The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the $K$ files, where each file is of size $L$ bits, and several databases with storage size constraint $\mu K L$ bits exist in the system. Each database independently chooses $\mu K L$ bits out of the total $KL$ bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses $N$ databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum_{n=1}^{N+1} \binom{N}{n-1} \mu^{n-1} (1-\mu)^{N+1-n} \left( 1+ \frac{1}{n} + \dots+ \frac{1}{n^{K-1}} \right)$. We show that uniform and random caching scheme which is originally proposed for decentralized coded caching by Maddah-Ali and Niesen, along with Sun and Jafar retrieval scheme which is originally proposed for PIR from replicated databases surprisingly result in the lowest normalized download cost. This is the decentralized counterpart of the recent result of Attia, Kumar and Tandon for the centralized case. The converse proof contains several ingredients such as interference lower bound, induction lemma, replacing queries and answering string random variables with the content of distributed databases, the nature of decentralized uncoded caching databases, and bit marginalization of joint caching distributions.Comment: Submitted for publication, November 201

분산 컴퓨팅과 캐시를 접목한 정보 검색에서의 보안 및 프라이버시

학위논문(박사)--서울대학교 대학원 :공과대학 전기·정보공학부,2020. 2. 이정우.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.1. Introduction 1 1.1 Related work 3 1.1.1 Private information retrieval 3 1.1.2 Coded computation 4 1.2 Contributions and Organization 5 2. Cache-aided Private Information Retrieval 8 2.1 Introduction 8 2.2 System model 9 2.3 Main results : 12 2.4 Achievable scheme 17 2.4.1 Cacheless phase 17 2.4.2 Cache-assisted phase 21 2.4.3 Cache-aided PIR 24 2.5 Tightness of achievable scheme 29 2.6 Conclusions and follow-up works 30 3. Private Coded Computation 32 3.1 Introduction 32 3.2 System model 37 3.3 Main results 41 3.4 Private polynomial codes 42 3.4.1 First example 42 3.4.2 Second example 48 3.4.3 General description 52 3.4.4 Privacy proof 56 3.4.5 Performance analysis 59 3.4.6 Special cases 61 3.5 Simulation results 62 3.5.1 Computation time 62 3.5.2 Communication load 68 3.6 Conclusion 69 4. Private Secure Coded Computation 71 4.1 Introduction 71 4.2 Main results 75 4.3 Private secure polynomial codes 76 4.3.1 Illustrative example 76 4.3.2 General description 80 4.3.3 Performance analysis 83 4.3.4 Privacy and security proof 84 4.4 Simulation results 85 4.4.1 Computation time 86 4.4.2 Communication load 90 4.5 Conclusion 91 5 Conclusion 93 5.1 Summary 93 5.2 Future directions 94 국문초록 105 Acknowledgement 107Docto

Information-Theoretically Private Federated Submodel Learning with Storage Constrained Databases

In federated submodel learning (FSL), a machine learning model is divided into multiple submodels based on different types of data used for training. Each user involved in the training process only downloads and updates the submodel relevant to the user's local data, which significantly reduces the communication cost compared to classical federated learning (FL). However, the index of the submodel updated by the user and the values of the updates reveal information about the user's private data. In order to guarantee information-theoretic privacy in FSL, the model is stored at multiple non-colluding databases, and the user sends queries and updates to each database in such a way that no information is revealed on the updating submodel index or the values of the updates. In this work, we consider the practical scenario where the multiple non-colluding databases are allowed to have arbitrary storage constraints. The goal of this work is to develop read-write schemes and storage mechanisms for FSL that efficiently utilize the available storage in each database to store the submodel parameters in such a way that the total communication cost is minimized while guaranteeing information-theoretic privacy of the updating submodel index and the values of the updates. As the main result, we consider both heterogeneous and homogeneous storage constrained databases, and propose private read-write and storage schemes for the two cases.Comment: arXiv admin note: text overlap with arXiv:2302.0367

Quantum Symmetric Private Information Retrieval with Secure Storage and Eavesdroppers

We consider both the classical and quantum variations of $X$-secure, $E$-eavesdropped and $T$-colluding symmetric private information retrieval (SPIR). This is the first work to study SPIR with $X$-security in classical or quantum variations. We first develop a scheme for classical $X$-secure, $E$-eavesdropped and $T$-colluding SPIR (XSETSPIR) based on a modified version of cross subspace alignment (CSA), which achieves a rate of $R= 1 - \frac{X+\max(T,E)}{N}$. The modified scheme achieves the same rate as the scheme used for $X$-secure PIR with the extra benefit of symmetric privacy. Next, we extend this scheme to its quantum counterpart based on the $N$-sum box abstraction. This is the first work to consider the presence of eavesdroppers in quantum private information retrieval (QPIR). In the quantum variation, the eavesdroppers have better access to information over the quantum channel compared to the classical channel due to the over-the-air decodability. To that end, we develop another scheme specialized to combat eavesdroppers over quantum channels. The scheme proposed for $X$-secure, $E$-eavesdropped and $T$-colluding quantum SPIR (XSETQSPIR) in this work maintains the super-dense coding gain from the shared entanglement between the databases, i.e., achieves a rate of $R_Q = \min\left\{ 1, 2\left(1-\frac{X+\max(T,E)}{N}\right)\right\}$