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The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Privacy-preserving techniques for distributed computation have been proposed recently as a promising framework in collaborative inter-domain network monitoring. Several different approaches exist to solve such class of problems, e.g.,…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…
An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with…
CRYSTAL-Kyber (Kyber) is one of the post-quantum cryptography (PQC) key-encapsulation mechanism (KEM) schemes selected during the standardization process. This paper addresses optimization for Kyber architecture with respect to latency and…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…
We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works focus on fully…
Hypergraph partitioning is an important preprocessing step for optimizing data placement and minimizing communication volumes in high-performance computing applications. To cope with ever growing problem sizes, it has become increasingly…
Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…
Arikan has shown that systematic polar codes (SPC) outperform nonsystematic polar codes (NSPC). However, the performance gain comes at the price of elevated encoding complexity, i.e., compared to NSPC, the available encoding methods for SPC…
Mass spectrometry (MS) based omics data analysis require significant time and resources. To date, few parallel algorithms have been proposed for deducing peptides from mass spectrometry-based data. However, these parallel algorithms were…
The Lyness map is a birational map in the plane which provides one of the simplest discrete analogues of a Hamiltonian system with one degree of freedom, having a conserved quantity and an invariant symplectic form. As an example of a…
Sparse Ternary General Matrix-Matrix Multiplication (GEMM) remains under-optimized in existing libraries for Apple Silicon CPUs. We present a Sparse Ternary GEMM kernel optimized specifically for Apple's M-series processors. We propose a…
Resource constraints in smart devices demand an efficient cryptosystem that allows for low power and memory consumption. This has led to popularity of comparatively efficient Elliptic curve cryptog-raphy (ECC). Prior to this paper, much of…