In this work, we consider the problem of secure multi-party computation (MPC), consisting of $Γ$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is interested in the result of a polynomial function of the input matrices. Each source sends a randomized functions of its matrix, called as its share, to each worker. The workers process their shares in interaction with each other, and send some results to the master such that it can derive the final result. There are several constraints: (1) each worker can store a function of each input matrix, with the size of $\frac{1}{m}$ fraction of that input matrix, (2) up to $t$ of the workers, for some integer $t$, are adversary and may collude to gain information about the private inputs or can do malicious actions to make the final result incorrect. The objective is to design an MPC scheme with the minimum number the workers, called the recovery threshold, such that the final result is correct, workers learn no information about the input matrices, and the master learns nothing beyond the final result. In this paper, we propose an MPC scheme that achieves the recovery threshold of $3t+2m-1$ workers, which is order-wise less than the recovery threshold of the conventional methods. The challenge in dealing with this set up is that when nodes interact with each other, the malicious messages that adversarial nodes generate propagate through the system, and can mislead the honest nodes. To deal with this challenge, we design some subroutines that can detect erroneous messages, and correct or drop them.
We investigate the problem of privacy preserving distributed matrix multiplication in edge networks using multi-party computation (MPC). Coded multi-party computation (CMPC) is an emerging approach to reduce the required number of workers in MPC by employing coded computation. Existing CMPC approaches usually combine coded computation algorithms designed for efficient matrix multiplication with MPC. We show that this approach is not efficient. We design a novel CMPC algorithm; PolyDot coded MPC (PolyDot-CMPC) by using a recently proposed coded computation algorithm; PolyDot codes. We exploit "…
The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference betw…
We introduce a variation of coded computation that ensures data security and master's privacy against workers, which is referred to as private secure coded computation. In private secure coded computation, the master needs to compute a function of its own dataset and one of the datasets in a library exclusively shared by external workers. After recovering the desired function, the workers must not be able to know which dataset in the library was desired by the master or obtain any information about the master's own data. We propose a private secure coded computation scheme for matrix multiplic…
We introduce a new protocol for secure two-party computation of linear functions in the semi-honest model, based on coding techniques. We first establish a parallel between the second version of the wire-tap channel model and secure two-party computation. This leads us to our protocol, that combines linear coset coding and oblivious transfer techniques. Our construction requires the use of binary intersecting codes or $q$-ary minimal codes, which are also studied in this paper.
In the secure two-party computation problem, two parties wish to compute a (possibly randomized) function of their inputs via an interactive protocol, while ensuring that neither party learns more than what can be inferred from only their own input and output. For semi-honest parties and information-theoretic security guarantees, it is well-known that, if only noiseless communication is available, only a limited set of functions can be securely computed; however, if interaction is also allowed over general communication primitives (multi-input/output channels), there are "complete" primitives …
The multi-access variant of the coded caching problem in the presence of an external wiretapper is investigated . A multi-access coded caching scheme with $K$ users, $K$ caches and $N$ files, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is proposed, which is secure against the wiretappers. Each transmission in the conventional insecure scheme will be now encrypted by a random key. The proposed scheme uses a novel technique for the key placement in the caches. It is also shown that the proposed secure multi-access coded caching scheme is within a constan…
In a secure coded caching system, a central server balances the traffic flow between peak and off-peak periods by distributing some public data to the users' caches in advance. Meanwhile, these data are securely protected against the possible colluding users, who might share their cache. We model the system as a flow network and study its capacity region via a network information-theoretic approach. Due to the difficulty of characterizing the capacity region straightforwardly, our approach is two folded from the perspective of network information theory. On one hand, we identify the inner boun…
In this paper, we consider multiple cache-enabled end-users connected to multiple transmitters through a linear network. We also prevent a totally passive eavesdropper, who sniffs the packets in the delivery phase, from obtaining any information about the original files in cache-aided networks. Three different secure centralized multi-transmitter coded caching scenarios namely, secure multi-transmitter coded caching, secure multi-transmitter coded caching with reduced subpacketization, and secure multi-transmitter coded caching with reduced feedback, are considered and closed-form coding delay…
In secure multi-party computations (SMC), parties wish to compute a function on their private data without revealing more information about their data than what the function reveals. In this paper, we investigate two Shannon-type questions on this problem. We first consider the traditional one-shot model for SMC which does not assume a probabilistic prior on the data. In this model, private communication and randomness are the key enablers to secure computing, and we investigate a notion of randomness cost and capacity. We then move to a probabilistic model for the data, and propose a Shannon …
We propose an information theoretic framework for the secure two-party function computation (SFC) problem and introduce the notion of SFC capacity. We study and extend string oblivious transfer (OT) to sample-wise OT. We propose an efficient, perfectly private OT protocol utilizing the binary erasure channel or source. We also propose the bootstrap string OT protocol which provides disjoint (weakened) privacy while achieving a multiplicative increase in rate, thus trading off security for rate. Finally, leveraging our OT protocol, we construct a protocol for SFC and establish a general lower b…
A secure multi-party batch matrix multiplication problem (SMBMM) is considered, where the goal is to allow a master to efficiently compute the pairwise products of two batches of massive matrices, by distributing the computation across S servers. Any X colluding servers gain no information about the input, and the master gains no additional information about the input beyond the product. A solution called Generalized Cross Subspace Alignment codes with Noise Alignment (GCSA-NA) is proposed in this work, based on cross-subspace alignment codes. The state of art solution to SMBMM is a coding sch…
Elaborate protocols in Secure Multi-party Computation enable several participants to compute a public function of their own private inputs while ensuring that no undesired information leaks about the private inputs, and without resorting to any trusted third party. However, the public output of the computation inevitably leaks some information about the private inputs. Recent works have introduced a framework and proposed some techniques for quantifying such information flow. Yet, owing to their complexity, those methods do not scale to practical situations that may involve large input spaces.…
Coded caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user's local cache memory without knowledge of later demands. The goal of coded caching design is to minimize the transmission rate and the subpacketization. In practice the demand for each user is sensitive since one can get the other users' preferences when it gets the other users' demands. The first coded caching scheme with private demands was proposed by Wan et al. However the transmission rate and the subpacketization of their scheme increase with the file number stored…
Caching aims to store data locally in some nodes within the network to be able to retrieve the contents in shorter time periods. However, caching in the network did not always consider secure storage (due to the compromise between time performance and security). In this paper, a novel decentralized secure coded caching approach is proposed. In this solution, nodes only transmit coded files to avoid eavesdropper wiretapping and protect the user contents. In this technique random vectors are used to combine the contents using XOR operation. We modeled the proposed coded caching scheme by a Shann…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion algorithm which does not require a matrix factorization, but uses a black-box least squares optimization solver as a subroutine, to give an estimate of the inverse of a real full-rank matrix. We then present a distributed framework for which our algorithm can be implemented, and show how we can leverage sparsest-balanced MDS generator matrices to devise matrix …
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party's output than what its own output reveals. To aid in this, they have available a set up - correlated random variables whose distribution is different from the desired distribution - as well as unlimited noiseless communication. In this paper we present an upperbound on how efficiently a given set up can be…
In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample in \textit{blocks}, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an \textit{approximate} gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling workers; in a…
In this paper, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share's size is assumed to be at most $1/k$ fraction of the input matrix, for some $k \in \mathbb{N}$. The objective …
In this paper we generalize the notion of common information of two dependent variables introduced by Gács & Körner. They defined common information as the largest entropy rate of a common random variable two parties observing one of the sources each can agree upon. It is well-known that their common information captures only a limited form of dependence between the random variables and is zero in most cases of interest. Our generalization, which we call the Assisted Common Information system, takes into account almost-common information ignored by Gács-Körner common information. In the assist…
