Perfectly Reliable and Secure Communication Tolerating Static and Mobile Mixed Adversary

Abstract

In this paper, we study the issues related to the possibility, feasibility and optimality for perfectly secure message transmission (PSMT) in an undirected synchronous network, under the influence of a mixed adversary having unbounded computing power, who can corrupt some of the nodes in the network in Byzantine, fail-stop and passive fashion respectively. Specifically, we answer the following questions: (a) Possibility: Given a network and a mixed adversary, what is the necessary and sufficient condition for the existence of any PSMT protocol over the network tolerating the adversary? (b) Feasibility: Once the existence of a protocol is ensured, then does there exist a polynomial time and efficient protocol on the given network? (c) Optimality: Given a message of specific length, what is the minimum communication complexity (lower bound) needed by any PSMT protocol to transmit the message and how to design a polynomial time protocol whose total communication complexity matches the lower bound on the communication complexity? We answer the above questions by considering two different types of mixed adversary, namely static mixed adversary and mobile mixed adversary. Intuitively, it is more difficult to tolerate a mobile mixed adversary (who can corrupt different set of nodes during different stages of the protocol) in comparison to its static counter part (who corrupts the same set of nodes throughout the protocol). However, surprisingly, we show that the connectivity requirement in the network and lower bound on communication 6 This is an extended, modified and elaborate version of [10]

Simple and Efficient Single Round almost Perfectly Secure Message Transmission Tolerating Generalized Adversary

“…3. Adversary Behavior: The adversary may be static who corrupts the same channels throughout the protocol [12,31,36,19] or the adversary may be mobile, who corrupts different set of channels, during different stages of the protocol [39,26,5,27]. 4.…”

Unconditionally reliable and secure message transmission in undirected synchronous networks: possibility, feasibility and optimality

“…for r = 1 (Fitzi et al, 2007;Srinathan et al, 2007b) PSMT (Byzantine adversary) n ≥ 2t b + 1 for r ≥ 2 (Dolev et al, 1993) ( ) Srinathan, 2006) n ≥ 3t b + 2t o + t f + t p + 1 for r = 1 (Srinathan, 2006) ( ) Choudhury et al, 2008) ( ) Srinathan, 2006) Note: r denotes number of phases and ℓ denotes the message size in terms of field elements. …”

Brief announcement

“…In [2], the authors have studied PSMT tolerating mobile mixed adversary A mobile (t b ,t f ,tp) . In [2], it is shown that PSMT tol-…”

“…Any PSMT protocol, whose communication complexity (which is the number of field elements communicated by S and R throughout the protocol) satisfies this lower bound is called optimal PSMT (OPSMT). In [2], the authors have designed a nine phase OPSMT, which sends a message containing ℓ (ℓ = Ω(n)) field elements, by overall communicating O(nℓ) field elements over n = 2t b + t f + tp + 1 wires against A mobile (t b ,t f ,tp) . In this paper, we improve the existing OPSMT protocol of [2] by designing a three phase OPSMT protocol, having the same communication complexity as [2].…”