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Search results “Group ring cryptography history”

23:42
This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
Views: 53125 James Hamblin

13:22
This video is useful for students of BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

03:13
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 130166 Socratica

07:49
Familiar algebraic systems: review and a look ahead. GRF is an ALGEBRA course, and specifically a course about algebraic structures. This introductory section revisits ideas met in the early part of Analysis I and in Linear Algebra I, to set the scene and provide motivation. https://people.maths.ox.ac.uk/flynn/genus2/sheets0405/grfnotes1011.pdf
Views: 857 Mysterious Mind

28:19
This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

31:28
Views: 6858 Internetwork Security

07:18
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! ➢➢➢➢➢➢➢➢➢➢ To​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ Socratica at: ​Patreon​: https://www.patreon.com/socratica Socratica Paypal: https://www.paypal.me/socratica We also accept Bitcoin! :) Our​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ➢➢➢➢➢➢➢➢➢➢ You can also follow Socratica on: - Twitter: @socratica - Instagram: @SocraticaStudios - Facebook: @SocraticaStudios ➢➢➢➢➢➢➢➢➢➢ Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison (@mlh496 on Twitter) Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 73149 Socratica

01:03:30
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 50870 nptelhrd

01:15:21
Coding Theory by Dr. Andrew Thangaraj, Department of Electronics & Communication Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 26858 nptelhrd

50:14
We're in Dummit and Foote's 3rd edition, Part III
Views: 5526 James Cook

57:12
After the work of Diophantus, there was something of a lapse in interest in pure number theory for quite some while. Around 1300 Gersonides developed the connection between the Binomial theorem and combinatorics, and then in the 17th century the topic was again taken up, notably by Fermat, and then by Euler, Lagrange, Legendre and Gauss. We discuss several notable results of Fermat, including of course his famous last theorem, also his work on sums of squares, Pell's equation, primes, and rational points on curves. The rational parametrization of the Folium of Descartes is shown, using the technique of Fermat. We also state Fermat's little theorem using the modular arithmetic language introduced by Gauss. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

51:09
The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns that can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption scheme is homomorphic, the cloud can still perform meaningful computations on the data, even though it is encrypted. In fact, we now know a number of constructions of fully homomorphic encryption schemes that allow arbitrary computation on encrypted data. In the last two years, solutions for fully homomorphic encryption have been proposed and improved upon, but all currently available options seem to be too inefficient to be used in practice. However, for many applications it is sufficient to implement somewhat homomorphic encryption schemes, which support a limited number of homomorphic operations. They can be much faster, and more compact than fully homomorphic schemes. This talk will focus on describing the recent somewhat homomor- phic encryption scheme of Brakerski and Vaikuntanathan, whose security relies on the ring learning with errors (RLWE) problem.
Views: 816 Microsoft Research

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Views: 33578 Lalit Vashishtha

05:24
Views: 14837 Laura Rickhoff

03:32
This video explores the Cryptography research group at the University of Bristol through an interview with the head of the group, Prof. Nigel Smart.

01:10:23
The Ring Learning-with-Errors problem, proposed by Lyubashevsky, Peikert and Regev in 2010, is a variant of the traditional Learning-with-Errors problem, and is an active research area in lattice based cryptography. It has drawn increased attention due to the important application to constructing homomorphic encryption schemes. The security of RLWE problems relies on the hardness of certain standard problems over ideal lattices. In the first part of the talk, I will review the basics of RLWE problems, the hardness proofs, and major RLWE encryption schemes. Then I will survey different attacks to RLWE, including our new attacks to non-dual RLWE in sub-cyclotomic fields and small error dual RLWE on prime cyclotomic fields. I will end by summarizing the security situation for various RLWE problems. This is joint work with Kristin Lauter and Katherine Stange.
Views: 2059 Microsoft Research

14:46
Learn and understand GF and various operations on elements using polynomial representation

13:59
Group Theory 69, Polynomial Rings

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Learn the definition of a group - one of the most fundamental ideas from abstract algebra. If you found this video helpful, please give it a "thumbs up" and share it with your friends! To see more videos on Abstract Algebra, please watch our playlist: https://www.youtube.com/watch?v=QudbrUcVPxk&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6 If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 215304 Socratica

01:04:43
Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2927 barilanuniversity

