Skip to main content
Springer Nature Link
Log in

Secure Message Transmission by Public Discussion: A Brief Survey

  • Conference paper
Coding and Cryptology (IWCC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

Included in the following conference series:

Abstract

In the problem of Secure Message Transmission in the public discussion model (SMT-PD), a Sender wants to send a message to a Receiver privately and reliably. Sender and Receiver are connected by n channels, up to t < n of which may be maliciously controlled by a computationally unbounded adversary, as well as one public channel, which is reliable but not private. The SMT-PD abstraction has been shown instrumental in achieving secure multi-party computation on sparse networks, where a subset of the nodes are able to realize a broadcast functionality, which plays the role of the public channel.

In this short survey paper, after formally defining the SMT-PD problem, we overview the basic constructions starting with the first, rather communication-inefficient solutions to the problem, and ending with the most efficient solutions known to-date—optimal private communication and sublinear public communication.

These complexities refer to resource use for a single execution of an SMT-PD protocol. We also review the amortized complexity of the problem, which would arise in natural use-case scenarios where \(\mathcal{S}\) and \(\mathcal{R}\) must send several messages back and forth, where later messages depend on earlier ones.

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
$34.99 /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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agarwal, S., Cramer, R., de Haan, R.: Asymptotically optimal two-round perfectly secure message transmission. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 394–408. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Bennett, C.H., Brassard, G., Crèpeau, C., Maurer, U.: Generalized privacy amplification. IEEE Transactions on Information Theory 41(6), 1015–1923 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Robert, J.M.: Privacy amplification by public discussion. Siam Journal of Computing 17(2) (1988)

    Google Scholar 

  4. Berman, P., Garay, J.: Fast consensus in networks of bounded degree. Distributed Computing 2(7), 62–73 (1991); Preliminary version in WDAG 1990

    Google Scholar 

  5. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC, pp. 1–10 (1988)

    Google Scholar 

  6. Chaum, D., Crepeau, C., Damgard, I.: Multiparty unconditionally secure protocols. In: STOC, pp. 11–19 (1988)

    Google Scholar 

  7. Chandran, N., Garay, J., Ostrovsky, R.: Improved fault tolerance and secure computation on sparse networks. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 249–260. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Choudhary, A., Patra, A., Pandu Rangan, C., Srinathan, K.: Unconditionally reliable and secure message transmission in undirected synchronous networks: Possibility, feasibility and optimality. Cryptology ePrint Archive, Report 2008/141 (2008)

    Google Scholar 

  9. Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. Journal of ACM 1(40), 17–47 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J. Comput. (2008)

    Google Scholar 

  11. Dwork, C., Peleg, D., Pippinger, N., Upfal, E.: Fault tolerance in networks of bounded degree. In: STOC, pp. 370–379 (1986)

    Google Scholar 

  12. Fitzi, M., Franklin, M.K., Garay, J.A., Vardhan, S.H.: Towards optimal and efficient perfectly secure message transmission. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 311–322. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Feldman, P., Micali, S.: An optimal probabilistic protocol for synchronous Byzantine agreement. SIAM J. Comput. 26(4), 873–933 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Franklin, M., Wright, R.: Secure communication in minimal connectivity models. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 346–360. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Garay, J.A.: Partially connected networks: Information theoretically secure protocols and open problems (Invited talk). In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, p. 1. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Garay, J., Givens, C., Ostrovsky, R.: Secure message transmission with small public discussion. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 177–196. Springer, Heidelberg (2010); Full version in Cryptology ePrint Archive, Report 2009/519

    Chapter  Google Scholar 

  17. Garay, J., Moses, Y.: Fully polynomial Byzantine agreement for n > 3t processors in t + 1 rounds. SIAM J. Comput. 27(1), 247–290 (1998); Prelim. in STOC 1992

    Article  MathSciNet  MATH  Google Scholar 

  18. Garay, J.A., Ostrovsky, R.: Almost-everywhere secure computation. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 307–323. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Katz, J., Koo, C.-Y.: On expected constant-round protocols for byzantine agreement. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 445–462. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Kurosawa, K., Suzuki, K.: Almost secure (1-round, n-channel) message transmission scheme. Cryptology ePrint Archive, Report 2007/076 (2007)

    Google Scholar 

  21. Kurosawa, K., Suzuki, K.: Truly efficient 2-round perfectly secure message transmission scheme. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 324–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Kamp, J., Zuckerman, D.: Deterministic extractors for bit-fixing sources and exposure-resilient cryptography. SIAM J. Comput. 36(5), 1231–1247 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Transactions on Programming Languages and Systems, 382–401 (July 1982)

    Google Scholar 

  24. Macwilliams, F., Sloane, N.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1983)

    MATH  Google Scholar 

  25. Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM, JACM 27(2) (April 1980)

    Google Scholar 

  26. Sayeed, H., Abu-Amara, H.: Efficient perfectly secure message transmission in synchronous networks. Information and Computation 1(126), 53–61 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  27. Shi, H., Jiang, S., Safavi-Naini, R., Tuhin, M.: Optimal secure message transmission by public discussion. In: IEEE Symposium on Information Theory (2009)

    Google Scholar 

  28. Srinathan, K., Narayanan, A., Pandu Rangan, C.: Optimal perfectly secure message transmission. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 545–561. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  29. Srinathan, K., Prasad, N.R., Pandu Rangan, C.: On the optimal communication complexity of multiphase protocols for perfect communication. In: IEEE Symposium on Security and Privacy, pp. 311–320 (2007)

    Google Scholar 

  30. Upfal, E.: Tolerating linear number of faults in networks of bounded degree. In: PODC, pp. 83–89 (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Labs – Research, USA

    Juan Garay

  2. Department of Mathematics, UCLA, USA

    Clint Givens

  3. Departments of Computer Science and Mathematics, UCLA, USA

    Rafail Ostrovsky

Authors
  1. Juan Garay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clint Givens
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rafail Ostrovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, 637371, Singapore

    Yeow Meng Chee , San Ling , Huaxiong Wang  & Chaoping Xing , ,  & 

  2. College of Information Engineering, Qingdao University, 266071, Shandong, P.R. China

    Zhenbo Guo

  3. Qingdao University, 266071, Shandong, P.R. China

    Fengjing Shao

  4. School of Mathematical Sciences, Yangzhou University, 225002, Jiangsu, P.R. China

    Yuansheng Tang

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Garay, J., Givens, C., Ostrovsky, R. (2011). Secure Message Transmission by Public Discussion: A Brief Survey. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20901-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics