相关论文: A multifactor RSA-like scheme with fast decryption…
Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME…
In this paper, we introduce a novel explicit family of subcodes of Reed-Solomon (RS) codes that efficiently achieve list decoding capacity with a constant output list size. Our approach builds upon the idea of large linear subcodes of RS…
Cyber-physical systems are inherently complex due to their connection between software and the physical world. Iterative design reduces their complexity, but increases the need to repeatedly recheck their safety in full after every change.…
This paper proposes the hardware implementation of RSA encryption/decryption algorithm using the algorithms of Ancient Indian Vedic Mathematics that have been modified to improve performance. The recently proposed hierarchical overlay…
Rank Decoding (RD) is the main underlying problem in rank-based cryptography. Based on this problem and quasi-cyclic versions of it, very efficient schemes have been proposed recently, such as those in the ROLLO and RQC submissions, which…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
In this letter we describe the pseudoparticle multipole method (P2M2), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the…
[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…
The Rank metric decoding problem is the main problem considered in cryptography based on codes in the rank metric. Very efficient schemes based on this problem or quasi-cyclic versions of it have been proposed recently, such as those in the…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
We propose a computationally efficient approach to safe reinforcement learning (RL) for frequency regulation in power systems with high levels of variable renewable energy resources. The approach draws on set-theoretic control techniques to…
This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
Regular expression (RE) matching is a very common functionality that scans a text to find occurrences of patterns specified by an RE; it includes the simpler function of RE recognition. Here we address RE parsing, which subsumes matching by…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of…
The Shamir secret sharing scheme requires a Maximum Distance Separable (MDS) code, and in its most common implementation, a Reed-Solomon (RS) code is used. In this paper, we observe that the encoding procedure can be made simpler and faster…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel…