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Introduction to Elliptic Curves - Part 1 of 8
 
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“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves. This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see http://ctnt-summer.math.uconn.edu/
Views: 3180 UConn Mathematics
Introduction to Elliptic Curves - Part 2 of 8
 
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“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves. This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see http://ctnt-summer.math.uconn.edu/
Views: 743 UConn Mathematics
Introduction to Elliptic Curves - Part 3 of 8
 
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“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves. This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see http://ctnt-summer.math.uconn.edu/
Views: 611 UConn Mathematics
Introduction to Elliptic Curves - Part 4 of 8
 
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“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves. This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see http://ctnt-summer.math.uconn.edu/
Views: 404 UConn Mathematics
Elliptic curve cryptography
 
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Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC cryptography is the same level of security provided by keys of smaller size. Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 2863 Audiopedia
Introduction to Elliptic Curves - Part 5 of 8
 
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“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves. This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see http://ctnt-summer.math.uconn.edu/
Views: 389 UConn Mathematics
José Felipe Voloch: Generators of elliptic curves over finite fields
 
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Abstract: We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin's conjecture for primitive roots. Recording during the thematic meeting: "Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects" the March 31, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
The Jacobi Symbol, Math 706 Section 5.3
 
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Math 706 Section 5.3 The Jacobi Symbol
Views: 2000 Todd Cochrane
John Coates: (1/4) Classical algebraic Iwasawa theory [AWS 2018]
 
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slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture1Slides.pdf lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf CLASSICAL ALGEBRAIC IWASAWA THEORY. JOHN COATES If one wants to learn Iwasawa theory, the starting point has to be the basic material covered in §1 - §8 of Iwasawa’s paper [1]. The aim of these lectures will be to give a concise account of this work, concentrating on proving one of the main results of the paper, which is the so called weak Leopoldt conjecture for the cyclotomic Zp-extension of any number field, i.e. that the p-adic defect of Leopoldt is always bounded as one goes up the cyclotomic Zp-extension. The course will also include a brief introduction to the notion of the Iwasawa algebra of Zp, and the structure theory of modules for this Iwasawa algebra. The background required for the lectures will be basic algebraic number theory, including a knowledge of the main facts of abelian global class field theory. References [1] K. Iwasawa On Zl-extensions of algebraic number fields, Ann. of Math. 98 (1973), 246- 326. [2] J. Coates Infinite descent on elliptic curves with complex multiplication, in Arithmetic and Geometry, Progress in Mathematics 35 (1983), Birkhauser, 107-137. http://swc.math.arizona.edu/index.html
Encryption.mp4
 
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How to write a program to encrypt a message in Mathematica, using linear algebra.
Views: 175 vigvig
Geometric noncommutative schemes, their gluing and finite dimensional algebras - Dmitry Orlov
 
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Dmitry Orlov March 10, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
fermat's last theorem, the original proof
 
