SpringerLink
Log in

Secure Two-Party Computation in a Quantum World

  • Conference paper
  • First Online:
Applied Cryptography and Network Security (ACNS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12146))

Included in the following conference series:

  • 1075 Accesses

Abstract

Secure multi-party computation has been extensively studied in the past years and has reached a level that is considered practical for several applications. The techniques developed thus far have been steadily optimized for performance and were shown to be secure in the classical setting, but are not known to be secure against quantum adversaries.

In this work, we start to pave the way for secure two-party computation in a quantum world where the adversary has access to a quantum computer. We show that post-quantum secure two-party computation has comparable efficiency to their classical counterparts. For this, we develop a lattice-based OT protocol which we use to implement a post-quantum secure variant of Yao’s famous garbled circuits (GC) protocol (FOCS’82). Along with the OT protocol, we show that the oblivious transfer extension protocol of Ishai et al. (CRYPTO’03), which allows running many OTs using mainly symmetric cryptography, is post-quantum secure. To support these results, we prove that Yao’s GC protocol achieves post-quantum security if the underlying building blocks do.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Note, however, that both schemes have yet to be proven post-quantum secure.

  2. 2.

    We formally define post-quantum security under double encryption (\(\mathrm {pq{\text{- }}2Enc}\) security) in Definition 3.

References

  1. Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_8

    Chapter  Google Scholar 

  2. Alkim, E., Alkim, E., et al.: Revisiting TESLA in the quantum random Oracle model. In: Lange, T., Takagi, T. (eds.) PQCrypto 2017. LNCS, vol. 10346, pp. 143–162. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59879-6_9

    Chapter  MATH  Google Scholar 

  3. Almeida, J.B., et al.: A fast and verified software stack for secure function evaluation. In: ACM CCS 2017, pp. 1989–2006. ACM Press (2017)

    Google Scholar 

  4. Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    Article  Google Scholar 

  5. Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer extensions. J. Cryptol. 30(3), 805–858 (2017)

    Article  MathSciNet  Google Scholar 

  6. Bauer, B., Wecker, D., Millis, A.J., Hastings, M.B., Troyer, M.: Hybrid quantum-classical approach to correlated materials (2015)

    Google Scholar 

  7. Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd ACM STOC, pp. 503–513. ACM Press (1990)

    Google Scholar 

  8. Bellare, M., Hoang, V.T., Keelveedhi, S., Rogaway, P.: Efficient garbling from a fixed-key blockcipher. In: 2013 IEEE Symposium on Security and Privacy, pp. 478–492. IEEE Computer Society Press (2013)

    Google Scholar 

  9. Bellare, M., Rogaway, P.: The security of triple encryption and a frameworkfor code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_25

    Chapter  Google Scholar 

  10. Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-Quantum Cryptography. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-88702-7

    Book  MATH  Google Scholar 

  11. Brakerski, Z., Döttling, N.: Two-message statistically sender-private OT from LWE. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 370–390. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_14

    Chapter  Google Scholar 

  12. Büscher, N., et al.: Secure two-party computation in a quantum world. Cryptology ePrint Archive, Report 2020/441 (2020). https://eprint.iacr.org/2020/411

  13. Canetti, R.: Universally Composable security: a new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, 14–17 October 2001, Las Vegas, Nevada, USA, pp. 136–145. IEEE Computer Society (2001)

    Google Scholar 

  14. Choi, S.G., Katz, J., Kumaresan, R., Zhou, H.-S.: On the security of the “Free-XOR” technique. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 39–53. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_3

    Chapter  MATH  Google Scholar 

  15. Degabriele, J.P., Janson, C., Struck, P.: Sponges resist leakage: the case of authenticated encryption. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11922, pp. 209–240. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34621-8_8

    Chapter  Google Scholar 

  16. Demmler, D., Schneider, T., Zohner, M.: ABY - a framework for efficient mixed-protocol secure two-party computation. In: NDSS 2015. The Internet Society (2015)

    Google Scholar 

  17. Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12

    Chapter  Google Scholar 

  18. Dobraunig, C., Eichlseder, M., Mangard, S., Mendel, F., Unterluggauer, T.: ISAP - towards side-channel secure authenticated encryption. IACR Trans. Symm. Cryptol. 2017(1), 80–105 (2017)

    Google Scholar 

  19. Dowsley, R., van de Graaf, J., Müller-Quade, J., Nascimento, A.C.A.: Oblivious transfer based on the McEliece assumptions. In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 107–117. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85093-9_11

    Chapter  Google Scholar 

  20. Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive, Report 2012/144 (2012). http://eprint.iacr.org/2012/144

  21. Gagliardoni, T.: Quantum security of cryptographic primitives. Darmstadt University of Technology, Germany (2017)

    Google Scholar 

  22. Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The relationship between public key encryption and oblivious transfer. In: 41st FOCS, pp. 325–335. IEEE Computer Society Press (2000)

    Google Scholar 

  23. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: 19th ACM STOC, pp. 218–229. ACM Press (1987)

    Google Scholar 

  24. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th ACM STOC, pp. 212–219. ACM Press (1996)

    Google Scholar 

  25. Gueron, S., Lindell, Y., Nof, A., Pinkas, B.: Fast garbling of circuits under standard assumptions. J. Cryptol. 31(3), 798–844 (2018)

