Private Retrieval, Computing and Learning: Recent Progress and Future Challenges

Abstract

Most of our lives are conducted in the cyberspace. The human notion of privacy translates into a cyber notion of privacy on many functions that take place in the cyberspace. This article focuses on three such functions: how to privately retrieve information from cyberspace (privacy in information retrieval), how to privately leverage large-scale distributed/parallel processing (privacy in distributed computing), and how to learn/train machine learning models from private data spread across multiple users (privacy in distributed (federated) learning). The article motivates each privacy setting, describes the problem formulation, summarizes breakthrough results in the history of each problem, and gives recent results and discusses some of the major ideas that emerged in each field. In addition, the crosscutting techniques and interconnections between the three topics are discussed along with a set of open problems and challenges. I. INTRODUCTIONPrivacy is an important part of human life. This article considers privacy in the context of three distinct but related engineering applications, namely, privacy in retrieving information, privacy in computing functions, and privacy in learning. In the first sub-topic of private information retrieval, a user wishes to download a content from publicly accessible databases in such a way that the databases do not learn which particular content the user has downloaded. Towards that goal, the user creates ambiguity by its actions during the download. This strategy prevents databases from guessing which content the user has downloaded. This in turn preserves the user's privacy because what is downloaded leaks information about interest and intent on the part of the user. In the second sub-topic of private computing, a user wishes to compute a function but

On Single Server Private Information Retrieval with Private Coded Side Information

“…In the information theoretic framework, which requires perfect privacy and assumes long messages, the capacity of PIR is the maximum number of bits of desired information that can be retrieved per bit of download from the server(s) [3]. Capacity characterizations have recently been obtained for various forms of PIR, especially for the multi-server setting [3]- [22].…”

Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound

“…Information-theoretic privacy and straggler mitigation in coded computing (for polynomial evaluation, matrix-matrix and matrix-vector multiplication) is achieved by using secret sharing [26]- [39]. For a very recent survey on private distributed computing and its connections we refer the reader to [40]. Security against malicious workers is considered in [28], [41]- [44].…”

Conditional Disclosure of Secrets and Storage over Graphs

“…For arbitrary collection of security input sets and colluding user sets, I characterize the optimal randomness assumption, i.e., the minimum number of key bits that need to be held by the users, per input bit, for weakly secure summation to be feasible, which generally involves solving a linear program. In a seminal work [78], Shannon introduced the notion of information theoretic security [16,94] based on statistical independence and established the fundamental limits of a single-user secure communication system. While [78] provided an elegant theoretical foundation for cryptography, the optimal solutions are deemed too inefficient to im plement in practice [47].…”

“…≥ max H(Z 4 ), H(Z 5 ), H(Z 3 ) + a * L (6. 94) where in (6.93), we split the non-redundant Z k term in set S m ∪ T n to that in T n \ S and A m,n ; in (6.94), we use Lemma 6.66 to bound the A m,n term conditioned on T n \ S (note that we consider only A m,n where |A m,n | = a * , i.e., A m,n = S). Next, we proceed to bound the term max (H(Z 4 ), H(Z 5 ), H(Z 3 )), where it turns out that the only constraints required are from Lemma 6.44.…”