In this paper we study Perfectly Secure Message Transmission (PSMT) between a sender S and a receiver R, connected in a directed synchronous network through multiple parallel edges (called wires), each of which are directed from S to R or vice-versa. The unreliability of the network is modeled by a Byzantine adversary with infinite computing power. We investigate the problem with two different adversarial settings: (i) threshold and (ii) non-threshold. In [1], the authors have characterized PSMT against a t-active threshold adversary in directed networks1. However, their PSMT protocol was exponential both in terms of number of phases2 and communication complexity. In addition, they also presented a polynomial phase PSMT protocol with n′ = max(3t-u+1, 2t+1) wires from S to R. In this paper, we significantly improve the exponential phase protocol and present an elegant and efficient three phase PSMT protocol with polynomial communication complexity (and computational complexity) with n= max(3t-2u+1, 2t+1) wires from S to R. Also with n′ = max(3t - u + 1, 2t + 1) wires from S to R, we are able to further improve the communication complexity of our three phase PSMT protocol. Our second contribution in this paper is the first ever characterization for any two phase PSMT protocol. Finally, we also characterize PSMT protocol in directed networks tolerating nonthreshold adversary. In [3], the authors have given the characterization for PSMT against non-threshold adversary. However, in their characterization, they have only considered the paths from S to R, excluding the feedback paths (i.e paths from R to S) and hence their characterization holds good only for single phase protocols. We characterize multiphase PSMT considering feedback paths.

Perfectly secure message transmission in directed networks tolerating threshold and non threshold adversary

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(tb,tf), who has unbounded computing power and can corrupt tb and tf nodes in the network in Byzantine and fail-stop fashion respectively.

On tradeoff between network connectivity, phase complexity and communication complexity of reliable communication tolerating mixed adversary

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 O(l) 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.

On communication complexity of secure message transmission in directed networks

Consider the following problem: a sender S and a receiver R are part of an unreliable, connected, distributed network. The distrust in the network is modelled by an entity called adversary, who has unbounded computing power and who can corrupt some of the nodes of the network (excluding S and R) in a variety of ways. S wishes to send to R a message m that consists of l elements, where l ≥ 1, selected uniformly from a finite field F. The challenge is to design a protocol, such that after interacting with S as per the protocol, R should output m without any error (perfect reliability). Moreover, this hold irrespective of the disruptive actions done by the adversary. This problem is called reliable message transmission or RMT in short. The problem of secure message transmission or SMT in short requires an additional constraint that the adversary should not get any information about the message what so ever in information theoretic sense (perfect secrecy). Security against an adversary with infinite computing power is also known as non-cryptographic or information theoretic or Shannon security and this is the strongest notion of security. Notice that since the adversary has unbounded computing power, we cannot solve RMT and SMT problem by using classical cryptographic primitives such as public key cryptography, digital signatures, authentication schemes, etc as the security of all these primitives holds good only against an adversary having polynomially bounded computing power. RMT and SMT problem can be studied in various network models and adversarial settings. We may use the following parameters to describe different settings/models for studying RMT/SMT: 1. Type of Underlying Network — Undirected Graph, Directed Graph, Hypergraph. 2. Type of Communication — Synchronous, Asynchronous. 3. Adversary capacity — Threshold Static, Threshold Mobile, Non-threshold Static, Non-threshold Mobile. 4. Type of Faults — Fail-stop, Passive, Byzantine, Mixed. Irrespective of the settings in which RMT/SMT is studied, the following issues are common: 1. Possibility: What are the necessary and sufficient structural conditions to be satisfied by the underlying network for the existence of any RMT/SMT protocol, tolerating a given type of adversary? 2. Feasibility: Once the existence of a RMT/SMT protocol in a network is ascertained, the next natural question is, does there exist an efficient protocol on the given network? 3. Optimality: Given a message of specific length, what is the minimum communication complexity (lower bound) needed by any RMT/SMT protocol to transmit the message and how to design a polynomial time RMT/SMT protocol whose total communication complexity matches the lower bound on the communication complexity (optimal protocol)? In this dissertation, we look into the above issues in several network models and adversarial settings. This thesis reports several new/improved/efficient/optimal solutions, gives affirmative/negative answers to several significant open problems and last but not the least, provides first solutions to several newly formulated problems.

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Protocols for Reliable and Secure Message Transmission.

We study the problem of perfectly reliable message transmission (PRMT) and perfectly secure message transmission (PSMT) in an undirected synchronous network tolerating an all powerful threshold mobile Byzantine adversary Specifically, we show that the mobility of the threshold adversary does not affect the possibility and optimality of PRMT and PSMT protocols We also characterise PSMT in directed networks tolerating mobile adversary All existing PRMT and PSMT protocols abstract the paths between the sender and the receiver as wires, neglecting the intermediate nodes in the paths, thus causing significant over estimation in the communication and round complexity of protocols Here, we consider the underlying paths as a whole instead of abstracting them as wires and derive a tight bound on the number of rounds required to achieve reliable communication tolerating a threshold mobile adversary with arbitrary roaming speed Finally, we briefly study PRMT and PSMT protocols in the presence of non-threshold mobile Byzantine adversary Even though the characterisation for PRMT/PSMT is shown to be same against both threshold static and threshold mobile adversary (in this article), we show that the characterisation for PRMT/PSMT against non-threshold static and non-threshold mobile adversary are not same

Perfectly reliable and secure message transmission tolerating mobile adversary

An arrangement for controlling the advancing device of a machine for repetitive operations, especially for controlling the advancing speed of a slide carrying a cutting device of a cutting machine for cutting an elongated workpiece, such as a profile emanating at a predetermined speed from an extrusion press, a straightening machine or the like, into sections of uniform length. The arrangement performs the steps of preaccelerating the slide before a front end of the workpiece hits an abutment located on the slide in the path of the front end of the workpiece to a speed smaller than the speed at which the workpiece advances, and accelerating the speed of the slide to the speed of the workpiece upon engagement of the front end of the workpiece with the abutment, and subsequently thereto actuating the cutting device, whereby the impact force of the workpiece on the abutment is reduced, so that buckling of the workpiece upon impact on the abutment is prevented and the accuracy of the cutting operation is increased.

Chanrasekharan Pandu Rangan

Papers

Constant phase efficient protocols for secure message transmission in directed networks