Post-quantum cryptography | Computational hardness assumptions | Lattice-based cryptography | Computational problems | Cryptography
In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought. Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization and discrete logarithm problem have served as the base for public key cryptography since the early 1980s. An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem can be used to solve the NP-hard shortest vector problem (SVP) in a lattice (a polynomial-time reduction from the SVP problem to the RLWE problem has been presented). (Wikipedia).
What Are Error Intervals? GCSE Maths Revision
What are error Intervals and how do we find them - that's the mission in this episode of GCSE Maths minis! Error Intervals appear on both foundation and higher tier GCSE maths and IGCSE maths exam papers, so this is excellent revision for everyone! DOWNLOAD THE QUESTIONS HERE: https://d
From playlist Error Intervals & Bounds GCSE Maths Revision
Teach Astronomy - Random and Systematic Errors
http://www.teachastronomy.com/ In science we deal with two fundamentally different types of errors. Random errors are usually associated with limitations in the measuring apparatus. A random error can displace a measurement either to the high or low side of the true value. Random errors
From playlist 01. Fundamentals of Science and Astronomy
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist Machine Learning
How to pick a machine learning model 2: Separating signal from noise
Part of the End-to-End Machine Learning School course library at http://e2eml.school See these concepts used in an End to End Machine Learning project: https://end-to-end-machine-learning.teachable.com/p/polynomial-regression-optimization/ Watch the rest of the How to Choose a Model serie
From playlist E2EML 171. How to Choose Model
How to detect and correct an error using the Hamming Code. Hamming codes are a type of linear code, see link for intro to linear code: https://www.youtube.com/watch?v=oYONDEX2sh8 Questions? Feel free to post them in the comments and I'll do my best to answer!
From playlist Cryptography and Coding Theory
Introduction (4): Complexity and Overfitting
Simple vs complex models; training vs testing error; overfitting
From playlist cs273a
Katherine E. Stange: Ring learning with errors and rounding
CIRM HYBRID EVENT Among the main candidates for post-quantum cryptography are systems based on the Ring Learning with Errors and Ring Learning with Rounding problems. I’ll give an overview of the number theory involved in these problems and try to persuade you to join in cryptanalyzing th
From playlist Number Theory
Kristin Lauter, Microsoft Research Redmond The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/kristin-lauter-2015-07-07
From playlist My Collaborators
Machine Learning by Andrew Ng [Coursera] 06-02 Machine learning system design
From playlist Machine Learning by Professor Andrew Ng
Systems of linear equations -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Adeline Roux-Langlois : Using structured variants in lattice-based cryptography - Lecture 2
CONFERENCE Recording during the thematic meeting : « Francophone Computer Algebra Days» the March 07, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIR
From playlist Mathematical Aspects of Computer Science
Mathematics of Post-Quantum Cryptograhy - Kristin Lauter
Woman and Mathematics - 2018 More videos on http"//video.ias.edu
From playlist My Collaborators
Paul Andersen steps you through eight types of animal behavior. He starts by defining ethology and explaining that behavior varies from innate to learned. He discusses each of the following with examples; instinct, fixed action pattern, imprinting, associative learning, trial and error l
From playlist Biology
Chris Peikert - Post Quantum assumptions - IPAM at UCLA
Recorded 27 July 2022. Chris Peikert of the University of Michigan presents "Post Quantum assumptions" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Learn more online at: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-on-post-quantum-and-
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
Tuples and Sets are a lot like Lists which we learned about in our last video. They both store multiple data. However, there are some big differences. Sets cannot have any duplicate values and a set is also unordered (no index). Tuples are like lists that cannot be changed (immutable). Th
From playlist Intro to Python Programming for Materials Engineers
What Can Wobbling Muons Tell Us About the Particles in our Universe?
Fermilab's Dr. Adam Lyon breaks down the first results from the Muon g-2 experiment in this special public lecture, part of the Fermilab Arts and Lecture Series. On April 7, 2021, the Muon g-2 experiment hosted at the U.S. Department of Energy’s Fermi National Accelerator Laboratory relea
From playlist Muon g-2
Katie Bouman “Imaging a Black Hole with the Event Horizon Telescope”
Dr. Katie Bouman, who starts as assistant professor of computing and mathematical sciences at Caltech in June 2019, describes how the Event Horizon Telescope team captured the first-ever image of a black hole.
From playlist Our Research