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Here's Fermat's original proof. See the drawing that was too large to fit into margin .https://www.youtube.com/watch?v=wFyX5uqyLLA&t=157s I am looking for someone to helpo write proof of beawl conj3ecture. there is a 1 $1,000,000 prize. This proof has been verified by a former professor of mathematics at Harvard. I am presenting this video in order to get any possible objections. http://en.wikipedia.org/wiki/Square_root_of_2 Here is one use of irreducible fractions to prove square root of 2 is irrational. October 23, 2013 The view count is now over 1200. No person has come forth with a counter proof in the last 200 views. So my proof must be correct. Sept. 23, 2013I was waiting until the view count reached 1000 to make this statement, but the statement at 960 view count (September 28, 2013) spurred me to make it now. No one has been able to disprove the Theorem and there has been attempts to disprove the proof that were incorrect. So, I am making the challenge that the proof is correct. There have been a number of people that have read the proof but have been afraid of saying the proof is correct. That includes Sean Gomes. Even the mathematicians at Chapman University have been silent on the veracity of the proof. David B. Moore has tried several times to get faculty to respond, with no success. You can call him at 714-516-4590 to verify this for yourself. Ferrmat's Dilemma The problem with this proof is that it may be possible for the larger denominator that makes the presumed smallest ratio for the rational number, in front of the term (x^n-1 + y^n-1), divides into this term perfectly. So which number is the real ratio? Is the proof really dependent on the language used? This question is what prompted Fermat to go on to prove the case for n=4, I am sure. August 16, 2013 Dear reader Look at what Sean Gomes has written about you "Youtube is not a system for peer review. That is like asking a deaf man to distinguish mozart from cannibal corpse." All you have to do to prove him wrong is to invoke social media intelligence. retweet this link or post on facebook, etc. This is a solution using infinite descent along with Diophantine equations, a technique used by Fermat in many other theorems. This probably is the proof that he thought of, and it only uses very simple math. I prayed to God for the answer for the proof. He has delivered once again. This time I am remembering that he did it. July 17, 2013 My friend, Mike Slack, mentioned that I misused the term 'infinite descent in the proof. I did go back and check and the term was misused. Fortunately, infinite descent is not used in the proof. In thinking back on this mistake, I think I was seeing how Fermat started looking at this as a possible path to proof with infinite descent and discovered that the square of factor was double that of the calculated rational ratio, like I did.Thanks to Mike, I am able to explain this inconsistency. If you get smarter like I did, here is a video on how to do it. http://youtu.be/Dn0awOfrgBk I am attempting another impossible task, creating a space elevator. Here is a link to the contest I am in. http://contest.techbriefs.com/2013/entries/aerospace-and-defense/3823
Views: 10125 michael weir
What is EPHEMERAL KEY? What does EPHEMERAL KEY mean? EPHEMERAL KEY meaning & explanation
 
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What is EPHEMERAL KEY? What does EPHEMERAL KEY mean? EPHEMERAL KEY meaning - EPHEMERAL KEY definition - EPHEMERAL KEY explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ A cryptographic key is called ephemeral if it is generated for each execution of a key establishment process. In some cases ephemeral keys are used more than once, within a single session (e.g., in broadcast applications) where the sender generates only one ephemeral key pair per message and the private key is combined separately with each recipient's public key. Contrast with a static key. Private ephemeral key agreement key: Private ephemeral key agreement keys are the private keys of asymmetric key pairs that are used only once to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors). Public ephemeral key agreement key: Public ephemeral key agreement keys are the public keys of asymmetric key pairs that are used in a single key establishment transaction to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).
Views: 1112 The Audiopedia
A High-Speed FPGA Implementation of an RSD-Based ECC Processor
 
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A High-Speed FPGA Implementation of an RSD-Based ECC Processor 2015 VLSI Project Training Contact: IIS TECHNOLOGIES ph:9952077540,landline:044 42637391 mail:[email protected] www.iistechnologies.in
Views: 171 IIS Technologies
Fermat's Last Theorem Simple Proof (General) by S.Haridas
 
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FLT Proof is given in simple way which can be easily followed by UG students as well.
Views: 3423 Sadasivan Haridasan
John Coates: (3/4) Classical algebraic Iwasawa theory [AWS 2018]
 
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slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture3Slides.pdf lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf CLASSICAL ALGEBRAIC IWASAWA THEORY. JOHN COATES If one wants to learn Iwasawa theory, the starting point has to be the basic material covered in §1 - §8 of Iwasawa’s paper [1]. The aim of these lectures will be to give a concise account of this work, concentrating on proving one of the main results of the paper, which is the so called weak Leopoldt conjecture for the cyclotomic Zp-extension of any number field, i.e. that the p-adic defect of Leopoldt is always bounded as one goes up the cyclotomic Zp-extension. The course will also include a brief introduction to the notion of the Iwasawa algebra of Zp, and the structure theory of modules for this Iwasawa algebra. The background required for the lectures will be basic algebraic number theory, including a knowledge of the main facts of abelian global class field theory. References [1] K. Iwasawa On Zl-extensions of algebraic number fields, Ann. of Math. 98 (1973), 246- 326. [2] J. Coates Infinite descent on elliptic curves with complex multiplication, in Arithmetic and Geometry, Progress in Mathematics 35 (1983), Birkhauser, 107-137. http://swc.math.arizona.edu/index.html
Privacy, Security, and Cryptography
 
