Common Randomness Principles of Secrecy

This dissertation concerns the secure processing of distributed data by multi- ple terminals, using interactive public communication among themselves, in order to accomplish a given computational task. In the setting of a probabilistic multitermi- nal source model in which several terminals observe correlated random signals, we analyze secure distributed data processing protocols that harness the correlation in the data. The specific tasks considered are: computing functions of the data under secrecy requirements; generating secretly shared bits with minimal rate of public communication; and securely sharing bits in presence of a querying eavesdropper. In studying these various secure distributed processing tasks, we adopt a unified approach that entails examining the form of underlying common randomness (CR) that is generated at the terminals during distributed processing. We make the case that the exact form of established CR is linked inherently to the data processing task at hand, and its characterization can lead to a structural understanding of the associated algorithms. An identification of the underlying CR and its decomposi- tion into independent components, each with a different operational significance, is a recurring fundamental theme at the heart of all the proofs in this dissertation. In addition to leading to new theoretical insights, it brings out equivalences between seemingly unrelated problems. Another distinguishing feature of this work is that it considers interactive communication protocols. In fact, understanding the structure of such interactive communication is a key step in proving our results. We make the following contributions. First, we propose a new information theoretic formulation to study secure distributed computing using public communi- cation. The parties observing distributed data are trusted but an eavesdropper has access to the public communication network. We examine distributed communica- tion protocols that allow the trusted parties to accomplish their required computa- tion tasks while giving away negligible information about a specified portion of the data to an eavesdropper with access to the communication. Our theoretical results provide necessary and sufficient conditions that characterize the feasibility of vari- ous secure computing tasks; in many cases of practical importance, these conditions take a simple form and can be verified easily. When secure computing is feasible, we propose new algorithms in special cases. Next, we revisit the problem of generating shared secret keys (SKs). We investigate minimum communication requirements for generating information theo- retically secure SKs of maximum rates from correlated observations using interactive public communication. In particular, our approach allows us to examine the role of interaction in such communication. On the one hand, we find that interaction is not needed when the observed correlated bits are symmetrically correlated and therefore, in this case, simple noninteractive protocols are the most efficient means of generating optimum rate SKs. On the other hand, we illustrate that interactive pro- tocols can require a strictly lower rate of overall communication than noninteractive protocols. Finally, we consider the task of ensuring security against an eavesdropper who makes queries about a portion of the distributed data that the terminals share by communicating over a public network. We introduce an alternative notion of secrecy which requires rendering the task of a querying eavesdropper as onerous as possible. Our main contribution in this part is the development of a new technique for proving converse results for secrecy problems involving CR with interactive communication, which is employed then to obtain an upper bound for the maximum number of queries that can be inflicted on the eavesdropper for any CR and corresponding communication. Surprisingly, there is an equivalence between this notion of secrecy and that of information theoretic security, which leads to new theoretical results for SK generation; for instance, we prove a strong converse for the SK capacity. We conclude by hypothesizing the basic principles of secrecy generation that emerge from the results developed in this dissertation

Secret Key Agreement: General Capacity and Second-Order Asymptotics

We revisit the problem of secret key agreement using interactive public communication for two parties and propose a new secret key agreement protocol. The protocol attains the secret key capacity for general observations and attains the second-order asymptotic term in the maximum length of a secret key for independent and identically distributed observations. In contrast to the previously suggested secret key agreement protocols, the proposed protocol uses interactive communication. In fact, the standard one-way communication protocol used prior to this work fails to attain the asymptotic results above. Our converse proofs rely on a recently established upper bound for secret key lengths. Both our lower and upper bounds are derived in a single-shot setup and the asymptotic results are obtained as corollaries

A Bound For Multiparty Secret Key Agreement And Implications For A Problem Of Secure Computing

We consider secret key agreement by multiple parties observing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, without making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of ``how far is the joint distribution of the initial observations of the parties and the eavesdropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper\u27s side information. The closeness of the two distributions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypothesis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers several known upper bounds for the asymptotic rate of a secret key that can be generated, without requiring the agreement error probability or the security index to vanish to 0 asymptotically. Also, we consider the following problem of secure function computation with trusted parties: Multiple parties observing correlated data seek to compute a function of their collective data. To this end, they communicate interactively over an insecure communication channel. It is required that the value of the function be concealed from an eavesdropper with access to the communication. When is such a secure computation of a given function feasible? Using the aforementioned upper bound, we derive a necessary condition for the existence of a communication protocol that allows the parties to reliably recover the value of a given function, while keeping this value concealed from an eavesdropper with access to (only) the communication

Algorithms for interactive, distributed and networked systems

In recent years, massive growth in internet usage has spurred the emergence of complex large-scale networking systems to serve growing user bases, bandwidth and computation requirements. For example, data center facilities -- workhorses of today's internet -- have evolved to house upward of several hundreds of thousands of servers; content distribution networks with high capacity and wide coverage have emerged as a de facto content dissemination modality, and peer-to-peer applications with hundreds of thousands of users are increasingly becoming popular. At these scales, it becomes critical to operate at high efficiencies as the price of idling resources can be significant. In particular, the interaction between agents (servers, peers etc.) is a defining factor of efficiency in these systems -- applications are often communication intensive, whereas agents share links of only limited bandwidth. This necessitates the use of principled algorithms, as efficient communication to a large extent depends on the interaction protocols. We study data center networks and peer-to-peer networks as canonical examples of modern-day large-scale networking systems. Server-to-server interaction is an integral part of the data center's operation. The latency of these interactions is often a significant bottleneck toward overall job completion times. We study complementary approaches toward reducing this latency: (i) design of computation algorithms that minimize interaction and (ii) optimal scheduling algorithms to maximally utilize the network fabric. We also consider peer-to-peer networks as an emerging mode of content distribution and sharing. Unlike data centers, these networks are flexible in their network structure and also scale well, but require decentralized algorithms for control. Of central importance here is the design of a network topology that enables efficient peer interactions for optimal application performance. We propose novel topology designs for two popular applications: (i) multimedia streaming and (ii) anonymity in Bitcoin's peer-to-peer network