Multi-Party Set Reconciliation Using Characteristic Polynomials

In the standard set reconciliation problem, there are two parties $A_1$ and $A_2$, each respectively holding a set of elements $S_1$ and $S_2$. The goal is for both parties to obtain the union $S_1 \cup S_2$. In many distributed computing settings the sets may be large but the set difference $|S_1-S_2|+|S_2-S_1|$ is small. In these cases one aims to achieve reconciliation efficiently in terms of communication; ideally, the communication should depend on the size of the set difference, and not on the size of the sets. Recent work has considered generalizations of the reconciliation problem to multi-party settings, using a framework based on a specific type of linear sketch called an Invertible Bloom Lookup Table. Here, we consider multi-party set reconciliation using the alternative framework of characteristic polynomials, which have previously been used for efficient pairwise set reconciliation protocols, and compare their performance with Invertible Bloom Lookup Tables for these problems.Comment: 6 page

Set reconciliation

Olgu erinevad seadmed, mis omavad failide hulga erinevaid alamhulki. Talletades neid hulki pilves, kaasneb sellega failide sünkroniseerimise probleem. Eesmärgiks on igas seadmes leida nende hulkade ühend. Naiivne lahendus sellele probleemile on kõikide hulkade edastamine kõikide osapoolte poolt. Selline lähenemine toob kaasa suure andmeedastuskeerukuse. Soovitav oleks leida algoritm, mille andmeedastuskeerukus oleks proportsionaalne hulkade sümmeetrilise vahe suurusega, mis on tüüpiliselt väike võrreldes kõikide failide arvuga. Me defineerime mitmeid erinevaid andmete edastamise võrkude mudeleid. Efektiivsed algoritmid hulkade ühendamiseks on teada kahe osapoolega võrkude jaoks, kuid sarnased algoritmid üldiste võrkude jaoks on veel teadmata. Me uurime võrgu topoloogiate ja hulkade ühendamise algoritmide vahelist seost. Me paneme tähele, et andmeedastuskeerukust on võimalik vähendada spetsiifilise topoloogiaga võrkudes. Me samuti uurime juhtmega võrkudes iteratsioonide minimiseerimise ülesannet. Me defineerime ühenduste kaaludena ühenduste otspunktideks olevates seadmetes asuvate erinevate failide arvu. Me uurime katseliselt maksimaalsete kaalude valikumeetodi efektiivsust suhtlevate seadmepaaride valikuks. Tulemused viitavad, et see algoritm annab paremaid tulemusi võrreldes suhtlevate seadmepaaride juhusliku valikuga. Selle magistritöö põhitulemuseks on algebraline analüütiline raamistik hulkade ühendamise algoritmide uurimiseks juhtmeta võrkudes. Raamistiku abil on võimalik optimeerida hulkade ühendamise algoritme, mis kasutavad lineaarselt kodeeritud teateid. See lähenemine üritab minimiseerida iteratsioonide ja edastavate teadete arvu.Assume that we have several devices with different subsets of a set of files. The problem of file synchronization arises in cloud storage. The goal is to find a union of the sets at each of these devices. The naive solution to the problem is to transmit the whole sets by all parties in the network. This, however, results in high communicational complexity. It would be desirable to find an algorithm with communicational complexity that is proportional to the size of the symmetric difference of the sets, which is typically small when compared to the total number of files. We define a number of communication network models. Several efficient algorithms for set reconciliation over a network with two devices have been described in the literature, but similar algorithms for general networks are still unknown. We study the connection between the network topologies and the communicational cost in the set reconciliation algorithms. We observe that it is possible to reduce the communicational cost in networks of specific topology. We also study a problem of minimization of a number of communication rounds in a wired network. We define weights on the edges of the graph according to the number of different files in the communicating devices. Then, we experimentally test the efficiency of choosing the communicating pairs using maximum weight matching. The results imply that this algorithm provides better results than its counterpart which chooses the communicating pairs randomly. The main result of this Thesis is an algebraic analytical framework for studying the set reconciliation algorithms in wireless networks. This frameworks allows for optimizing set reconciliation protocols which use linearly coded messages. This approach aims at minimizing the number of iterations and the number of transmissions during each iteration

Quantum information with continuous variables

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.Comment: accepted for publication in Reviews of Modern Physic

Quantum cryptography: key distribution and beyond

Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and other applications.Comment: It's a review on quantum cryptography and it is not restricted to QK

Scather: programming with multi-party computation and MapReduce

We present a prototype of a distributed computational infrastructure, an associated high level programming language, and an underlying formal framework that allow multiple parties to leverage their own cloud-based computational resources (capable of supporting MapReduce [27] operations) in concert with multi-party computation (MPC) to execute statistical analysis algorithms that have privacy-preserving properties. Our architecture allows a data analyst unfamiliar with MPC to: (1) author an analysis algorithm that is agnostic with regard to data privacy policies, (2) to use an automated process to derive algorithm implementation variants that have different privacy and performance properties, and (3) to compile those implementation variants so that they can be deployed on an infrastructures that allows computations to take place locally within each participant’s MapReduce cluster as well as across all the participants’ clusters using an MPC protocol. We describe implementation details of the architecture, discuss and demonstrate how the formal framework enables the exploration of tradeoffs between the efficiency and privacy properties of an analysis algorithm, and present two example applications that illustrate how such an infrastructure can be utilized in practice.This work was supported in part by NSF Grants: #1430145, #1414119, #1347522, and #1012798

Theory and Practice of Cryptography and Network Security Protocols and Technologies

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities