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On Communication Complexity of Secure Message Transmission in Directed Networks

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Distributed Computing and Networking (ICDCN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5935))

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Abstract

We re-visit the problem of perfectly secure message transmission (PSMT) in a directed network under the presence of a threshold adaptive Byzantine adversary, having unbounded computing power. Specifically, we derive the lower bounds on communication complexity of (a) two phase PSMT protocols and (b) three or more phase PSMT protocols in directed networks. Moreover, we show that our lower bounds are asymptotically tight, by designing communication optimal PSMT protocols in directed networks, which are first of their kind.

We re-visit the problem of perfectly reliable message transmission (PRMT) as well. Any PRMT protocol that sends a message containing ℓ field elements by communicating \({\cal O}(\ell)\) field elements, is referred as communication optimal PRMT or PRMT with constant factor overhead. Here, we characterize the class of directed networks over which communication optimal PRMT or PRMT with constant factor overhead is possible. Moreover, we design a communication optimal PRMT over a directed network that satisfies the conditions stated in our characterization.

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Author information

Authors and Affiliations

  1. Dept of Computer Science and Engineering, IIT Madras Email: partho_31@yahoo.co.in, Chennai, India, 600036

    Arpita Patra, Ashish Choudhary & C. Pandu Rangan

Authors
  1. Arpita Patra
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  2. Ashish Choudhary
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  3. C. Pandu Rangan
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Editor information

Editors and Affiliations

  1. National Science Foundation, 4201 Wilson Blvd, Arlington, 22130, VA, USA

    Krishna Kant

  2. Department of Computer Science, The University of Iowa, 52242-1419, Iowa City, IA, USA

    Sriram V. Pemmaraju

  3. Department of Computer Science and Engineering, Madras, Indian Institute of Technology (IIT), 600036, Chennai, India

    Krishna M. Sivalingam

  4. Department of Computer and Information Science, Temple University, 119122, Philadelphia, PA, USA

    Jie Wu

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Patra, A., Choudhary, A., Rangan, C.P. (2010). On Communication Complexity of Secure Message Transmission in Directed Networks. In: Kant, K., Pemmaraju, S.V., Sivalingam, K.M., Wu, J. (eds) Distributed Computing and Networking. ICDCN 2010. Lecture Notes in Computer Science, vol 5935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11322-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-11322-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11321-5

  • Online ISBN: 978-3-642-11322-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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