Computational hardness assumptions | Computational number theory

Higher residuosity problem

In cryptography, most public key cryptosystems are founded on problems that are believed to be intractable. The higher residuosity problem (also called the n th-residuosity problem) is one such problem. This problem is easier to solve than integer factorization, so the assumption that this problem is hard to solve is stronger than the assumption that integer factorization is hard. (Wikipedia).

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Resilience

The route to greater resilience is to explore how well we would cope if so much of what we think we need were to be taken away from us. We would, almost certainly, manage far better than we think in our timid moments. If you like our films, take a look at our shop (we ship worldwide): http

From playlist WORK + CAPITALISM

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On The Complexity of Computing Roots and Residuosity Over Finite Fields - Swastik Kopparty

Swastik Kopparty Member, School of Mathematics February 1, 2011 We study the complexity of computing some basic arithmetic operations over GF(2^n), namely computing q-th root and q-th residuosity, by constant depth arithmetic circuits over GF(2) (also known as AC^0(parity)). Our main resul

From playlist Mathematics

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Now You Know: Buoyancy

Many objects float in water due to buoyancy. What happens to the buoyant force when you mix air and water? Watch this video to find out!

From playlist Now You Know

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Volume and Capacity (Converting between units of volume)

More resources available at www.misterwootube.com

From playlist Applications of Measurement

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The human nature of failure & resiliency

Projects fail in droves. Systems hiccup and hours of downtime follows. Screws fall out all the time; the world is an imperfect place. We talk a lot about building resilient systems, but all systems are (at least for now) built by humans. Humans who have been making the same types of mista

From playlist Talks

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Density

Learn more about density! http://www.flippingphysics.com/density.html

From playlist Vertical Videos

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Show Me Some Science! Can Crush

A metal can and a hose are filled with water, and the hose is lowered off of a second floor balcony. The water drains and the can is crushed! In a fluid, like air or water, the pressure is always greater on the bottom than on the top. This is because the weight of all of the fluid pushes

From playlist Show Me Some Science!

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How Is the ADHD Brain Different?

If you’re online, you may notice that conversations around ADHD are everywhere. You may even be starting to wonder, as you flick from one app to the next, that you yourself may have ADHD. So in Part 1 of this series about ADHD, Julian explores what this disorder is, what’s happening in the

From playlist Seeker+

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Why You Think You Might Have ADHD

Most people experience many symptoms of ADHD to some degree, and one of the most well known is the inability to stay focused. However, there are other less common symptoms of ADHD that people often struggle with. In this episode on ADHD, Julian describes these other symptoms and how they c

From playlist Seeker+

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Show Me Some Science! Balloon Buoyancy

There’s nothing intrinsically “floaty” about helium. You can make a helium balloon that sinks, if it’s cold enough, as we see in this video. At normal room temperature, a helium balloon will rise, as you know. The weight of the rubber balloon plus the gas inside is less than that weight o

From playlist Show Me Some Science!

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17. Theories of Consciousness that Neuroscientists Take Seriously

MIT 24.08J Philosophical Issues in Brain Science, Spring 2009 View the complete course: http://ocw.mit.edu/24-08JS09 Instructor: Prof. Ned Block License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 24.08J Philosophical Issues in Brain Science, Spring 09

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MFEM Workshop 2022 | High-Order Solvers + GPU Acceleration

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s second community workshop was held on October 25, 2022, with participants around the world. Learn more about MFEM at https://mfem.o

From playlist MFEM Community Workshop 2022

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Incidence Theory and Uniform Distribution in Higher Dimensions - Alex Iosevich

Special Year Research Seminar Topic: Incidence Theory and Uniform Distribution in Higher Dimensions Speaker: Alex Iosevich Affiliation: University of Rochester Date: February 14, 2023 2:00pm Simonyi Hall 101 Incidence bound for points and spheres in higher dimensions generally becomes tr

From playlist Mathematics

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Does the Universe have Higher Dimensions? Part 1

Signup for your FREE trial to The Great Courses Plus here: http://ow.ly/6ymM30rvhBa What do physicists mean when they talk about higher dimensional spaces, or space-times? How could we possibly not have noticed if space was not three-dimensional? In this first part, we will talk about th

From playlist Physics

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Arthur Krener: "Al'brekht’s Method in Infinite Dimensions"

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "Al'brekht’s Method in Infinite Dimensions" Arthur Krener, Naval Postgraduate School Abstract: Al'brekht's method is a way optimally stabilize a finite dimens

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Lecture 27 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his discussion on higher dimensions and the outer reaches while helping the students understand higher dimensions Fourier Transforms.

From playlist Lecture Collection | The Fourier Transforms and Its Applications

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Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture II

Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations

From playlist Hausdorff School: Trending Tools

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MFEM Workshop 2021 | High-Order Matrix-Free Solvers

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s first community workshop was held virtually on October 20, 2021, with participants around the world. Learn more about MFEM at https

From playlist MFEM Community Workshop 2021

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How To VISUALIZE Density!!

A Visual Example Of MASS Density!! #Chemistry #Physics #Engineering #Density #NicholasGKK #Shorts

From playlist Heat and Chemistry

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GCSE Higher Maths General Certificate of Secondary Education – MATHS PRATICE PROBLEM

Passing the GCSE Higher Maths (General Certificate of Secondary Education) will require your ability to increase your focus and commitment. The GCSE Higher Maths (General Certificate of Secondary Education) is not easy to pass and most students don’t appreciate the level of effort it take

From playlist Test Prep Math

Related pages

Prime number | Integer factorization | Chinese remainder theorem | Semantic security | Quadratic residuosity problem | Unit (ring theory) | Integer | Ring (mathematics) | Cyclic group | Public-key cryptography | Naccache–Stern cryptosystem | Modular arithmetic | Cryptography | Benaloh cryptosystem | Index of a subgroup | Group (mathematics)