Event
Ph.D. Research Proposal: Mohamed Nomeir
Tuesday, November 18, 2025
1:00 p.m.
AVW 2328
Sarah Pham
301 473 2449
spham124@umd.edu
ANNOUNCEMENT: Ph.D. Research Proposal Exam
Name: Mohamed Nomeir
Committee:
Professor Sennur Ulukus (Chair)
Professor Sanghamitra Dutta
Professor Kaiqing Zhang
Date/time: Nov. 18th, 2025 from 1 PM - 3 PM
Location: AVW 2328
Title: Classical and Quantum Privacy in Multi-Server Systems
Abstract: Multi-server systems appear in many real-world applications to ensure reliability, low latency, and high throughput. We focus on information-theoretic measures to quantify privacy and security in multi-server systems. We address privacy problems in both classical and classical-quantum settings. In the classical setting, we analyze three private information retrieval (PIR) problems. In the classical-quantum setting, we address a problem related to the PIR problem, and a problem concerning the private distributed matrix multiplication (PDMM) that arise in machine learning applications.
In the PIR setting, a user wishes to retrieve one out of K messages from N servers privately by sending queries to each server. In the usual PIR setting, the chosen message index is uniformly random and the message lengths are equal. In the first problem we consider in the classical setting, we relax the equal-priors and equal-message-lengths assumptions. This setting was previously considered only in the case of no collusion among the servers, i.e., the servers do not share the user's queries. We generalize the scheme developed for the no-collusion case to the case of arbitrary numbers of colluding servers. In addition, we determine the exact capacity for this problem.
In the second problem, we focus on the case where servers communicate with each other to learn the encoded messages. In this setting, the messages are hidden from the servers storing them. We develop a graph-based approach where the communication graph among the servers is asymmetric. This contrasts the work in the literature where any set of servers with fixed cardinality can communicate. We formulate an optimization problem to provide a way to distribute the messages among the servers. We provide a retrieval scheme for this setting and an upper bound on the retrieval rate. We show that they match in certain settings thus giving the capacity in these cases.
Finally, in the last problem in the classical setting, we develop a new definition for Byzantine servers in PIR. In general, Byzantine servers send random independent symbols to the user. In our setting, we allow the Byzantine servers to be more harmful, i.e., to coordinate to temper with the system integrity in any possible manner. In addition, we require symmetric privacy, i.e., the user can only know the message required and nothing about the rest of the messages. We design a scheme to provide symmetric privacy and maintain the system integrity. In addition, we derive the asymptotic capacity of this setting, i.e., when the number of messages is arbitrarily large.
In the second part of this proposal, we consider the classical-quantum setting for multi-server systems, and we focus on two different tasks. The first is the quantum version of PIR (QPIR). In this setting, the classical messages are encoded over quantum states available at each server and sent over to the user on quantum channels. We analyze the QPIR problem with three different threat models, all with symmetric privacy requirement. The first is the presence of a dynamic eavesdropper along with unresponsive servers. The second is the presence of harmful Byzantine servers along with static eavesdroppers and unresponsive servers. Finally, the third is the case of harmful Byzantine entities along with dynamic eavesdroppers and unresponsive servers.
The second problem in the classical-quantum setting is PDMM with the outer product partitioning (OPP) setup. We formulate a feasibility condition on the classical codes, which when satisfied, the codes can be extended to their quantum counterparts. Next, we drive a second-order degree polynomial to find the minimum privacy value given the dimensions of matrices, in order for the feasibility condition to work. Finally, we introduce new families of codes to compensate when the feasibility requirement is not satisfied.
We present four different proposed works. The first is to generalize the PIR scheme with unequal priors and message lengths to additional threat models, i.e., to incorporate Byzantine and unresponsive servers. Second, we aim to optimize the QPIR scheme with the alliance between eavesdroppers and Byzantine servers using our asymptotic capacity result, thus achieving better rates. Third, we use the asymmetric communication setting for PIR with colluding servers to minimize the storage cost at each server and find the storage-rate tradeoff. Finally, we propose a new primitive related to graph-based PIR that relaxes the requirements for the graph-based PIR adopted in the literature. This primitive allows the user to communicate only with the servers that has the required message index as opposed to all servers. This expands the threat models that can be defined.
