English
Related papers

Related papers: Computing Individual Discrete Logarithms Faster in…

200 papers

Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…

Numerical Analysis · Mathematics 2024-12-20 Hanyu Li , Mary F. Wheeler

The Differential Privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this…

Cryptography and Security · Computer Science 2024-09-30 Sachin Kadam , Anna Scaglione , Nikhil Ravi , Sean Peisert , Brent Lunghino , Aram Shumavon

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and…

Cryptography and Security · Computer Science 2016-11-28 Aurore Guillevic , François Morain , Emmanuel Thomé

We prove that $\mathbb{F}_p$ sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when $p\in(0, 1]$. $\mathbb{F}_p$ sketch uses only polylogarithmic space, exponentially better than…

Cryptography and Security · Computer Science 2021-10-04 Lun Wang , Iosif Pinelis , Dawn Song

The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…

Computational Complexity · Computer Science 2022-03-16 Simran Tinani , Joachim Rosenthal

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2019-06-13 Hadrien Hendrikx , Francis Bach , Laurent Massoulie

Recent years have witnessed the remarkable success of implicit neural representation methods. The recent work Local Implicit Image Function (LIIF) has achieved satisfactory performance for continuous image representation, where pixel values…

Computer Vision and Pattern Recognition · Computer Science 2023-09-26 Zongyao He , Zhi Jin

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-09-16 Andreas Plesner , Hans Henrik Brandenborg Sørensen , Søren Hauberg

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2020-05-22 Hadrien Hendrikx , Francis Bach , Laurent Massoulie

Recent work using Fully Homomorphic Encryption (FHE) has made non-interactive privacy-preserving inference of deep Convolutional Neural Networks (CNN) possible. However, the performance of these methods remain limited by their heavy…

Cryptography and Security · Computer Science 2026-02-10 Eduardo Chielle , Manaar Alam , Jinting Liu , Jovan Kascelan , Michail Maniatakos

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets…

Chemical Physics · Physics 2022-11-15 Jiashu Liang , Zhe Wang , Jie Li , Jonathan Wong , Xiao Liu , Brad Ganoe , Teresa Head-Gordon , Martin Head-Gordon

Personalized Federated Learning (PFL) enables clients to collaboratively train personalized models tailored to their individual objectives, addressing the challenge of model generalization in traditional Federated Learning (FL) due to high…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-06-10 Mrinmay Sen , Chalavadi Krishna Mohan

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality…

Number Theory · Mathematics 2019-11-19 Thorsten Kleinjung , Benjamin Wesolowski

Linear programs (LPs) can be solved by polynomially many moves along the circuit direction improving the objective the most, so-called deepest-descent steps (dd-steps). Computing these steps is NP-hard (De Loera et al., arXiv, 2019), a…

Optimization and Control · Mathematics 2021-01-26 Steffen Borgwardt , Cornelius Brand , Andreas Emil Feldmann , Martin Koutecký

Deep neural networks (DNNs) are currently predominantly trained using first-order methods. Some of these methods (e.g., Adam, AdaGrad, and RMSprop, and their variants) incorporate a small amount of curvature information by using a diagonal…

Machine Learning · Computer Science 2022-10-28 Achraf Bahamou , Donald Goldfarb , Yi Ren

Representing deep neural networks (DNNs) in low-precision is a promising approach to enable efficient acceleration and memory reduction. Previous methods that train DNNs in low-precision typically keep a copy of weights in high-precision…

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

Optimization and Control · Mathematics 2024-10-22 Xi Gao , Jinxin Xiong , Akang Wang , Qihong Duan , Jiang Xue , Qingjiang Shi

Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise,…

Quantum Physics · Physics 2026-05-08 Li Gong , Aonan Zhang , Madhura Ghosh Dastidar , Alexander Duplinskii , A. I. Lvovsky

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…

Disordered Systems and Neural Networks · Physics 2019-08-22 Yohai Bar-Sinai , Stephan Hoyer , Jason Hickey , Michael P. Brenner

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron