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Paper: Perfectly Reliable and Secure Communication Tolerating Static and Mobile Mixed Adversary

Authors:
Ashish Choudhary
Arpita Patra
AshwinKumar B.V
Kannan Srinathan
C. Pandu Rangan
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URL: http://eprint.iacr.org/2008/232
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Abstract: In the problem of perfectly reliable message transmission} (PRMT), a sender {\bf S} and a receiver {\bf R} are connected by $n$ bidirectional synchronous channels. A mixed adversary ${\mathcal A}_{(t_b,t_f,t_p)}$ with {\it infinite computing power} controls $t_b, t_f$ and $t_p$ channels in Byzantine, fail-stop and passive fashion respectively. Inspite of the presence of ${\mathcal A}_{(t_b,t_f,t_p)}$, {\bf S} wants to reliably send a message $m$ to {\bf R}, using some protocol, without sharing any key with {\bf R} beforehand. After interacting in phases\footnote{A phase is a send from {\bf S} to {\bf R} or vice-versa} as per the protocol, {\bf R} should output $m' = m$, without any error. In the problem of {\it perfectly secure message transmission} (PSMT), there is an additional constraint that ${\mathcal A}_{(t_b,t_f,t_p)}$ should not know {\it any} information about $m$ in {\it information theoretic} sense. The adversary can be either static\footnote{A static adversary corrupts the same set of channels in each phase of the protocol. The choice of the channel to corrupt is decided before the beginning of the protocol.} or mobile.\footnote{A mobile adversary can corrupt different set of channels in different phases of the protocol.} The {\it connectivity requirement}, {\it phase complexity} and {\it communication complexity} are three important parameters of any interactive PRMT/PSMT protocol and are well studied in the literature when the channels are controlled by a static/mobile Byzantine adversary. However, when the channels are controlled by mixed adversary ${\mathcal A}_{(t_b,t_f,t_p)}$ , we encounter several surprising consequences. In this paper, we study the problem of PRMT and PSMT tolerating "static/mobile mixed adversary". We prove that even though the connectivity requirement for PRMT is same against both static and mobile mixed adversary, the lower bound on communication complexity for PRMT tolerating mobile mixed adversary is more than its static mixed counterpart. This is interesting because against only "Byzantine adversary", the connectivity requirement and the lower bound on the communication complexity of PRMT protocols are same for both static and mobile case. Thus our result shows that for PRMT, mobile mixed adversary is more powerful than its static counterpart. As our second contribution, we design a four phase communication optimal PSMT protocol tolerating "static mixed adversary". Comparing this with the existing three phase communication optimal PSMT protocol against "static Byzantine adversary", we find that additional one phase is enough to design communication optimal protocol against static mixed adversary. Finally, we show that the connectivity requirement and lower bound on communication complexity of any PSMT protocol is same against both static and mobile mixed adversary, thus proving that mobility of the adversary has no effect in PSMT. To show that our bound is tight, we also present a worst case nine phase communication optimal PSMT protocol tolerating mobile mixed adversary which is first of it's kind. This also shows that the mobility of the adversary does not hinder to design constant phase communication optimal PSMT protocol. In our protocols, we have used new techniques which can be effectively used against both static and mobile mixed adversary and are of independent interest.
BibTeX
@misc{eprint-2008-17909,
  title={Perfectly Reliable and Secure Communication Tolerating Static and Mobile Mixed Adversary},
  booktitle={IACR Eprint archive},
  keywords={foundations /},
  url={http://eprint.iacr.org/2008/232},
  note={An extended abstract of this paper is going to appear in ICITS 2008 arpitapatra_10@yahoo.co.in 14021 received 22 May 2008},
  author={Ashish Choudhary and Arpita Patra and AshwinKumar B.V and Kannan Srinathan and C. Pandu Rangan},
  year=2008
}