This paper studies device to device (D2D) coded-caching with information theoretic security guarantees. A broadcast network consisting of a server, which has a library of files, and end users equipped with cache memories, is considered. Information theoretic security guarantees for confidentiality are imposed upon the files. The server populates the end user caches, after which D2D communications enable the delivery of the requested files. Accordingly, we require that a user must not have access to files it did not request, i.e., secure caching. First, a centralized coded caching scheme is pro…
This work investigates a system where each user aims to retrieve a scalar linear function of the files of a library, which are Maximum Distance Separable coded and stored at multiple distributed servers. The system needs to guarantee robust decoding in the sense that each user must decode its demanded function with signals received from any subset of servers whose cardinality exceeds a threshold. In addition, (a) the content of the library must be kept secure from a wiretapper who obtains all the signals from the servers;(b) any subset of users together can not obtain any information about the…
The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner. Adversaries in a distributed system deliberately send erroneous data in order to affect the computation for their benefit. Boolean functions are the key components of many applications, e.g., verification functions in blockchain systems and design of cryptographic algorithms. We consider the problem of computing a Boolean function in a distributed computing system with particular focus on \emph{security against Byzantine workers}. Any Boolean funct…
The problem of $X$-secure $T$-private information retrieval from MDS coded storage is studied in this paper, where the user wishes to privately retrieve one out of $K$ independent messages that are distributed over $N$ servers according to an MDS code. It is guaranteed that any group of up to $X$ colluding servers learn nothing about the messages and that any group of up to $T$ colluding servers learn nothing about the identity of desired message. A lower bound of achievable rates is proved by presenting a novel scheme based on \emph{cross-subspace alignment} and a successive decoding with int…
Consider a network of k parties, each holding a long sequence of n entries (a database), with minimum vertex-cut greater than t. We show that any empirical statistic across the network of databases can be computed by each party with perfect privacy, against any set of t < k/2 passively colluding parties, such that the worst-case distortion and communication cost (in bits per database entry) both go to zero as n, the number of entries in the databases, goes to infinity. This is based on combining a striking dimensionality reduction result for random sampling with unconditionally secure multi-pa…
We introduce an information-theoretic framework, named Coded State Machine (CSM), to securely and efficiently execute multiple state machines on untrusted network nodes, some of which are Byzantine. The standard method of solving this problem is using State Machine Replication, which achieves high security at the cost of low efficiency. We propose CSM, which achieves the optimal linear scaling in storage efficiency, throughput, and security simultaneously with the size of the network. The storage efficiency is scaled via the design of Lagrange coded states and coded input commands that require…
In this paper, we study the problem of \emph{private and secure distributed matrix multiplication (PSDMM)}, where a user having a private matrix $A$ and $N$ non-colluding servers sharing a library of $L$ ($L>1$) matrices $B^{(0)}, B^{(1)},\ldots,B^{(L-1)}$, for which the user wishes to compute $AB^{(θ)}$ for some $θ\in [0, L)$ without revealing any information of the matrix $A$ to the servers, and keeping the index $θ$ private to the servers. Previous work is limited to the case that the shared library (\textit{i.e.,} the matrices $B^{(0)}, B^{(1)},\ldots,B^{(L-1)}$) is stored across the serve…
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 collu…
ByzSecAgg: A Byzantine-Resistant Secure Aggregation Scheme for Federated Learning Based on Coded Computing and Vector Commitment
Department of Electrical Engineering and Computer Science, Technische Universität Berlin（电气工程与计算机科学系，柏林技术大学）；Department of Electrical and Computer Engineering, University of Minnesota Twin Cities（电气与计算机工程系，明尼苏达大学双城分校）
We consider a secure source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source X and wishes to transmit this source losslessly to Bob over a rate-limited link. A helper (Helen), observes an i.i.d. correlated source Y and can transmit information to Bob over a separate rate-limited link. A passive eavesdropper (Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source X at Eve, is measured by the conditional entropy of the source given the coded output …
Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side and multiple workers in the cloud operating in parallel. For distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold and communication load. In this paper we impose an additional security constraint on the data matrices and assume that worke…
