Theory of cryptography | Computational hardness assumptions | Computational number theory
The phi-hiding assumption or Φ-hiding assumption is an assumption about the difficulty of finding small factors of φ(m) where m is a number whose factorization is unknown, and φ is Euler's totient function. The security of many modern cryptosystems comes from the perceived difficulty of certain problems. Since P vs. NP problem is still unresolved, cryptographers cannot be sure computationally intractable problems exist. Cryptographers thus make assumptions as to which problems are hard. It is commonly believed that if m is the product of two large primes, then calculating φ(m) is currently computationally infeasible; this assumption is required for the security of the RSA Cryptosystem. The Φ-Hiding assumption is a stronger assumption, namely that if p1 and p2 are small primes exactly one of which divides φ(m), there is no polynomial-time algorithm which can distinguish which of the primes p1 and p2 divides φ(m) with probability significantly greater than one-half. This assumption was first stated in the 1999 paper Computationally Private Information Retrieval with Polylogarithmic Communication, where it was used in a Private Information Retrieval scheme. (Wikipedia).
Hidden Identities: Numbers you didn't know were there!
There are numbers hiding in your math problems! An alternative way to look at negative numbers, fractions, exponents, and algebra, using the ideas of identities and inverses. Credit to 3Blue1Brown for inspiring my explanation of numbers as actions with his video on Euler's formula and g
From playlist Summer of Math Exposition Youtube Videos
How Much Dark Matter Exists in the Universe?
If you believe the world’s leading physicists, the vast majority of matter in the universe is hiding in plain sight. For nearly a century, evidence has mounted that the gravitational pull necessary to keep clusters of galaxies intact, as well as stars within galaxies from flying apart, req
From playlist Physics in the Dark: Searching for the Universe’s Missing Matter
Searching for WIMP Dark Matter
If you believe the world’s leading physicists, the vast majority of matter in the universe is hiding in plain sight. For nearly a century, evidence has mounted that the gravitational pull necessary to keep clusters of galaxies intact, as well as stars within galaxies from flying apart, req
From playlist Physics in the Dark: Searching for the Universe’s Missing Matter
Teach Astronomy - Pseudoscience
http://www.teachastronomy.com/ A pseudoscience is something that pretends to be scientific but is not. Science follows a rigorous method which relies on the sharing of data, the basis in observations, and the fact that any scientist can assert something, but it has to be supported by evid
From playlist 01. Fundamentals of Science and Astronomy
Secrets of the Universe Buried Under the Earth!
Share on Facebook: http://on.fb.me/1EHJ2d9 From the early optical telescopes of the 1600’s to Hubble, telescopes have expanded human perception and reshaped the way we view our universe. But some of the greatest secrets of the cosmos might not need an observatory at all – they could be bu
From playlist Jonathan's Top Videos of 2014!
What is a Shadow? | Don't Memorise
How can we describe a shadow? Is it just a spot of darkness? Yes that's correct! It is just a spot of darkness where the light is blocked by object(s)! To know more about it watch the entire video! To access all videos related to Shadows, enroll in our full course now: https://infinityle
From playlist Physics
What is a black hole? How do astronomers know they actually exist? Learn about black holes via a range of curriculum topics including kinetic energy, potential energy, universal gravitation, orbits, the behaviour of light, the electromagnetic spectrum, and scientific models. This video is
From playlist Classroom Resources
Vincent Guedj: Pluripotential Kähler-Ricci flows
Abstract: We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Ampere equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the Kähler-R
From playlist Analysis and its Applications
Dark Matter and Galaxy Rotation
Deducing the presence of Dark Matter from the rotational velocities of stars in galaxies.
From playlist Cosmology
Anne Broadbent - Information-Theoretic Quantum Cryptography Part 2 of 2 - IPAM at UCLA
Recorded 27 July 2022. Anne Broadbent of the University of Ottawa presents "Information-Theoretic Quantum Cryptography" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: These lectures are an introduction to the interplay between quantum information and cryp
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
Camille Male: Freeness over the diagonal and the global fluctuations of Wigner matrice
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: We characterize the limiting second order distributions of independent complex Wigner and deterministic matrices using Voiculescu’s notions of freeness over the diago
From playlist Noncommutative geometry meets topological recursion 2021
Roland Bauerschmidt: Log-Sobolev inequality for the continuum Sine-Gordon model
The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations. Abstract: We derive a multiscale generalisation of the Bakry–Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an
From playlist Workshop: Workshop: Singular SPDEs and Related Topics
Solving The Mystery Of The Mole
▶ NEW PUZZLE/SUDOKU HUNT INCOMING ◀ At the start of May we'll release a really amazing puzzle/sudoku hunt by Matyas Martinka. First correct solution wins some merch. Any correct solution gets a shout-out on the channel! https://www.patreon.com/crackingthecryptic ***********************
From playlist Phistomefel Puzzles
Testing Sparsity over Known and Unknown Bases by Arnab Bhattacharyya
Statistical Physics Methods in Machine Learning DATE:26 December 2017 to 30 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "th
From playlist Statistical Physics Methods in Machine Learning
Imaging of Small Inhomogeneities, Homogenization and Super Resolution - Yves Capdeboscq
Imaging of Small Inhomogeneities, Homogenization and Super Resolution Yves Capdeboscq University of Oxford; Institute for Advanced Study October 8, 2010 Over the past decades, much attention has been devoted to the detection of small inhomogeneities in materials or tissues, using non-invas
From playlist Mathematics
Supercuspidal L-packets - Tasho Kaletha
Computer Science/Discrete Mathematics Seminar I Topic: Supercuspidal L-packets Speaker: Tasho Kaletha Affiliation: Technion Date: March 5, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Statistical Mechanics of Athermal Systems: Edwards Ensemble, Entropy... (Lecture 3)
PROGRAM ENTROPY, INFORMATION AND ORDER IN SOFT MATTER ORGANIZERS: Bulbul Chakraborty, Pinaki Chaudhuri, Chandan Dasgupta, Marjolein Dijkstra, Smarajit Karmakar, Vijaykumar Krishnamurthy, Jorge Kurchan, Madan Rao, Srikanth Sastry and Francesco Sciortino DATE: 27 August 2018 to 02 Novemb
From playlist Entropy, Information and Order in Soft Matter
One parameter diagonal group action on homogeneous space (Lecture - 02) by Ronggang Shi
Program Probabilistic Methods in Negative Curvature ORGANIZERS: Riddhipratim Basu, Anish Ghosh and Mahan Mj DATE: 11 March 2019 to 22 March 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore The focal area of the program lies at the juncture of three areas: Probability theory o
From playlist Probabilistic Methods in Negative Curvature - 2019
Teach Astronomy - Spectroscopic Binary
http://www.teachastronomy.com/ A spectroscopic binary occurs when the two stars are too close to be resolved by a telescope or when one member of the pair is too faint to be detected. The binary is observed in terms of a periodic Doppler shift of narrow spectral features, absorption lines
From playlist 17. Galactic Mass Distribtuion and Galaxy Structure
Viviane Baladi: Linear and fractional response: a survey
When a dynamical system admitting a natural (SRB) measure is perturbed, it is natural to ask how the SRB measure responds to the perturbation. In the tamest cases, this response is linear, and the derivative of the SRB measure with respect to the parameter can be expressed as a sum of deco
From playlist Jean-Morlet Chair - Pollicott/Vaienti