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Launchpad Accelerator Engineer Bootcamp 2018 → http://bit.ly/2G1w5py Ananth Raghunathan is a computer scientist broadly interested in cryptography, security, and machine learning. At Google, he works in the security and privacy research team in Google Brain on differential privacy, applied crypto, and topics at the intersection of security and machine learning. About Launchpad Accelerator: Launchpad Accelerator is an acceleration program for the world’s top startups. Founders work closely with Google and Alphabet product teams and experts to solve specific technical challenges and optimize their businesses for growth with machine learning. Accelerator Startups are selected to be a part of the four month product acceleration program. Each startup is paired with a Google product manager to accelerate their product development, working alongside Google’s ML research and development teams. Learn more at → https://goo.gl/qFTrKD About Accelerator’s Engineering Bootcamp: Accelerator’s Engineering Bootcamp brings together each startup’s project team for a four-day event in San Francisco to learn best practices in experimenting, building, and implementing advanced tech within their startup. The teams are composed of Founders and VPs along with developers, data scientists, and product managers. Watch more in this playlist → http://bit.ly/2G1w5py Subscribe to Launchpad to learn all about startups → http://bit.ly/Launchpad9
Math313 Lec23 FermatLastThm
 
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Math 313: Introduction to Number Theory: Lecture 23: April 14, 2017: Method of Descent for Fermat and Introduction to p-adics
Views: 131 Steven Miller
Acclaim Forsaken PC Soundtrack - Track 2 - Forsaken
 
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Go to http://fly.thruhere.net to download the game and play online for free.
Views: 8406 sir fleshmorph
Mike Patton - 37 - Supersingular Primes
 
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The Solitude of Prime Numbers (Music from the Film and Inspired By the Book)
Views: 4368 MissMachine
Number theory | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Number_theory 00:01:39 1 History 00:01:48 1.1 Origins 00:01:56 1.1.1 Dawn of arithmetic 00:06:49 1.1.2 Classical Greece and the early Hellenistic period 00:10:09 1.1.3 Diophantus 00:14:18 1.1.4 Āryabhaṭa, Brahmagupta, Bhāskara 00:16:20 1.1.5 Arithmetic in the Islamic golden age 00:17:07 1.1.6 Western Europe in the Middle Ages 00:17:50 1.2 Early modern number theory 00:18:00 1.2.1 Fermat 00:22:36 1.2.2 Euler 00:25:47 1.2.3 Lagrange, Legendre, and Gauss 00:28:37 1.3 Maturity and division into subfields 00:30:30 2 Main subdivisions 00:30:39 2.1 Elementary tools 00:31:42 2.2 Analytic number theory 00:33:38 2.3 Algebraic number theory 00:38:56 2.4 Diophantine geometry 00:45:03 3 Recent approaches and subfields 00:45:38 3.1 Probabilistic number theory 00:47:16 3.2 Arithmetic combinatorics 00:49:50 3.3 Computations in number theory 00:52:57 4 Applications 00:53:55 5 Prizes 00:54:16 6 See also Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts "There is only one good, knowledge, and one evil, ignorance." - Socrates SUMMARY ======= Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation). The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.
Views: 11 wikipedia tts
KEITH HUNTER:  MEGALITHIC MONUMENTS AND SECRET MILITARY BASES
 
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I interview Keith Hunter regarding his latest research on Megalithic monuments and how they are linked to secret military bases. his website: http://www.occultphysics.com/ KERRY CASSIDY http://projectcamelot.tv
Views: 19224 Project Camelot