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Paper: Unconditionally Reliable and Secure Message Transmission in Undirected Synchronous Networks: Possibility, Feasibility and Optimality

Authors:
Arpita Patra
Ashish Choudhary
Kannan Srinathan
C. Pandu Rangan
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URL: http://eprint.iacr.org/2008/141
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Abstract: We study the interplay of network connectivity and the issues related to the possibility, feasibility and optimality for {\it unconditionally reliable message transmission} (URMT) and {\it unconditionally secure message transmission} (USMT) in an undirected {\it synchronous} network, under the influence of an adaptive {\it mixed} adversary ${\mathcal A}_{(t_b,t_o,t_f,t_p)}$, who has {\it unbounded computing power} and can corrupt $t_b$, $t_o$, $t_f$ and $t_p$ nodes in the network in Byzantine, {\it omission}, {\it fail-stop} and passive fashion respectively. In URMT problem, a sender {\bf S} and a receiver {\bf R} are part of a distributed network, where {\bf S} and {\bf R} are connected by intermediate nodes, of which at most $t_b, t_o, t_f$ and $t_p$ nodes can be under the control of ${\mathcal A}_{(t_b,t_o,t_f,t_p)}$. {\bf S} wants to send a message $m$ which is a sequence of $\ell$ field elements from a finite field ${\mathbb F}$ to {\bf R}. The challenge is to design a protocol, such that after interacting in phases\footnote{A phase is a send from {\bf S} to {\bf R} or viceversa.} as per the protocol, {\bf R} should output $m' = m$ with probability at least $1 - \delta$, where $0 < \delta < \frac{1}{2}$. Moreover, this should happen, irrespective of the adversary strategy of ${\mathcal A}_{(t_b,t_o,t_f,t_p)}$. The USMT problem has an additional requirement that ${\mathcal A}_{(t_b,t_o,t_f,t_p)}$ should not know anything about $m$ in {\it information theoretic} sense. In this paper, we answer the following in context of URMT and USMT: (a) {\sc Possibility:} when is a protocol possible in a given network? (b) {\sc Feasibility:} Once the existence of a protocol is ensured then does there exists a polynomial time protocol on the given network? (c) {\sc Optimality: } Given a message of specific length, what is the minimum communication complexity (lower bound) needed by any protocol to transmit the message and how to design a protocol whose total communication complexity matches the lower bound on the communication complexity? Finally we also show that {\it allowing a negligible error probability significantly helps in the possibility, feasibility and optimality of both reliable and secure message transmission protocols.} To design our protocols, we propose several new techniques which are of independent interest.
BibTeX
@misc{eprint-2008-17818,
  title={Unconditionally Reliable and Secure Message Transmission in Undirected Synchronous Networks: Possibility, Feasibility and Optimality},
  booktitle={IACR Eprint archive},
  keywords={foundations /},
  url={http://eprint.iacr.org/2008/141},
  note={A preliminary version of this paper appeared in INDOCRYPT 2007 arpitapatra_10@yahoo.co.in 14039 received 30 Mar 2008, last revised 8 Jun 2008},
  author={Arpita Patra and Ashish Choudhary and Kannan Srinathan and C. Pandu Rangan},
  year=2008
}