arXiv subjects

Jinbao Zhu

Publications and source records attributed to Jinbao Zhu.

13 recordsLinked to original sources

arXiv2026

Secure Aggregation with Top-K Sparsification in Decentralized Federated Learning

Secure aggregation is a vital component for mitigating gradient leakage in federated learning, but its communication cost conventionally scales with the gradient dimension. This becomes prohibitive for large models and even more pronounced in decentralized federated learning with limited bandwidth and unreliable nodes. Top-K gradient sparsification is an effective approach to reduce communication by transmitting only a few entries of the full gradient, while maintaining competitive model accuracy. Nevertheless, the top-K entries selected by each user are unpredictable and vary across users, which poses a challenge for efficient sparse secure aggregation. This paper studies information-theoretic secure aggregation with top-K sparsification in decentralized federated learning under user dropouts and user collusion. We propose a communication-efficient sparse secure aggregation scheme that offloads dimension-dependent overhead to an offline phase and protects private gradients using random masks and permutations. Experimental results demonstrate that our scheme preserves accuracy comparable to full-gradient aggregation even with only 1% gradient sparsification, while substantially reducing the communication cost.

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arXiv2026

The Capacity of Information-Theoretic Secure Aggregation in Federated Learning

Secure aggregation allows a server to aggregate users' local updates while preserving update privacy. Existing information-theoretic problems typically assume that correlated random keys are provided by a trusted third party (TTP) or generated via prescribed groupwise structures, while the communication cost for establishing such correlated keys is often ignored. Consequently, the fundamental limits under general key-distribution mechanisms remain unknown. In this paper, we study the $T$-colluding information-theoretic secure aggregation problem with $N$ users under a general two-phase framework consisting of a key distribution phase and an update aggregation phase. Unlike prior work, we model key distribution through user-to-user communication and allow arbitrary user-generated key-distribution mechanisms, eliminating TTP or prescribed structures. This enables a joint characterization of three resources: randomness for security, key-distribution communication, and aggregation communication. We completely characterize the capacity region among these three resources by constructing a novel secure aggregation scheme together with a matching information-theoretic converse. In particular, we develop an explicit deterministic capacity-achieving construction over any finite field of size at least $N$, whereas most existing schemes either rely on TTP or employ randomized or existential constructions over sufficiently large finite fields. We further show that the optimal performance can be achieved using only pairwise shared keys, enabling implementation via Diffie--Hellman key exchange. Compared with Google's seminal secure aggregation scheme, the proposed scheme requires fewer random masking keys while preserving the same aggregation communication overhead.

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arXiv2025

A General Coding Framework for Adaptive Private Information Retrieval

The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any group of up to $T$ colluding servers. In the considered storage system, the $M$ files are stored across the $N$ distributed servers in an $X$-secure $K$-coded manner such that any group of up to $X$ colluding servers learns nothing about the files; the storage overhead at each server is reduced by a factor of $\frac{1}{K}$ compared to the total size of the files; and the files can be reconstructed from any $K+X$ servers. However, in practical scenarios, when the user retrieves the desired file from the distributed system, some servers may respond to the user very slowly or not respond at all. These servers are referred to as \emph{stragglers}, and particularly their identities and numbers are unknown in advance and may change over time. This paper considers the adaptive PIR problem that can be capable of tolerating the presence of a varying number of stragglers. We propose a general coding method for designing adaptive PIR schemes by introducing the concept of a \emph{feasible PIR coding framework}. We demonstrate that any \emph{feasible PIR coding framework} over a finite field $\mathbb{F}_q$ with size $q$ can be used to construct an adaptive PIR scheme that achieves a retrieval rate of $1-\frac{K+X+T-1}{N-S}$ simultaneously for all numbers of stragglers $0\leq S\leq N-(K+X+T)$ over the same finite field. Additionally, we provide an implementation of the \emph{feasible PIR coding framework}, ensuring that the adaptive PIR scheme operates over any finite field $\mathbb{F}_q$ with size $q\geq N+\max\{K, N-(K+X+T-1)\}$.

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arXiv2024

Generalized Lagrange Coded Computing: A Flexible Computation-Communication Tradeoff for Resilient, Secure, and Private Computation

We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a master node and multiple worker nodes. Generalized Lagrange Coded Computing (GLCC) codes are proposed to simultaneously provide resiliency against stragglers who do not return computation results in time, security against adversarial workers who deliberately modify results for their benefit, and information-theoretic privacy of the dataset amidst possible collusion of workers. GLCC codes are constructed by first partitioning the dataset into multiple groups, then encoding the dataset using carefully designed interpolating polynomials, and sharing multiple encoded data points to each worker, such that interference computation results across groups can be eliminated at the master. Particularly, GLCC codes include the state-of-the-art Lagrange Coded Computing (LCC) codes as a special case, and exhibit a more flexible tradeoff between communication and computation overheads in optimizing system efficiency. Furthermore, we apply GLCC to distributed training of machine learning models, and demonstrate that GLCC codes achieve a speedup of up to $2.5\text{--}3.9\times$ over LCC codes in training time, across experiments for training image classifiers on different datasets, model architectures, and straggler patterns.

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arXiv2024

Private Multiple Linear Computation: A Flexible Communication-Computation Tradeoff

We consider the problem of private multiple linear computation (PMLC) over a replicated storage system with colluding and unresponsive constraints. In this scenario, the user wishes to privately compute $P$ linear combinations of $M$ files from a set of $N$ replicated servers without revealing any information about the coefficients of these linear combinations to any $T$ colluding servers, in the presence of $S$ unresponsive servers that do not provide any information in response to user queries. Our focus is on more general performance metrics where the communication and computational overheads incurred by the user are not neglected. Additionally, the communication and computational overheads for servers are also taken into consideration. Unlike most previous literature that primarily focused on download cost from servers as a performance metric, we propose a novel PMLC scheme to establish a flexible tradeoff between communication costs and computational complexities.

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arXiv2023

Secure Embedding Aggregation for Federated Representation Learning

We consider a federated representation learning framework, where with the assistance of a central server, a group of $N$ distributed clients train collaboratively over their private data, for the representations (or embeddings) of a set of entities (e.g., users in a social network). Under this framework, for the key step of aggregating local embeddings trained privately at the clients, we develop a secure embedding aggregation protocol named \scheme, which leverages all potential aggregation opportunities among all the clients, while providing privacy guarantees for the set of local entities and corresponding embeddings \emph{simultaneously} at each client, against a curious server and up to $T < N/2$ colluding clients.

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arXiv2023

Information-Theoretically Private Matrix Multiplication From MDS-Coded Storage

We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers that collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix $\mathbf{A}$ with a target matrix stored on the servers, without revealing any information about $\mathbf{A}$ and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication (FPMM) from colluding servers, the matrix $\mathbf{A}$ is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for the two PSMM and FPMM problems, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. We compare the proposed PSMM strategy with a previous PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation overheads. Moreover, compared with a baseline FPMM strategy that uses the idea of Private Information Retrieval (PIR) to directly retrieve the desired matrix multiplication, the proposed FPMM strategy significantly reduces storage overhead, but slightly incurs large communication and computation overheads.

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arXiv2022

A Systematic Approach towards Efficient Private Matrix Multiplication

We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing the indices of the selected matrices, even when a certain number of workers collude with each other. We propose a novel systematic approach to solve PSMM and FPMM with colluding workers, which leverages solutions to a related Secure Matrix Multiplication (SMM) problem where the data (rather than the indices) of the multiplied matrices are kept private from colluding workers. Specifically, given an SMM strategy based on polynomial codes or Lagrange codes, one can exploit the special structure inspired by the matrix encoding function to design private coded queries for PSMM/FPMM, such that the algebraic structure of the computation result at each worker resembles that of the underlying SMM strategy. Adopting this systematic approach provides novel insights in private query designs for private matrix multiplication, substantially simplifying the processes of designing PSMM and FPMM strategies. Furthermore, the PSMM and FPMM strategies constructed following the proposed approach outperform the state-of-the-art strategies in one or more performance metrics including recovery threshold (minimal number of workers the master needs to wait for before correctly recovering the multiplication result), communication cost, and computation complexity, demonstrating a more flexible tradeoff in optimizing system efficiency.

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arXiv2021

Symmetric Private Polynomial Computation From Lagrange Encoding

The problem of $X$-secure $T$-colluding symmetric Private Polynomial Computation (PPC) from coded storage system with $B$ Byzantine and $U$ unresponsive servers is studied in this paper. Specifically, a dataset consisting of $M$ files is stored across $N$ distributed servers according to $(N,K+X)$ Maximum Distance Separable (MDS) codes such that any group of up to $X$ colluding servers can not learn anything about the data files. A user wishes to privately evaluate one out of a set of candidate polynomial functions over the $M$ files from the system, while guaranteeing that any $T$ colluding servers can not learn anything about the identity of the desired function and the user can not learn anything about the $M$ data files more than the desired polynomial function evaluations, in the presence of $B$ Byzantine servers that can send arbitrary responses maliciously to confuse the user and $U$ unresponsive servers that will not respond any information at all. A novel symmetric PPC scheme using Lagrange encoding is proposed. This scheme achieves a PPC rate of $1-\frac{G(K+X-1)+T+2B}{N-U}$ with secrecy rate $\frac{G(K+X-1)+T}{N-(G(K+X-1)+T+2B+U)}$ and finite field size $N+\max\{K,N-(G(K+X-1)+T+2B+U)\}$, where $G$ is the maximum degree over all the candidate polynomial functions. Moreover, to further measure the efficiency of PPC schemes, upload cost, query complexity, server computation complexity and decoding complexity required to implement the scheme are analyzed. Remarkably, the PPC setup studied in this paper generalizes all the previous MDS coded PPC setups and the degraded schemes strictly outperform the best known schemes in terms of (asymptotical) PPC rate, which is the main concern of the PPC schemes.

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arXiv2021

Multi-User Blind Symmetric Private Information Retrieval from Coded Servers

The problem of Multi-user Blind $X$-secure $T$-colluding Symmetric Private Information Retrieval from Maximum Distance Separable (MDS) coded storage system with $B$ Byzantine and $U$ unresponsive servers (U-B-MDS-MB-XTSPIR) is studied in this paper. Specifically, a database consisting of multiple files, each labeled by $M$ indices, is stored at the distributed system with $N$ servers according to $(N,K+X)$ MDS codes over $\mathbb{F}_q$ such that any group of up to $X$ colluding servers learn nothing about the data files. There are $M$ users, in which each user $m,m=1,\ldots,M$ privately selects an index $θ_m$ and wishes to jointly retrieve the file specified by the $M$ users' indices $(θ_1,\ldots,θ_M)$ from the storage system, while keeping its index $θ_m$ private from any $T_m$ colluding servers, where there exists $B$ Byzantine servers that can send arbitrary responses maliciously to confuse the users retrieving the desired file and $U$ unresponsive servers that will not respond any message at all. In addition, each user must not learn information about the other users' indices and the database more than the desired file. An U-B-MDS-MB-XTSPIR scheme is constructed based on Lagrange encoding. The scheme achieves a retrieval rate of $1-\frac{K+X+T_1+\ldots+T_M+2B-1}{N-U}$ with secrecy rate $\frac{K+X+T_1+\ldots+T_M-1}{ N-(K+X+T_1+\ldots+T_M+2B+U-1)}$ on the finite field of size $q\geq N+\max\{K, N-(K+X+T_1+\ldots+T_M+2B+U-1)\}$ for any number of files.

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arXiv2021

Improved Constructions for Secure Multi-Party Batch Matrix Multiplication

This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products $\mathbf{A}\divideontimes\mathbf{B}\triangleq(\mathbf{A}^{(1)}\mathbf{B}^{(1)},\ldots,\mathbf{A}^{(M)}\mathbf{B}^{(M)})$ of two batch of massive matrices $\mathbf{A}$ and $\mathbf{B}$ that are generated from two sources, through $N$ honest but curious servers which share some common randomness. The matrices $\mathbf{A}$ (resp. $\mathbf{B}$) must be kept secure from any subset of up to $X_{\mathbf{A}}$ (resp. $X_\mathbf{B}$) servers even if they collude, and the user must not obtain any information about $(\mathbf{A},\mathbf{B})$ beyond the products $\mathbf{A}\divideontimes\mathbf{B}$. A novel computation strategy for single secure matrix multiplication problem (i.e., the case $M=1$) is first proposed, and then is generalized to the strategy for SMBMM by means of cross subspace alignment. The SMBMM strategy focuses on the tradeoff between recovery threshold (the number of successful computing servers that the user needs to wait for), system cost (upload cost, the amount of common randomness, and download cost) and system complexity (encoding, computing, and decoding complexities). Notably, compared with the known result by Chen et al., the strategy for the degraded case $X= X_{\mathbf{A}}=X_{\mathbf{B}}$ achieves better recovery threshold, amount of common randomness, download cost and decoding complexity when $X$ is less than some parameter threshold, while the performance with respect to other measures remain identical.

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arXiv2021

Capacity-Achieving Private Information Retrieval Schemes from Uncoded Storage Constrained Servers with Low Sub-packetization

This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to retrieve one out of $K$ files from $N$ servers while revealing nothing about its identity to any individual server, in which the $K$ files are stored at the $N$ servers in an uncoded form and each server can store up to $μK$ equivalent files, where $μ$ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if and only if all the packets are stored exactly at $M\triangleq μN$ servers for $μ$ such that $M=μN\in\{2,3,\ldots,N\}$. Then, the optimal sub-packetization for capacity-achieving linear SC-PIR schemes is characterized as the solution to an optimization problem, which is typically hard to solve because of involving indicator functions. Moreover, a new notion of array called Storage Design Array (SDA) is introduced for the SC-PIR system. With any given SDA, an associated capacity-achieving SC-PIR scheme is constructed. Next, the SC-PIR schemes that have equal-size packets are investigated. Furthermore, the optimal equal-size sub-packetization among all capacity-achieving linear SC-PIR schemes characterized by Woolsey et al. is proved to be $\frac{N(M-1)}{\gcd(N,M)}$. Finally, by allowing unequal size of packets, a greedy SDA construction is proposed, where the sub-packetization of the associated SC-PIR scheme is upper bounded by $\frac{N(M-1)}{\gcd(N,M)}$. Among all capacity-achieving linear SC-PIR schemes, the sub-packetization is optimal when $\min\{M,N-M\}|N$ or $M=N$, and within a multiplicative gap $\frac{\min\{M,N-M\}}{\gcd(N,M)}$ of the optimal one otherwise. In particular, for the case $N=d\cdot M\pm1$ where $d\geq 2$, another SDA is constructed to obtain lower sub-packetization.

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arXiv2019

A new Capacity-Achieving Private Information Retrieval Scheme with (Almost) Optimal File Length for Coded Servers

In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate $(N,K,M)$ coded sever model of PIR, where each of $M$ files is distributed to the $N$ servers in the form of $(N,K)$ maximum distance separable (MDS) code for some $N>K$ and $M>1$. As a result, we propose a new capacity-achieving $(N,K,M)$ coded linear PIR scheme such that it can be implemented with file length $\frac{K(N-K)}{\gcd(N,K)}$, which is much smaller than the previous best result $K\big(\frac{N}{\gcd(N,K)}\big)^{M-1}$. Notably, among all the capacity-achieving coded linear PIR schemes, we show that the file length is optimal if $M>\big\lfloor \frac{K}{\gcd(N,K)}-\frac{K}{N-K}\big\rfloor+1$, and within a multiplicative gap $\frac{K}{\gcd(N,K)}$ of a lower bound on the minimum file length otherwise.

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