Abstract

(URMT) problem, two non-faulty players, the sender S and the receiver R are part of a synchronous network modeled as a directed graph. S has a message that he wishes to send to R; the challenge is to design a protocol such that after exchanging messages as per the protocol, the receiver R should correctly obtain S’s message with arbitrarily small error probability δ, in spite of the influence of a Byzantine adversary that may actively corrupt up to t nodes in the network (we denote such a URMT protocol as (t,(1− δ))-reliable). While it is known that (2t+ 1) vertex disjoint directed paths from S to R are necessary and sufficient for (t, 1)-reliable URMT (that is with zero error probability), we prove that a strictly weaker condition, which we define and denote as (2t, t)-special-connectivity, together with just (t+ 1) vertex disjoint directed paths from S to R, is necessary and sufficient for (t,(1− δ))-reliable URMT with arbitrarily small (but non-zero) error probability, δ. Thus, we demonstrate the power of randomization in the context of reliable message transmission. In fact, for any positive integer k> 0, we show that there always exists a digraph Gk such that (k, 1)-reliable URMT is impossible over Gk whereas there exists a (2k,(1− δ))-reliable URMT protocol, δ> 0 in Gk. In a digraph G on which (t,(1− δ))-reliable URMT is possible, an edge is called critical if the deletion of that edge renders (t,(1− δ))-reliable URMT impossible. We give an example of a digraph G on n vertices such that G has Ω (n2) critical edges. This is quite baffling since no such graph exists for the case of perfect reliable message transmission (or equivalently (t, 1)-reliable URMT) or when the underlying graph is undirected. Such is the anomalous behavior of URMT protocols (when “randomness meet directedness”) that it makes it extremely hard to design efficient protocols over arbitrary digraphs. However, if URMT is possible between every pair of vertices in the network, then we present efficient protocols for the same.

Abstract

Protocols for Generalized Oblivious Transfer(GOT) were introduced by Ishai and Kushilevitz [10]. They built it by reducing GOT protocols to standard 1-out-of-2 oblivious transfer protocols based on private protocols. In our protocols, we provide alternative reduction by using secret sharing schemes instead of private protocols. We therefore show that there exist a natural correspondence between GOT and general secret sharing schemes and thus the techniques and tools developed for the latter can be applied equally well to the former.

Abstract

In the problem of USMT [1, 2] 1, a sender S and a receiver R. are connected by n= 2t+ 1 bi-directional synchronous channels (also called as wires) such that any t out of the n channels are corrupted in Byzantine fashion by an adversary jA. t, having unbounded computing power. S intends to communicate a message m to R (where m£ F and I> 1 with F being a finite field) by executing a protocol such that after interacting in terms of phases, 2 R outputs m with probability at least (1—2~") and At gets no information about m. In [2], it shown that in any single phase USMT protocol with n= 2t+ 1,Xi>'J'+ 1, where 5 denotes the message space of S, X, denotes the set of possible data sent through the ith wire and 0< 6<^ is the error probability. 4 In [2], a single phase inefficient USMT protocol with communication complexity approximately matching the above bound has been proposed. We present a single phase polynomial time USMT protocol whose communication complexity is

Abstract

In this paper, we study the inherent tradeoff between the network connectivity, phase complexity and communication complexity of perfectly reliable message transmission (PRMT) problem in undirected synchronous network, tolerating a mixed adversary A^ b, t,) i who has unbounded computing power and can corrupt£(, and tf nodes in the network in Byzantine and fail-stop fashion respectively.

Abstract

The present study outlines an approach to classify forest density and to estimate canopy closure of the forest of the Andaman and Nicobar archipelago. The vector layers generated for the study area using satellite data was validated with the field knowledge of the surveyed ground control points. The methodology adopted in this present analysis is three-tiered. First, the density stratification into five zones using visual

Abstract

We consider the problem of probabilistic reliable communication (PRC) over synchronous networks modeled as directed graphs in the presence of a Byzantine adversary when players’ knowledge of the network topology is not complete. We show that possibility of PRC is extremely sensitive to the changes in players’ knowledge of the topology. This is in complete contrast with earlier known results on the possibility of perfectly reliable communication over undirected graphs where the case of each player knowing only its neighbours gives the same result as the case where players have complete knowledge of the network. Specifically, in either case,(2t+ 1)-vertex connectivity is necessary and sufficient, where t is the number of nodes that can be corrupted by the adversary [DDWY93, SKR+05]. We introduce a novel model for quantifying players’ knowledge of network topology, denoted by T K. Given a directed graph G, influenced by a Byzantine adversary that can corrupt up to any t players, we give a necessary and sufficient condition for possibility of PRC over G for any arbitrary topology knowledge T K. It follows from our main characterization theorem that knowledge of up to d=⌊ n− 2t

Abstract

We address the problem of message authentication in communication networks which are resource constrained or are performance bound. Recent research has focused on development of symmetric key protocols for authentication in such networks. In these protocols, the sender generates a pool of keys -used to sign the messages, and distributes a different subset of keys -used to verify the signatures, to each user. However, in these protocols, users can collude to combine their keys and impersonate the sender by generating the sender signatures. In this work, we describe a family of collusion resistant symmetric key distribution protocols for authentication which address the problem of collusion. We show that the collusion resistance achieved using our protocols is practical (and hence, sufficient) for networks whose communication diameter is known or is within fixed bounds. Furthermore, we show that some existing protocols in literature are members of our family of protocols.

Abstract

This paper focuses on anti-magic labellings of planar graphs of type (a, b, c) introduced by Lih (Util. Math. 24 (1983), 165–197). We show that a certain class of planar graphs defined using the complete graphs and a class of planar graphs defined using the complete bipartite graphs are (1, 1, 0) and (1, 1, 1)-anti-magic under certain mild conditions.

Abstract

This paper deals with the tracking and following of a person with a camera mounted mobile robot. A modified energy based optical flow approach is used for motion segmentation from a pair of images. Further a spatial relative veolcity based filering is used to extract prominently moving objects. Depth and color information are also used to robustly identify and follow a person.

Abstract

This paper explains how to singularize a robot to a unique hypothesis state from a state of multiple hypotheses. This it does by computing a path whose expected distance is minimum from a tree where each path to the leaf from the root results in a singular hypothesis. At various nodes of the tree the number of hypotheses is reduced as it proceeds down from the root. The nodes of the tree are computed as the best locations to move from an earlier higher hypotheses state. They are either frontier regions or a direction of traversal that result in reduction of hypotheses from an earlier multi hypotheses state. The method has been tested robustly in various simulation situations and its efficacy confirmed.