    Article  MathSciNet  Google Scholar 

  26. Halevi, S., Shoup, V.: HElib-an implementation of homomorphic encryption. Cryptology ePrint Archive, Report 2014/039. http://eprint.iacr.org/2014/039

  27. Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: 21st Annual ACM Symposium on Theory of Computing, 14–17 May 1989, Seattle, Washigton, USA, pp. 44–61 (1989)

    Google Scholar 

  28. Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_9

    Chapter  Google Scholar 

  29. Jao, D., De Feo, L.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 19–34. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25405-5_2

    Chapter  MATH  Google Scholar 

  30. Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70583-3_40

    Chapter  MATH  Google Scholar 

  31. Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)

    Article  MathSciNet  Google Scholar 

  32. Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computationin the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_4

    Chapter  MATH  Google Scholar 

  33. Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: USENIX Security 2004, pp. 287–302. USENIX Association (2004)

    Google Scholar 

  34. Masny, D., Rindal, P.: Endemic oblivious transfer. In: ACM CCS 2019, pp. 309–326. ACM Press (2019)

    Google Scholar 

  35. McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report (1978)

    Google Scholar 

  36. Mosca, M.: Cybersecurity in an era with quantum computers: will we be ready? IEEE Secur. Priv. 16(5), 38–41 (2018)

    Article  Google Scholar 

  37. Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: 12th SODA, pp. 448–457. ACM-SIAM (2001)

    Google Scholar 

  38. Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: ACM Conference on Electronic Commerce, pp. 129–139 (1999)

    Google Scholar 

  39. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press (2011)

    Google Scholar 

  40. NIST: PQ Cryptography Standardization Process (2017)

    Google Scholar 

  41. Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: USENIX Security 2015, pp. 515–530. USENIX Association (2015)

    Google Scholar 

  42. Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure two-party computation is practical. In: ASIACRYPT 2009, pp. 250–267 (2009)

    Google Scholar 

  43. Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on OT extension. In: USENIX Security 2014, pp. 797–812. USENIX Association (2014)

    Google Scholar 

  44. Pinkas, B., Schneider, T., Zohner, M.: Scalable private set intersection based on OT extension. ACM TOPS 21(2), 7:1–7:35 (2018)

    Google Scholar 

  45. Schwabe, R., et al.: CRYSTALS-KYBER. Technical report, National Institute of Standards and Technology (2019). https://csrc.nist.gov/projects/post-quantum-cryptography/round-2-submissions

  46. “Microsoft SEAL (release 3.3)”. Microsoft Research, Redmond, WA (2019). https://github.com/Microsoft/SEAL

  47. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: FOCS (1994)

    Google Scholar 

  48. Unruh, D.: Universally composable quantum multi-party computation. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 486–505. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_25

    Chapter  Google Scholar 

  49. Wang, X.: A New Paradigm for Practical Maliciously Secure Multi-Party Computation. University of Maryland, College Park (2018)

    Google Scholar 

  50. Wang, X., Malozemoff, A.J., Katz, J.: EMP-toolkit: efficient multiparty computation toolkit (2016). https://github.com/emp-toolkit

  51. Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd FOCS, pp. 160–164. IEEE Computer Society Press (1982)

    Google Scholar 

  52. Zahur, S., Evans, D.: Obliv-C: a language for extensible data-oblivious computation. Cryptology ePrint Archive, Report 2015/1153 (2015). http://eprint.iacr.org/2015/1153

  53. Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8

    Chapter  MATH  Google Scholar 

Download references

Acknowledgements

This work was co-funded by the Deutsche Forschungsgemeinschaft (DFG)—SFB 1119 CROSSING/236615297 and GRK 2050 Privacy & Trust/251805230, by the German Federal Ministry of Education and Research and the Hessen State Ministry for Higher Education, Research and the Arts within ATHENE, and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 850990 PSOTI).

Author information

Authors and Affiliations

  1. SecEng, Technische Universität Darmstadt, Darmstadt, Germany

    Niklas Büscher & Nikolaos P. Karvelas

  2. SVS, Universität Hamburg, Hamburg, Germany

    Daniel Demmler

  3. Universität Passau, Passau, Germany

    Stefan Katzenbeisser

  4. QPC, Technische Universität Darmstadt, Darmstadt, Germany

    Juliane Krämer & Patrick Struck

  5. Department of Computer Science, IIT (BHU) Varanasi, Varanasi, India

    Deevashwer Rathee

  6. ENCRYPTO, Technische Universität Darmstadt, Darmstadt, Germany

    Thomas Schneider

Authors
  1. Niklas Büscher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Demmler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nikolaos P. Karvelas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stefan Katzenbeisser
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Juliane Krämer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Deevashwer Rathee
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Thomas Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Patrick Struck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Demmler .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Padua, Padua, Italy

    Mauro Conti

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  3. Dipt di Informatica Sistemi e Produ, Università di Roma “Tor Vergata”, Rome, Roma, Italy

    Emiliano Casalicchio

  4. Sapienza University of Rome, Rome, Italy

    Angelo Spognardi

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Büscher, N. et al. (2020). Secure Two-Party Computation in a Quantum World. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds) Applied Cryptography and Network Security. ACNS 2020. Lecture Notes in Computer Science(), vol 12146. Springer, Cham. https://doi.org/10.1007/978-3-030-57808-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-57808-4_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57807-7

  • Online ISBN: 978-3-030-57808-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation