Anuj Gupta

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First n foremost, I would like to thank Dr. Kannan Srinathan who has had a tremendous influence o... more First n foremost, I would like to thank Dr. Kannan Srinathan who has had a tremendous influence on me. On top of being an expert, he has been a dear friend, a profound philosopher and a devoted guide, far beyond ordinary. He introduced me to research and closely guided my first steps. He has this special property of always searching for the crux of any matter. This, together with his sharpness, energy and amazing sense of humour makes him a remarkable person and pleasure to work with. His feedback and encouragement greatly helped me to keep my spirits up. He always encouraged me to develop a broader perspective towards research and life in general. We would spent hours on discussing over a wide variety topics ranging from cricket, education to the realms of life, human existence and what not ! Today, as I look back, I find these discussion very close to my heart and by far the most cherished part of my journey. These interactions introduced me to a newer perspective of looking at things around me and have greatly influenced my understanding of life in general. I also would like to acknowledge the members of my graduate review committee namely, Prof. C. V. Jawahar, Dr. Navin Goel, and Dr. Suresh Purini for their encouragement and invaluable suggestions. I am also thankful to all the faculty members of CSTAR-Prof. V. Ch. Venkaiah, Dr Kannan Srinathan, Dr. Kishore Kothapalli and Dr. Bruhadeshwar Bezawada for providing a wonderful research center. I also take this opportunity to thank IIIT-Hyderabad for giving me an opportunity to see the world of research so closely. My research mates Prasant Gopal, Piyush Bansal, Pranav Kumar Vasishta, Sandeep Hans and Sarat Addepalli deserve a special acknowledgement. Without these people this thesis would not have been possible. I would also like to thank my seniors Ritesh Kumar Tiwari, Ananda Swarup Das and G. Bhavani Shankar for their guidance. My lab-mates were very kind and helpful. They include

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On Composition of Authenticated Byzantine Generals Or Should Not Hard Work Always Pay in All Environments ? ( Extended

Consider a player who diligently executes (only) the delegated protocol but the adversary steals ... more Consider a player who diligently executes (only) the delegated protocol but the adversary steals some private information from him. Should such a player be considered faulty? In a stand alone execution model, the answer can be either yes or no depending on the context/settings. However, with respect to composition of protocols, we show that the answer has to be no even though the literature answers this as yes. We show that an affirmative answer to this question leads to several undesirable side effects. In light of these findings we propose a new model to study composition of protocols. For our study we use the problem of parallel composition of Authenticated Byzantine Generals (ABG) as a case study. In our model we show that in spite of using unique session identifiers, if n < 2t, there cannot exist any ABG protocol that composes in parallel even twice. Further, for n ≥ 2t, we design ABG protocols that compose for any number of parallel executions.

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How Far Must You See To Hear Reliably

IACR Cryptol. ePrint Arch., 2008

We consider the problem of probabilistic reliable communication (PRC) over synchronous networks m... more 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, SKR05]. We introduce a novel model for quantifying players’ knowledge of network topology, denoted by TK. Given a directed graph G, influenced by a Byzantine adversary that can corrupt up to any t players, we giv...

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A New Look at Composition of Authenticated Byzantine Generals

ArXiv, 2012

The problem of Authenticated Byzantine Generals (ABG) aims to simulate a virtual reliable broadca... more The problem of Authenticated Byzantine Generals (ABG) aims to simulate a virtual reliable broadcast channel from the General to all the players via a protocol over a real (point-to-point) network in the presence of faults. We propose a new model to study the self-composition of ABG protocols. The central dogma of our approach can be phrased as follows: Consider a player who diligently executes (only) the delegated protocol but the adversary steals some private information from him. Should such a player be considered faulty? With respect to ABG protocols, we argue that the answer has to be no. In the new model we show that in spite of using unique session identifiers, if $n < 2t$, there cannot exist any ABG protocol that composes in parallel even twice. Further, for $n \geq 2t$, we design ABG protocols that compose for any number of parallel executions. Besides investigating the composition of ABG under a new light, our work also brings out several new insights into Canetti's ...

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On Composability of Reliable Unicast and Broadcast

In the recent past composability has emerged as a key requirement for various distributed protoco... more In the recent past composability has emerged as a key requirement for various distributed protocols. It is not enough for a protocol to be robust when it runs in isolation or in a “stand-alone” setting but it should be robust even in an environment where several copies of the same protocol or other protocol(s) are running simultaneously. In this work, we investigate the composability for protocols that tolerate a bounded adversary modeled as a probabilistic polynomial time Turing machine. We examine composability of protocols for two fundamental problems in distributed computing - reliable unicast and reliable broadcast. We show that any composable protocol – for reliable unicast tolerating an adversary, that corrupts up to any t nodes, requires 2t + 1 connectivity and for reliable broadcast tolerating an adversary, that corrupts up to any t nodes, requires n > 3t and 2t + 1 connectivity.

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A New Look at Composition of Authenticated Byzantine Generals

In the new model we show that in spite of using unique session identifiers, if $n < 2t$, there ca... more In the new model we show that in spite of using unique session identifiers, if $n < 2t$, there cannot exist any ABG protocol that composes in parallel even twice. Further, for $n \geq 2t$, we design ABG protocols that compose for any number of parallel executions. Besides investigating the composition of ABG under a new light, our work also brings out several new insights into Canetti's Universal Composability framework. Specifically, we show that there are several undesirable effects if one deviates from our dogma. This provides further evidence as to why our dogma is the right framework to study the composition of ABG protocols.

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On Privacy Preserving Convex Hull

2009 International Conference on Availability, Reliability and Security, 2009

Computing convex hull for a given set of points is one of the most explored problems in the area ... more Computing convex hull for a given set of points is one of the most explored problems in the area of computational geometry (CG). If the set of points is distributed among a set of parties who jointly wish to compute the convex hull, each party can send his points to every other party, and can then locally compute the hull

Byzantine Agreement Using Partial Authentication

Lecture Notes in Computer Science, 2011

... Specifically, Borcherd-ing [Bor95, Bor96b] investigated the case when signatures are used in ... more

Authenticated Byzantine Generals in Dual Failure Model

Lecture Notes in Computer Science, 2010

Pease et al. introduced the problem of Byzantine Generals (BGP) to study the effects of Byzantine... more Pease et al. introduced the problem of Byzantine Generals (BGP) to study the effects of Byzantine faults in distributed protocols for reliable broadcast. It is well known that BGP among n players tolerating up to t faults is (efficiently) possible if and only if n > 3t. To overcome this severe limitation, Pease et al. introduced a variant of BGP, Authenticated Byzantine General (ABG). Here players are supplemented with digital signatures (or similar tools) to thwart the challenge posed by Byzantine faults. Subsequently, they proved that with the use of authentication, fault tolerance of protocols for reliable broadcast can be amazingly increased to n > t (which is a huge improvement over the n > 3t). Byzantine faults are the most generic form of faults. In a network not all faults are always malicious. Some faulty nodes may only leak their data while others are malicious. Motivated from this, we study the problem of ABG in (t b ,t p)-mixed adversary model where the adversary can corrupt up to any t b players actively and control up to any other t p players passively. We prove that in such a setting, ABG over a completely connected synchronous network of n nodes tolerating a (t b ,t p)-adversary is possible if and only if n > 2t b +min(t b , t p) when t p > 0. Interestingly, our results can also be seen as an attempt to unify the extant literature on BGP and ABG.

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How Far Must You See to Hear Reliably (Extended Abstract)

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Topology Knowledge Versus Fault Tolerance:The Case of Probabilistic Reliable Communication Or: How Far Must You See to Hear Reliably (Extended Abstract)

We consider the problem of probabilistic reliable communication (PRC) over synchronous networks m... more 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 sucient, where t is the number of nodes that can be corrupted by the adversary (2,9). 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 gi...

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Anuj Gupta

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