O ct 2 01 9 The Role of Coded Side Information in Single-Server Private Information Retrieval (original) (raw)
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Capacity of Single-Server Single-Message Private Information Retrieval with Coded Side Information
2018 IEEE Information Theory Workshop (ITW), 2018
This paper considers the problem of single-server single-message private information retrieval with coded side information (PIR-CSI). In this problem, there is a server storing a database, and a user which knows a linear combination of a subset of messages in the database as a side information. The number of messages contributing to the side information is known to the server, but the indices and the coefficients of these messages are unknown to the server. The user wishes to download a message from the server privately, i.e., without revealing which message it is requesting, while minimizing the download cost. In this work, we consider two different settings for the PIR-CSI problem depending on the demanded message being or not being one of the messages contributing to the side information. For each setting, we prove an upper bound on the maximum download rate as a function of the size of the database and the size of the side information, and propose a protocol that achieves the rate upper-bound.
2019 IEEE International Symposium on Information Theory (ISIT)
This paper considers the problem of single-server single-message private information retrieval with coded side information (PIR-CSI). In this problem, there is a server storing a database, and a user which knows a linear combination of a subset of messages in the database as a side information. The number of messages contributing to the side information is known to the server, but the indices and the coefficients of these messages are unknown to the server. The user wishes to download a message from the server privately, i.e., without revealing which message it is requesting, while minimizing the download cost. In this work, we consider two different settings for the PIR-CSI problem depending on the demanded message being or not being one of the messages contributing to the side information. For each setting, we prove an upper bound on the maximum download rate as a function of the size of the database and the size of the side information, and propose a protocol that achieves the rate upper-bound.
Private Information Retrieval with Side Information
IEEE Transactions on Information Theory
We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of K independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of M messages, not containing the desired message and unknown to the servers. This problem is motivated by practical settings in which the user can obtain side information opportunistically from other users or has previously downloaded some messages using classical PIR schemes. The objective of the user is to retrieve the required message without revealing its identity while minimizing the amount of data downloaded from the servers. We focus on achieving information-theoretic privacy in two scenarios: (i) the user wants to protect jointly its demand and side information; (ii) the user wants to protect only the information about its demand, but not the side information. To highlight the role of side information, we focus first on the case of a single server (single database). In the first scenario, we prove that the minimum download cost is K − M messages, and in the second scenario it is ⌈ K M +1 ⌉ messages, which should be compared to K messages, the minimum download cost in the case of no side information. Then, we extend some of our results to the case of the database replicated on multiple servers. Our proof techniques relate PIR with side information to the index coding problem. We leverage this connection to prove converse results, as well as to design achievability schemes.
2022 IEEE International Symposium on Information Theory (ISIT)
This paper considers the problem of single-server Individually-Private Information Retrieval with side information (IPIR). In this problem, there is a remote server that stores a dataset of K messages, and there is a user that initially knows M of these messages, and wants to retrieve D other messages belonging to the dataset. The goal of the user is to retrieve the D desired messages by downloading the minimum amount of information from the server while revealing no information about whether an individual message is one of the D desired messages. In this work, we focus on linear IPIR schemes, i.e., the IPIR schemes in which the user downloads only linear combinations of the original messages from the server. We prove a converse bound on the download rate of any linear IPIR scheme for all K, D, M, and show the achievability of this bound for all K, D, M satisfying a certain divisibility condition. Our results characterize the linear capacity of IPIR, which is defined as the maximum achievable download rate over all linear IPIR schemes, for a wide range of values of K, D, M.
The Role of Coded Side Information in Single-Server Private Information Retrieval
IEEE Transactions on Information Theory
We study the role of coded side information in single-server Private Information Retrieval (PIR). An instance of the single-server PIR problem includes a server that stores a database of K independently and uniformly distributed messages, and a user who wants to retrieve one of these messages from the server. We consider settings in which the user initially has access to a coded side information which includes a linear combination of a subset of M messages in the database. We assume that the identities of the M messages that form the support set of the coded side information as well as the coding coefficients are initially unknown to the server. We consider two different models, depending on whether the support set of the coded side information includes the requested message or not. We also consider the following two privacy requirements: (i) the identities of both the demand and the support set of the coded side information need to be protected, or (ii) only the identity of the demand needs to be protected. For each model and for each of the privacy requirements, we consider the problem of designing a protocol for generating the user's query and the server's answer that enables the user to decode the message they need while satisfying the privacy requirement. We characterize the (scalar-linear) capacity of each setting, defined as the ratio of the number of information bits in a message to the minimum number of information bits downloaded from the server over all (scalar-linear) protocols that satisfy the privacy condition. Our converse proofs rely on new information-theoretic arguments-tailored to the setting of single-server PIR and different from the commonly-used techniques in multi-server PIR settings. We also present novel capacity-achieving scalar-linear protocols for each of the settings being considered.
Private Information Retrieval with Private Coded Side Information: The Multi-Server Case
2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2019
In this paper, we consider the multi-server setting of Private Information Retrieval with Private Coded Side Information (PIR-PCSI) problem. In this problem, there is a database of K messages whose copies are replicated across N servers, and there is a user who knows a random linear combination of a random subset of M messages in the database as side information. The user wishes to download one message from the servers, while protecting the identities of both the demand message and the messages forming the side information. We assume that the servers know the number of messages forming the user's side information in advance, whereas the indices of these messages and their coefficients in the side information are not known to any of the servers a priori. Our goal is to characterize (or derive a lower bound on) the capacity, i.e., the maximum achievable download rate, for the following two settings. In the first setting, the set of messages forming the linear combination available to the user as side information, does not include the user's demanded message. For this setting, we show that the capacity is equal to 1 + 1/N + • • • + 1/N K−M −1 −1. In the second setting, the demand message contributes to the linear combination available to the user as side information, i.e., the demand message is one of the messages that form the user's side information. For this setting, we show that the capacity is lower-bounded by 1 + 1/N + • • • + 1/N K−M −1. The proposed achievability schemes and proof techniques leverage ideas from both our recent methods proposed for the single-server PIR-PCSI problem as well as the techniques proposed by Sun and Jafar for multi-server private computation problem.
Single-Server Multi-Message Individually-Private Information Retrieval with Side Information
2019 IEEE International Symposium on Information Theory (ISIT), 2019
We consider a multiuser variant of the private information retrieval problem described as follows. Suppose there are D users, each of which wants to privately retrieve a distinct message from a server with the help of a trusted agent. We assume that the agent has a random subset of M messages that is not known to the server. The goal of the agent is to collectively retrieve the users' requests from the server. For protecting the privacy of users, we introduce the notion of individual-privacy-the agent is required to protect the privacy only for each individual user (but may leak some correlations among user requests). We refer to this problem as Individually-Private Information Retrieval with Side Information (IPIR-SI). We first establish a lower bound on the capacity, which is defined as the maximum achievable download rate, of the IPIR-SI problem by presenting a novel achievability protocol. Next, we characterize the capacity of IPIR-SI problem for M = 1 and D = 2. In the process of characterizing the capacity for arbitrary M and D we present a novel combinatorial conjecture, that may be of independent interest.
The Capacity of Private Information Retrieval with Partially Known Private Side Information
IEEE Transactions on Information Theory
We consider the problem of private information retrieval (PIR) of a single message out of K messages from N replicated and non-colluding databases where a cacheenabled user (retriever) of cache-size M possesses side information in the form of full messages that are partially known to the databases. In this model, the user and the databases engage in a two-phase scheme, namely, the prefetching phase where the user acquires side information and the retrieval phase where the user downloads desired information. In the prefetching phase, the user receives m n full messages from the nth database, under the cache memory size constraint N n=1 m n ≤ M. In the retrieval phase, the user wishes to retrieve a message such that no individual database learns anything about the identity of the desired message. In addition, the identities of the side information messages that the user did not prefetch from a database must remain private against that database. Since the side information provided by each database in the prefetching phase is known by the providing database and the side information must be kept private against the remaining databases, we coin this model as partially
Multi-Server Private Information Retrieval with Coded Side Information
2019 16th Canadian Workshop on Information Theory (CWIT), 2019
In this paper, we study the multi-server setting of the Private Information Retrieval with Coded Side Information (PIR-CSI) problem. In this problem, there are K messages replicated across N servers, and there is a user who wishes to download one message from the servers without revealing any information to any server about the identity of the requested message. The user has a side information which is a linear combination of a subset of M messages in the database. The parameter M is known to all servers in advance, whereas the indices and the coefficients of the messages in the user's side information are unknown to any server a priori. We focus on a class of PIR-CSI schemes, referred to as server-symmetric schemes, in which the queries/answers to/from different servers are symmetric in structure. We define the rate of a PIR-CSI scheme as its minimum download rate among all problem instances, and define the server-symmetric capacity of the PIR-CSI problem as the supremum of rates over all server-symmetric PIR-CSI schemes. Our main results are as follows: (i) when the side information is not a function of the user's requested message, the capacity is given by (1 + 1/N + • • • + 1/N ⌈ K M +1 ⌉−1) −1 for any 1 ≤ M ≤ K − 1; and (ii) when the side information is a function of the user's requested message, the capacity is equal to 1 for M = 2 and M = K, and it is equal to N/(N + 1) for any 3 ≤ M ≤ K − 1. The converse proofs rely on new information-theoretic arguments, and the achievability schemes are inspired by our recently proposed scheme for single-server PIR-CSI as well as the Sun-Jafar scheme for multi-server PIR.
On the Capacity of Single-Server Multi-Message Private Information Retrieval with Side Information
2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2018
We study Private Information Retrieval with Side Information (PIR-SI) in the single-server multi-message setting. In this setting, a user wants to download D messages from a database of K ≥ D messages, stored on a single server, without revealing any information about the identities of the demanded messages to the server. The goal of the user is to achieve information-theoretic privacy by leveraging the side information about the database. The side information consists of a random subset of M messages in the database which could have been obtained in advance from other users or from previous interactions with the server. The identities of the messages forming the side information are initially unknown to the server. Our goal is to characterize the capacity of this setting, i.e., the maximum achievable download rate. In our previous work, we have established the PIR-SI capacity for the special case in which the user wants a single message, i.e., D = 1 and showed that the capacity can be achieved through the Partition and Code (PC) scheme. In this paper, we focus on the case when the user wants multiple messages, i.e., D > 1. Our first result is that if the user wants more messages than what they have as side information, i.e., D > M , then the capacity is D K−M , and it can be achieved using a scheme based on the Generalized Reed-Solomon (GRS) codes. In this case, the user must learn all the messages in the database in order to obtain the desired messages. Our second result shows that this may not be necessary when D ≤ M , and the capacity in this case can be higher. We present a lower bound on the capacity based on an achievability scheme which we call Generalized Partition and Code (GPC).