Post-quantum cryptography | Computational hardness assumptions | Lattice-based cryptography | Computational problems | Number theory
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai who presented a family of one-way functions based on SIS problem. He showed that it is secure in an average case if the shortest vector problem (where for some constant ) is hard in a worst-case scenario. Average case problems are the problems that are hard to be solved for some randomly selected instances. For cryptography applications, worst case complexity is not sufficient, and we need to guarantee cryptographic construction are hard based on average case complexity. (Wikipedia).
Short vector problems and simultaneous approximation
Short vector problems and simultaneous approximation, by Daniel E. Martin, presented at ANTS XIV.
From playlist My Students
Learn how to solve a rational expression by multiplying by the LCD
👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa
From playlist How to Solve Rational Equations with an Integer
Learn to solve a rational equation by multiplying by the LCD
👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa
From playlist How to Solve Rational Equations with an Integer
Solve a Rational Equation with two solutions
👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa
From playlist How to Solve Rational Equations with an Integer
Solving a multi-step equation by multiplying by the denominator
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Jana Cslovjecsek: Efficient algorithms for multistage stochastic integer programming using proximity
We consider the problem of solving integer programs of the form min {c^T x : Ax = b; x geq 0}, where A is a multistage stochastic matrix. We give an algorithm that solves this problem in fixed-parameter time f(d; ||A||_infty) n log^O(2d) n, where f is a computable function, d is the treed
From playlist Workshop: Parametrized complexity and discrete optimization
Sums of Squares and Golden Gates - Peter Sarnak (Princeton)
Through the works of Fermat, Gauss, and Lagrange, we understand which positive integers can be represented as sums of two, three, or four squares. Hilbert's 11th problem, from 1900, extends this question to more general quadratic equations. While much progress has been made since its formu
From playlist Mathematics Research Center
Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
From playlist Mathematics
Solving an equation with variables on both side and one solution
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist Solve Multi-Step Equations......Help!
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
Ordine aritmetico e caos logico: congetture in teoria dei modelli
I numeri interi sono uno degli oggetti matematici dalla struttura più semplice e chiara, ma... lo sono per davvero? Negli occhi di un logico, essi potrebbero al contrario scoprirsi portatori di un caos insostenibile e inverecondo. Simone Ramello (Universität Münster) ci mostrerà come la te
From playlist Mathematics Münster News
How to use the LCD to help us solve a rational equation
👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for
From playlist How to Solve Rational Equations
Mathematical Ideas in Lattice Based Cryptography - Jill Pipher
2018 Program for Women and Mathematics Topic: Mathematical Ideas in Lattice Based Cryptography Speaker: Jill Pipher Affiliation: Brown University Date: May 21, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Solving an equation with a variable on both sides infinite solutions
👉 Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To
From playlist Solve Multi-Step Equations......Help!
Ex 1: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions
This video solves a two step equation with fractions by leaving the fractions in the equation and solving just like any other two step equation. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Solving Two-Step Equations
A Tricky Problem on Sums of Two Squares - Enrico Bombieri
Enrico Bombieri Institute for Advanced Study December 10, 2012 A `toy model' for studying the probabilistic distribution of nodal curves of eigenfunctions of linear operators arises from the Laplacian on the standard real 2-torus. Here the eigenvalues are associate to integers m that are s
From playlist Mathematics
Data Science with Mathematica -- LibraryLink, CUDA, CUDALink, and CUDA through LibraryLink
In this video of the Data Science with Mathematica track I provide a very rudimentary introduction to LibraryLink, the CUDALink package, and the use of CUDA through LibraryLink, the latter being my preference, as it offers the greatest flexibility, and one can use all the features of your
From playlist Data Science with Mathematica
Stanford Seminar - Deep Learning for Symbolic Mathematics - Guillaume Lample & Francois Charton
Guillaume Lample & Francois Charton Facebook AI Research April 16, 2020 View the full playlist: https://www.youtube.com/playlist?list=PLoROMvodv4rMWw6rRoeSpkiseTHzWj6vu 0:00 Introduction 1:06 Deep learning for symbolic mathematics 2:27 Starting point 4:22 Basic intuition 6:44 The plan
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
Solving a multi-step equation with fractions and variable on both sides
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides