Privacy and Security in Coded Computation and Cache-aided Information Retrieval

Abstract

많은 양의 데이터 저장이나 데이터 계산을 위해서는 분산 시스템이 필수적이다. 이러한 분산 시스템의 데이터 저장과 계산의 효율의 높이는 반면, 데이터의 보안과 프라이버시에 대한 위험도 증가시킨다. 본 논문에서는 데이터 저장과 데이터 계산을 위한 분산 시스템에서 데이터에 대한 보안과 프라이버시를 고려한다. 특히, 이러한 시스템에 대하여 보안과 프라이버시를 보장하는 부호화 기법을 제안한다.

우선, 유저가 사전에 캐시에 일정량의 데이터를 저장하고 있는 cache-aided PIR을 제안한다. 제안하는 기법은 기존 PIR 문제의 최적 기법을 기반으로 한다. 제안하는 기법에서, 캐시에 저장된 데이터는 부가정보로 이용되며, 이는 캐시가 없을 때 대비 다운로드양의 감소로 이어진다.

두 번째로, 부호화된 분산 컴퓨팅 시스템에서 마스터의 프라이버시를 고려한다. 이 시스템에서 워커들과 마스터는 각각 고유한 데이터를 가지며, 워커들의 데이터는 라이브러리 형태로 이루어진다. 마스터는 자신의 데이터와 데이터 라이브러리 내 특정 데이터의 함수를 계산해야 한다. 이 때 마스터의 프라이버시는 워커들이 마스터가 라이브러리 안의 어떤 데이터를 원하는지 모르는 것을 뜻한다. 이러한 시스템을 private coded computation이라 하며, 제안하는 기법을 private polynomial codes라 한다. 제안하는 기법에서는 기존의 polynomial codes에서는 고려되지 않았던 비동기적 기법이 도입된다. 이로 인하여 제안하는 기법은 변형된 최적의 RPIR 기법대비 더 빠른 계산시간을 달성한다.

끝으로, 부호화된 분산 컴퓨팅 시스템에서 마스터의 프라이버시와 데이터 보안을 동시에 고려한다. 데이터 보안은 마스터의 고유한 데이터를 워커들로부터 보호하는 것을 의미한다. 이러한 시스템을 private secure coded computation이라 하며, 제안하는 기법을 private secure polynomial codes라 한다. Private polynomial codes를 변형하여 private secure polynomial codes와 private polynomial codes를 계산시간과 통신량 측면에서 비교한다. 그 결과, 같은 양의 통신량에 대하여, private secure polynomial codes가 더 빠른 계산 시간을 달성한다.

As a major format of data changes from the text to the videos, the amount of memory for storing data increases exponentially, as well as the amount of computation for handling the data. As a result, to alleviate these burdens of storage and computations, the distributed systems are actively studied. Meanwhile, since low latency is one of the main objectives in 5G communications, recent techniques such as edge computing or federated learning in machine learning become important. Since the decentralized systems are fundamental characteristics of these techniques, the distributed systems which include the decentralized systems also become important.

In this dissertation, I consider the distributed systems for storage and computation. For the data storage, large-scale data centers collectively store a library of files where the size of each file is tremendous. When a user needs a specific file, it can be downloaded from distributed data centers. In this system, minimizing the amount of download is a significant concern. The user's privacy in this system implies that the user should conceal the index of its desired file against the databases. This kind of problem is referred to as private information retrieval (PIR) problem. The goal of PIR problem is to minimize the amount of download from the databases while ensuring the user's privacy.

Meanwhile, for a large amount of computation, the user can divide the whole computation into sub-computations and distribute them to external workers who constitute a distributed system. There can be three cases for the computation. Firstly, the user may own all of the data to be computed and sends both of its data and instructions for the computation to the workers. Secondly, the workers collectively own all of the data and the user just sends instructions for the data selection and computation to the workers. Thirdly, the user and the workers have their own data respectively and the user sends the data and instructions for the data selection and computation to the workers. Since some of the workers can be slow for various reasons, the user may use a coding technique, e.g., an erasure code, to avoid the delaying effect caused by the slow workers. This kind of technique is referred to as coded computation. In these systems, speeding up the computation process is a significant concern. In this dissertation, I focus on the third system. In the considered system, the privacy is similar to that of distributed systems for storage. On the other hand, the security implies that the user should conceal the content of its own data against the workers so that the workers do not have any information about the user's own data.

In this dissertation, I consider the user's privacy in distributed systems for storage, and both of the privacy and security in distributed systems for the computation. In case of the distributed systems for storage, since the user does not have its own data, the data security on the user's data cannot be considered. Particularly, I propose some achievable schemes that ensure the privacy and security in these systems.

To begin with, as a new variation of PIR problem, I consider a user's cache that has some pre-stored data of databases' library. I refer to this problem as cache-aided PIR problem. By introducing the user's cache in the PIR problem, the amount of download from the databases is significantly reduced. The achievable scheme is based on the optimal scheme for conventional PIR problem. In the achievable scheme, the pre-store cache was exploited as an side information, which reduces the amount of download, compared to the PIR problem without cache.

Secondly, I consider the master's privacy in coded computation. In the system model, the workers have their own data, as well as the master. The workers' data constitutes a library of several files. The master should compute a function of its own data and a specific file in the library. The master's privacy implies that the workers' should not know which file in the library is desired by the user. I refer to this problem as private coded computation and propose an achievable scheme of private coded computation, namely private polynomial codes. The private polynomial codes are based on the polynomial codes which were proposed in the conventional coded computation system. In the achievable scheme, the workers are grouped for the privacy and asynchronous scheme is considered, which was not considered in the conventional polynomial codes. Due to the asynchronous scheme, the proposed scheme achieves the faster computation time, compared to the modified optimal RPIR scheme.

Lastly, I consider the data security in coded computation, as well as the master's privacy. The system model is similar to that of private coded computation. The data security implies that the master should protect its own data against the workers. I refer to this problem as private secure coded computation and propose an achievable scheme, namely private secure polynomial codes. The private secure polynomial codes are based on the polynomial codes which were proposed in the conventional coded computation system. By modifying the private polynomial codes, the private secure polynomial codes and private secure polynomial codes are compared in terms of computation time and communication load. As a result, the private secure polynomial codes achieves faster computation time for the same communication load.