. 32.
    Goldreich O (2004) Foundations of cryptography: basic applications, vol 2. Cambridge University Press, New YorkCrossRefGoogle Scholar
  33. 33.
    Goldreich O, Micali S, Wigderson A (1987) How to play any mental game. In: 19th annual ACM symposium on theory of computing, pp 218–229. ACMGoogle Scholar
  34. 34.
    Goldwasser S, Micali S (1982) Probabilistic encryption & how to play mental poker keeping secret all partial information. In: 14th annual ACM symposium on Theory of Computing, pp 365–377. ACMGoogle Scholar
  35. 35.
    Gonzalez-Serrano FJ, Amor-Martın A, Casamayon-Anton J (2014) State estimation using an extended Kalman filter with privacy-protected observed inputs. In: IEEE international workshop on information forensics and security (WIFS), pp 54–59. IEEEGoogle Scholar
  36. 36.
    Hamlin A, Schear N, Shen E, Varia M, Yakoubov S, Yerukhimovich A (2016) Cryptography for big data security. In: Hu F (ed) Big data: storage, sharing, and security, Chap 10, pp 241–288. Taylor & Francis LLC, CRC PressGoogle Scholar
  37. 37.
    Ishai Y, Prabhakaran M, Sahai A (2008) Founding cryptography on oblivious transfer—efficiently. In: Annual international cryptology conference, pp 572–591. Springer, BerlinGoogle Scholar
  38. 38.
    Jeckmans A, Peter A, Hartel P (2013) Efficient privacy-enhanced familiarity-based recommender system. In: Proceedings of European symposium on research in computer security, pp 400–417. Springer, BerlinGoogle Scholar
  39. 39.
    Joye M, Libert B (2013) Efficient cryptosystems from \(2^k\)-th power residue symbols. In: International conference on the theory and applications of cryptographic techniques, pp 76–92. Springer, BerlinGoogle Scholar
  40. 40.
    Kim J, Lee C, Shim H, Cheon JH, Kim A, Kim M, Song Y (2016) Encrypting controller using fully homomorphic encryption for security of cyber-physical systems. IFAC-PapersOnLine 49(22):175–180CrossRefGoogle Scholar
  41. 41.
    Lindell Y (2017) How to simulate it–a tutorial on the simulation proof technique. In: Tutorials on the foundations of cryptography, pp 277–346. Springer International PublishingGoogle Scholar
  42. 42.
    Martins P, Sousa L, Mariano A (2018) A survey on fully homomorphic encryption: an engineering perspective. ACM Comput Surv (CSUR) 50(6):83Google Scholar
  43. 43.
    Mayne DQ, Rawlings JB, Rao CV, Scokaert PO (2000) Constrained model predictive control: stability and optimality. Automatica 36(6):789–814MathSciNetCrossRefGoogle Scholar
  44. 44.
    Mell P, Grance T et al (2011) The NIST definition of cloud computingGoogle Scholar
  45. 45.
    Mirhoseini A, Sadeghi AR, Koushanfar F (2016) Cryptoml: secure outsourcing of big data machine learning applications. In: IEEE International symposium on hardware oriented security and trust (HOST), pp 149–154. IEEEGoogle Scholar
  46. 46.
    Mohassel P, Zhang Y (2017) SecureML: a system for scalable privacy-preserving machine learning. Cryptology ePrint Archive, Report 2017/396. http://eprint.iacr.org/2017/396
  47. 47.
    Murguia C, Farokhi F, Shames I (2018) Secure and private implementation of dynamic controllers using semi-homomorphic encryption. arXiv preprint arXiv:1812.04168
  48. 48.
    Naehrig M, Lauter K, Vaikuntanathan V (2011) Can homomorphic encryption be practical? In: 3rd ACM workshop on cloud computing security workshop, pp 113–124. ACMGoogle Scholar
  49. 49.
    Naor M, Pinkas B (2001) Efficient oblivious transfer protocols. In: 12th annual ACM-SIAM symposium on discrete algorithms, pp 448–457. SIAMGoogle Scholar
  50. 50.
    Nesterov Y (2013) Introductory lectures on convex optimization: a basic course, vol 87. Springer Science & Business MediaGoogle Scholar
  51. 51.
    Nielsen JB, Nordholt PS, Orlandi C, Burra SS (2012) A new approach to practical active-secure two-party computation. In: Advances in cryptology–CRYPTO, pp 681–700. Springer, BerlinGoogle Scholar
  52. 52.
    Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In: Annual international conference on the theory and applications of cryptographic techniques, pp 223–238. Springer, BerlinGoogle Scholar
  53. 53.
    Pedersen TP (1991) Non-interactive and information-theoretic secure verifiable secret sharing. In: Annual international cryptology conference, pp 129–140. Springer, BerlinGoogle Scholar
  54. 54.
    Pettai M, Laud P (2015) Combining differential privacy and secure multiparty computation. In: 31st Annual computer security applications conference, pp 421–430. ACMGoogle Scholar
  55. 55.
    Rabin MO (2005) How to exchange secrets with oblivious transfer. Cryptology ePrint Archive, Report 2005/187. https://eprint.iacr.org/2005/187
  56. 56.
    Rastogi V, Nath S (2010) Differentially private aggregation of distributed time-series with transformation and encryption. In: ACM SIGMOD International Conference on Management of data, pp 735–746. ACMGoogle Scholar
  57. 57.
    Riazi MS, Rouhani BD, Koushanfar F (2018) Deep learning on private data. IEEE Secur Privacy MagGoogle Scholar
  58. 58.
    Rittinghouse JW, Ransome JF (2016) Cloud computing: implementation, management, and security. CRC PressGoogle Scholar
  59. 59.
    Rivest RL, Adleman L, Dertouzos ML (1978) On data banks and privacy homomorphisms. Found Secure Comput 4(11):169–180MathSciNetGoogle Scholar
  60. 60.
    Schulze Darup M, Redder A, Shames I, Farokhi F, Quevedo D (2018) Towards encrypted MPC for linear constrained systems. IEEE Control Syst Lett 2(2):195–200CrossRefGoogle Scholar
  61. 61.
    Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613MathSciNetCrossRefGoogle Scholar
  62. 62.
    Shi E, Chan HTH, Rieffel E, Chow R, Song D (2011) Privacy-preserving aggregation of time-series data. In: Network & distributed system security symposium (NDSS)Google Scholar
  63. 63.
    Singh S, Jeong YS, Park JH (2016) A survey on cloud computing security: issues, threats, and solutions. J Netw Comput Appl 75:200–222CrossRefGoogle Scholar
  64. 64.
    Vadhan S (2018) Multiparty differential privacy. In: Differential privacy meets multi-party computation (DPMPC) workshop. https://www.bu.edu/hic/dpmpc-2018/
  65. 65.
    Vernam GS (1926) Cipher printing telegraph systems: for secret wire and radio telegraphic communications. J AIEE 45(2):109–115Google Scholar
  66. 66.
    Veugen T (2010) Encrypted integer division. In: International workshop on information forensics and security, pp 1–6. IEEEGoogle Scholar
  67. 67.
    Veugen, T.: Improving the DGK comparison protocol. In: International workshop on information forensics and security, pp 49–54. IEEE (2012)Google Scholar
  68. 68.
    Yao AC (1982) Protocols for secure computations. In: 23rd Annual symposium on foundations of computer science, pp 160–164. IEEEGoogle Scholar
  69. 69.
    Zhu T, Li G, Zhou W, Philip SY (2017) Differential privacy and applications. Springer, ChamGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations