Related papers: Analog Secure Distributed Matrix Multiplication
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multiparty computation protocols. However, it remains open whether or not there exist efficient constructions of strongly…
Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged…
Privacy-sensitive users require deploying large language models (LLMs) within their own infrastructure (on-premises) to safeguard private data and enable customization. However, vulnerabilities in local environments can lead to unauthorized…
Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
Despite the cloud enormous technical and financial advantages, security and privacy have always been the primary concern for adopting cloud computing facility, especially for government agencies and commercial sectors with high-security…
Privacy is a major issue in learning from distributed data. Recently the cryptographic literature has provided several tools for this task. However, these tools either reduce the quality/accuracy of the learning algorithm---e.g., by adding…
Data security and availability for operational use are frequently seen as conflicting goals. Research on searchable encryption and homomorphic encryption are a start, but they typically build from encryption methods that, at best, provide…
Distributed computing systems are well-known to suffer from the problem of slow or failed nodes; these are referred to as stragglers. Straggler mitigation (for distributed matrix computations) has recently been investigated from the…
Cooperative control is crucial for the effective operation of dynamical multi-agent systems. Especially for distributed control schemes, it is essential to exchange data between the agents. This becomes a privacy threat if the data is…
We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our…
We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic-addition degree tables…
Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
With the assistance of singular value decomposition (SVD), a multi-beam directional modulation (DM) scheme based on symmetrical multi-carrier frequency diverse array (FDA) is proposed. The proposed DM scheme is capable of achieving…
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…
With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…