Perfectly Secure Message Transmission in Two Rounds

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9985)

Abstract

In the model that has become known as “Perfectly Secure Message Transmission” (PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely.

In this paper, we focus on protocols that work in two transmission rounds for \(n= 2t+1\). We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from \(O(n^3\log n)\) to \(O(n^2\log n)\). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size \(O(n^2 \log n)\) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of \(O(n \log n)\) bits.

Keyword

Perfectly Secure Message Transmission 

Notes

Acknowledgments

The authors would like to thank Serge Fehr and Ronald Cramer for their useful comments and suggestions.

References

  1. 1.
    Agarwal, S., Cramer, R., 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). doi:10.1007/11818175_24 CrossRefGoogle Scholar
  2. 2.
    Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. J. ACM 40(1), 17–47 (1993)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Griggio, J.: Perfectly secure message transmission protocols with low communication overhead and their generalization. Master thesis (2012). http://algant.eu/documents/theses/griggio.pdf
  4. 4.
    Kurosawa, K., Suzuki, K.: Truly efficient 2-round perfectly secure message transmission scheme. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 324–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78967-3_19 CrossRefGoogle Scholar
  5. 5.
    Kurosawa, K., Suzuki, K.: Truly efficient 2-round perfectly secure message transmission scheme. IEEE Trans. Inf. Theory 55(11), 5223–5232 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    MacWilliams, F., Sloane, N.: The Theory of Error Correcting Codes. North-Holland mathematical library. North-Holland Publishing Company (1977)Google Scholar
  7. 7.
    Massey, J.L.: Some applications of coding theory in cryptography. In: Codes, Ciphers: Cryptography and Coding IV, pp. 33–47 (1995)Google Scholar
  8. 8.
    Sayeed, H.M., Abu-Amara, H.: Efficient perfectly secure message transmission in synchronous networks. Inf. Comput. 126(1), 53–61 (1996)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    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). doi:10.1007/978-3-540-28628-8_33 CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bordeaux, UMR 5251, Université de BordeauxTalenceFrance
  2. 2.Mathematical InstituteLeiden UniversityLeidenThe Netherlands
  3. 3.CWI AmsterdamAmsterdamThe Netherlands

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