Movatterモバイル変換

[0]ホーム
URL:

Skip to main content

Advertisement

Springer Nature Link
Log in

On the Correlation Complexity of MPC with Cheater Identification

  • Conference paper
  • First Online:

Abstract

Composable protocols for Multi-Party Computation that provide security with Identifiable Abort against a dishonest majority require some form of setup, e.g. correlated randomness among the parties. While this is a very useful model, it has the downside that the setup’s randomness must beprogrammable, otherwise security becomes provably impossible. Since programmability is more realistic for smaller setups (in terms of number of parties), it is crucial to minimize the correlation complexity (degree of correlation) of the setup’s randomness.

We give a tight tradeoff between the correlation complexity\(\beta \) and the corruption threshold\(t\). Our bounds are strong in that\(\beta \)-wise correlation is sufficient for statistical security while\(\beta -1\)-wise correlation is insufficient even for computational security. In particular, for strong security, i.e.,\(t< n\), full\(n\)-wise correlation is necessary. However, for any constant fraction of honest parties, we provide a protocol withconstant correlation complexity which tightens the gap between the theoretical model and the setup’s implementation in the real world. In contrast, previous state-of-the-art protocols require full\(n\)-wise correlation regardless of\(t\).

Work done while the first author was supported by ERC Project PREP-CRYPTO 724307, the second author was at the Karlsruhe Institute of Technology, Germany, and the third author was at the FZI Research Center for Information Technology, Germany.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /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
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 7549
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 9437
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide -see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Similar content being viewed by others

Notes

  1. 1.

    Throughout the paper, we require a setup among each subset of parties of size\(\beta \).

  2. 2.

    To our knowledge this is the first full characterization of Identifiable Abort in the dishonest majority setting.

  3. 3.

    As a side note we generalize the notion of the minimal complete cardinality (MCC) from [16] to the setting where the number of parties varies in the security parameter\(\lambda \). This was not captured by the original definition of MCC in [16] and—to the best of our knowledge—not formally addressed in previous literature.

  4. 4.

    Throughout the paper we assume that each subset of parties of the appropriate cardinality has access to a setup.

  5. 5.

    In particular, Claim 3.1 in [29] and our Lemma3 share the same core idea but are stated in different terms with different applications in mind.

  6. 6.

    Recall that we only assume setups to have security with Identifiable Abort.

  7. 7.

    Note that is vertex is their own neighbor because the graph is reflexive.

  8. 8.

    We note that [28] state their results in the stand-alone model.

  9. 9.

    The postprocessing\(\phi \) corresponds to removing edges from parties with strictly more than\(t\) conflicts.

  10. 10.

    The sender inputs the same shares into each setup that it participates in.

References

  1. Baum, C., Orsini, E., Scholl, P.: Efficient secure multiparty computation with identifiable abort. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part I. LNCS, vol. 9985, pp. 461–490. Springer, Heidelberg (2016).https://doi.org/10.1007/978-3-662-53641-4_18

    Chapter  Google Scholar 

  2. Baum, C., Orsini, E., Scholl, P., Soria-Vazquez, E.: Efficient constant-round MPC with identifiable abort and public verifiability. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part II. LNCS, vol. 12171, pp. 562–592. Springer, Cham (2020).https://doi.org/10.1007/978-3-030-56880-1_20

    Chapter  Google Scholar 

  3. Beaver, D.: Multiparty protocols tolerating half faulty processors. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 560–572. Springer, New York (1990).https://doi.org/10.1007/0-387-34805-0_49

    Chapter  Google Scholar 

  4. Boyle, E., et al.: Compressing vector OLE. In: Lie, D., et al. (eds.) ACM CCS 2018, pp. 896–912. ACM Press, October 2018

    Google Scholar 

  5. Boyle, E., et al.: Correlated pseudorandom functions from variable-density LPN. In: 61st FOCS, pp. 1069–1080. IEEE Computer Society Press, November 2020

    Google Scholar 

  6. Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 489–518. Springer, Cham (2019).https://doi.org/10.1007/978-3-030-26954-8_16

    Chapter  Google Scholar 

  7. Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001

    Google Scholar 

  8. Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001).https://doi.org/10.1007/3-540-44647-8_2

    Chapter  Google Scholar 

  9. Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally composable security with global setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007).https://doi.org/10.1007/978-3-540-70936-7_4

    Chapter  Google Scholar 

  10. Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: 18th ACM STOC, pp. 364–369. ACM Press, May 1986

    Google Scholar 

  11. Couteau, G., Rindal, P., Raghuraman, S.: Silver: silent VOLE and oblivious transfer from hardness of decoding structured LDPC codes. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part III. LNCS, vol. 12827, pp. 502–534. Springer, Cham (2021).https://doi.org/10.1007/978-3-030-84252-9_17

    Chapter  Google Scholar 

  12. Crépeau, C.: Efficient cryptographic protocols based on noisy channels. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 306–317. Springer, Heidelberg (1997).https://doi.org/10.1007/3-540-69053-0_21

    Chapter  Google Scholar 

  13. Crépeau, C.: Verifiable disclosure of secrets and applications (abstract). In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 150–154. Springer, Heidelberg (1990).https://doi.org/10.1007/3-540-46885-4_17

    Chapter  Google Scholar 

  14. Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions (extended abstract). In: 29th FOCS, pp. 42–52. IEEE Computer Society Press, October 1988

    Google Scholar 

  15. Crépeau, C., van de Graaf, J., Tapp, A.: Committed oblivious transfer and private multi-party computation. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 110–123. Springer, Heidelberg (1995).https://doi.org/10.1007/3-540-44750-4_9

    Chapter  Google Scholar 

  16. Fitzi, M., Garay, J.A., Maurer, U., Ostrovsky, R.: Minimal complete primitives for secure multi-party computation. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 80–100. Springer, Heidelberg (2001).https://doi.org/10.1007/3-540-44647-8_5

    Chapter  Google Scholar 

  17. Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: On 2-round secure multiparty computation. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 178–193. Springer, Heidelberg (2002).https://doi.org/10.1007/3-540-45708-9_12

    Chapter  Google Scholar 

  18. Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010).https://doi.org/10.1007/978-3-642-11799-2_19

    Chapter MATH  Google Scholar 

  19. Ishai, Y., Kushilevitz, E., Paskin, A.: Secure multiparty computation with minimal interaction. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 577–594. Springer, Heidelberg (2010).https://doi.org/10.1007/978-3-642-14623-7_31

    Chapter  Google Scholar 

  20. Ishai, Y., Ostrovsky, R., Seyalioglu, H.: Identifying cheaters without an honest majority. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 21–38. Springer, Heidelberg (2012).https://doi.org/10.1007/978-3-642-28914-9_2

    Chapter  Google Scholar 

  21. Ishai, Y., Ostrovsky, R., Zikas, V.: Secure multi-party computation with identifiable abort. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 369–386. Springer, Heidelberg (2014).https://doi.org/10.1007/978-3-662-44381-1_21

    Chapter  Google Scholar 

  22. Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008).https://doi.org/10.1007/978-3-540-85174-5_32

    Chapter  Google Scholar 

  23. Ishai, Y., et al.: Zero-knowledge from secure multiparty computation. In: Johnson, D.S., Feige, U. (eds.) 39th ACM STOC, pp. 21–30. ACM Press, June 2007

    Google Scholar 

  24. Orlandi, C., Scholl, P., Yakoubov, S.: The rise of paillier: homomorphic secret sharing and public-key silent OT. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021, Part I. LNCS, vol. 12696, pp. 678–708. Springer, Cham (2021).https://doi.org/10.1007/978-3-030-77870-5_24

    Chapter  Google Scholar 

  25. Pass, R.: On deniability in the common reference string and random oracle model. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 316–337. Springer, Heidelberg (2003).https://doi.org/10.1007/978-3-540-45146-4_19

    Chapter  Google Scholar 

  26. Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: 21st ACM STOC, pp. 73–85. ACM Press, May 1989

    Google Scholar 

  27. Sadeghi, A.-R., Schneider, T., Winandy, M.: Token-based cloud computing. In: Acquisti, A., Smith, S.W., Sadeghi, A.-R. (eds.) Trust 2010. LNCS, vol. 6101, pp. 417–429. Springer, Heidelberg (2010).https://doi.org/10.1007/978-3-642-13869-0_30

    Chapter  Google Scholar 

  28. Simkin, M., Siniscalchi, L., Yakoubov, S.: On sufficient oracles for secure computation with identifiable abort. In: Galdi, C., Jarecki, S. (eds.) SCN 2022. LNCS, vol. 13409, pp. 494–515. Springer, Cham (2022).https://doi.org/10.1007/978-3-031-14791-3_22

    Chapter MATH  Google Scholar 

  29. Wan, J., Xiao, H., Shi, E., Devadas, S.: Expected constant round byzantine broadcast under dishonest majority. In: Pass, R., Pietrzak, K. (eds.) TCC 2020, Part I. LNCS, vol. 12550, pp. 381–411. Springer, Cham (2020).https://doi.org/10.1007/978-3-030-64375-1_14

    Chapter  Google Scholar 

  30. Wolf, S., Wullschleger, J.: Oblivious transfer is symmetric. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 222–232. Springer, Heidelberg (2006).https://doi.org/10.1007/11761679_14

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Nicholas Brandt

  2. CNRS, IRIF, Université de Paris, Paris, France

    Sven Maier

  3. Karlsruhe, Germany

    Tobias Müller

  4. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Jörn Müller-Quade

Authors
  1. Nicholas Brandt

    You can also search for this author inPubMed Google Scholar

  2. Sven Maier

    You can also search for this author inPubMed Google Scholar

  3. Tobias Müller

    You can also search for this author inPubMed Google Scholar

  4. Jörn Müller-Quade

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence toNicholas Brandt.

Editor information

Editors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

Rights and permissions

Copyright information

© 2024 International Financial Cryptography Association

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Brandt, N., Maier, S., Müller, T., Müller-Quade, J. (2024). On the Correlation Complexity of MPC with Cheater Identification. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_8

Download citation

Publish with us

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /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
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 7549
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 9437
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide -see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

[8]ページ先頭
©2009-2025 Movatter.jp