55:42
Discrete Mathematical Structures
Views: 104162 nptelhrd

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What is RING THEORY? What does RING THEORY mean? RING THEORY meaning - RING THEORY definition - RING THEORY explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major area of modern mathematics. Because these three fields (algebraic geometry, algebraic number theory and commutative algebra) are so intimately connected it is usually difficult and meaningless to decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry, and is stated and proved in terms of commutative algebra. Similarly, Fermat's last theorem is stated in terms of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry. Noncommutative rings are quite different in flavour, since more unusual behavior can arise. While the theory has developed in its own right, a fairly recent trend has sought to parallel the commutative development by building the theory of certain classes of noncommutative rings in a geometric fashion as if they were rings of functions on (non-existent) 'noncommutative spaces'. This trend started in the 1980s with the development of noncommutative geometry and with the discovery of quantum groups. It has led to a better understanding of noncommutative rings, especially noncommutative Noetherian rings. (Goodearl 1989) For the definitions of a ring and basic concepts and their properties, see ring (mathematics). The definitions of terms used throughout ring theory may be found in the glossary of ring theory.
Views: 2440 The Audiopedia

05:01
Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 151163 Socratica

19:18
This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

11:06
Properties of fields, groups and rings
Views: 15232 Janet Bowers

10:35
Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven using basic group theory. Prerequisites: To follow this video, you will want to first learn the basics of congruences. If you found this video helpful, please share it with your friends! You might like the other videos in our Number Theory Playlist: https://www.youtube.com/watch?v=VLFjOP7iFI0&list=PLi01XoE8jYojnxiwwAPRqEH19rx_mtcV_ Don't forget to Subscribe to our channels so you'll hear about our newest videos: http://www.youtube.com/subscription_center?add_user=SocraticaStudios Subject: Number Theory Teacher: Michael Harrison Artist: Katrina de Dios
Views: 151861 Socratica

30:36
Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics Groups are always lurking where symmetry arises. In this lecture, we explore many beautiful examples of groups that arise from natural symmetries in science, art, and mathematics. This includes shapes of molecules, repeating patterns in 1, 2, and 3 dimensions, and finally, how groups arise in braids. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
Views: 12964 Professor Macauley

07:20
A solution to a typical exam question. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Views: 303457 Randell Heyman

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It covers Euclid's Algorithm, Euclid's Algorithm: Tabular Method, Modular Arithmetic, Modular Arithmetic Operations, Modular Arithmetic Properties, Group, Cyclic Group, Ring, Field, Finite Fields or Galois Fields, Polynomial Arithmetic, Polynomial Arithmetic with Mod 2 Coefficients.
Views: 10002 Scholartica Channel

12:32
The notion of congruence modulo n is used to introduce the integers modulo n. Addition and multiplication are defined for the integers modulo n.
Views: 18302 learnifyable

12:28
B.Sc., B.C.A and other college courses Arupsmath
Views: 15829 Arup Majumdar

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Views: 131600 KNOWLEDGE GATE

08:04
During the IBM Research 5 in 5 Science Slam at IBM Think 2018, IBM researcher Cecilia Boschini explains one of the technologies that will change the world in the next five years: lattice cryptography. Learn more at http://ibm.biz/five-in-five.
Views: 4331 IBM Research

06:27
This was for the MAO Math Presentation Competition. I won! :D
Views: 32647 Riverninj4

08:11
The Integer Ring - Waterloo
Views: 131 Taiga

25:35
Benoît Libert and San Ling and Fabrice Mouhartem and Khoa Nguyen and Huaxiong Wang. Talk at Asiacrypt 2016. See http://www.iacr.org/cryptodb/data/paper.php?pubkey=27877
Views: 115 TheIACR

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Introduction Ensembles + Axiomes + Règles + Lois = Structure Algébrique Structures + extra Axiomes = Groupes Anneaux et Corps Problème des racines des équations polynomiales de degré supérieure a 4.
Views: 502 Lifenote School

01:50:46
Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 7588 barilanuniversity

01:00:08
Vadim Lyubashevsky's August 13, 2013 lecture at the UCI Workshop on Lattices with Symmetry. The last 10 minutes of audio are missing.

01:00:06
Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 3793 barilanuniversity

09:42
Algebra is my favorite branch of mathematics. In this video, I try to describe what the subject is about, assuming as little mathematical background as possible, and within 10 minutes.
Views: 2378 Hsing Liu

01:02:11
NULL
Views: 1663 Microsoft Research

50:40
Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2872 barilanuniversity

20:19
Part 2 of lecture 7 from my ring theory lecture playlist. Topics discussed include properties of rings of fractions and modules of fractions.

01:02:54
Jeff Hoffstein's August 31 presentation on "Somewhat Homomorphic Encryption via Number Fields and Finite Fields" at the 2015 UCI Mathematics of Cryptography Conference

14:40