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Elliptic Curve Cryptography(ECC) - GATE Computer Science
 
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The complete YouTube playlist can be viewed here: https://goo.gl/mjyDev This lesson explains the concept of the Elliptic Curve Cryptography(ECC), under the course, "Cryptography and Network Security for GATE Computer Science Engineering". The lesson explains the questions on the following subtopics: Elliptic Curve Cryptography(ECC) ECC - Public key cryptosystem ECC - Key Exchange ECC - Encryption and Decryption Elliptic curve Some important terminology and concepts are also illustrated, for the better understanding of the subject. For the entire course: https://goo.gl/aTMBNZ For more lessons by Ansha Pk: https://goo.gl/2DX9Wn Must watch for all the GATE/ESE/PSU Exams. Download the Unacademy Learning App from the Google Play Store here:- https://goo.gl/02OhYI Download the Unacademy Educator app from the Google Play Store here: https://goo.gl/H4LGHE Do Subscribe and be a part of the community for more such lessons here: https://goo.gl/UGFo7b Visit Our Facebook Group on GATE here: https://goo.gl/cPj5sb Elliptic Curve Cryptography(ECC) - GATE Computer Science - Unacademy
Elliptic Curve Cryptography Overview
 
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John Wagnon discusses the basics and benefits of Elliptic Curve Cryptography (ECC) in this episode of Lightboard Lessons. Check out this article on DevCentral that explains ECC encryption in more detail: https://devcentral.f5.com/articles/real-cryptography-has-curves-making-the-case-for-ecc-20832
Views: 169568 F5 DevCentral
Elliptic Curve Cryptography & Diffie-Hellman
 
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Today we're going over Elliptic Curve Cryptography, particularly as it pertains to the Diffie-Hellman protocol. The ECC Digital Signing Algorithm was also discussed in a separate video concerning Bitcoin's cryptography.
Views: 53371 CSBreakdown
Elliptic Curve Point Addition
 
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This was for the MAO Math Presentation Competition. I won! :D
Views: 31270 Riverninj4
Elliptic Curve Cryptography Tutorial - An Introduction to Elliptic Curve Cryptography
 
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Learn more advanced front-end and full-stack development at: https://www.fullstackacademy.com Elliptic Curve Cryptography (ECC) is a type of public key cryptography that relies on the math of both elliptic curves as well as number theory. This technique can be used to create smaller, faster, and more efficient cryptographic keys. In this Elliptic Curve Cryptography tutorial, we introduce the mathematical structure behind this new algorithm. Watch this video to learn: - What Elliptic Curve Cryptography is - The advantages of Elliptic Curve Cryptography vs. old algorithms - An example of Elliptic Curve Cryptography
Views: 11378 Fullstack Academy
Finite fields made easy
 
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Solutions to some typical exam questions. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Views: 37828 Randell Heyman
How to Multiply  in Modular Arithmetic - Cryptography - Lesson 5
 
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In this tutorial, I demonstrate two different approaches to multiplying numbers in modular arithmetic. Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm Donate - http://bit.ly/19AHMvX STILL NEED MORE HELP? Connect one-on-one with a Math Tutor. Click the link below: https://trk.justanswer.com/aff_c?offer_id=2&aff_id=8012&url_id=232 :)
Views: 33872 Learn Math Tutorials
An Introduction to Elliptic Curve Cryptography
 
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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: 30493 nptelhrd
The Beauty of Elliptic Curves
 
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Talk at the MathSoc at UCT in Cape Town, October 26, 2017.
Views: 1280 Linda Frey
Implementation of Elliptic Curve Cryptography
 
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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: 13184 nptelhrd
Bitcoin 101 - Elliptic Curve Cryptography - Part 4 - Generating the Public Key (in Python)
 
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Welcome to part four in our series on Elliptic Curve Cryptography. I this episode we dive into the development of the public key. In just 44 lines of code, with no special functions or imports, we produce the elliptic curve public key for use in Bitcoin. Better still, we walk you through it line by line, constant by constant. Nothing makes the process clearer and easier to understand than seeing it in straight forward code. If you've been wondering about the secp256k1 (arguably the most important piece of code in Bitcoin), well then this is the video for you. This is part 4 of our upcoming series on Elliptic Curves. Because of such strong requests, even though this is part 4, it is the first one we are releasing. In the next few weeks we will release the rest of the series. Enjoy. Here's the link to our Python code (Python 2.7.6): https://github.com/wobine/blackboard101/blob/master/EllipticCurvesPart4-PrivateKeyToPublicKey.py Here's the private key and the link to the public address that we use. Do you know why it is famous? Private Key : A0DC65FFCA799873CBEA0AC274015B9526505DAAAED385155425F7337704883E Public Address on Blockchain.info https://blockchain.info/address/1JryTePceSiWVpoNBU8SbwiT7J4ghzijzW Here's the private key we use at the end: 42F615A574E9CEB29E1D5BD0FDE55553775A6AF0663D569D0A2E45902E4339DB Public Address on Blockchain.info https://blockchain.info/address/16iTdS1yJhQ6NNQRJqsW9BF5UfgWwUsbF Welcome to WBN's Bitcoin 101 Blackboard Series -- a full beginner to expert course in bitcoin. Please like, subscribe, comment or even drop a little jangly in our bitcoin tip jar 1javsf8GNsudLaDue3dXkKzjtGM8NagQe. Thanks, WBN
Views: 21927 CRI
Introduction to the Post-Quantum Supersingular Isogeny Diffie-Hellman Protocol
 
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A talk given at the University of Waterloo on July 12th, 2016. The intended audience was mathematics students without necessarily any prior background in cryptography or elliptic curves. Apologies for the poor audio quality. Use subtitles if you can't hear.
Views: 2200 David Urbanik
Asymptotics of Elliptic Curves (Part 1)
 
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This was a lecture given by Manjul Bhargava in the Introductory Workshop on Arithmetic Statistics at MSRI.
Views: 1129 MathSciResInst
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: 3161 UConn Mathematics
Barry Mazur -  Logic, Elliptic curves, and Diophantine stability
 
01:04:09
This is the first lecture of the 2014 Minerva Lecture series at the Princeton University Mathematics Department October 14, 2014 An introduction to aspects of mathematical logic and the arithmetic of elliptic curves that make these branches of mathematics inspiring to each other. Specifically: algebraic curves - other than the projective line - over number fields tend to acquire no new rational points over many extension fields. This feature (which I call 'diophantine stability') makes elliptic curves, in particular, useful as vehicles to establish diophantine unsolvability for many large rings. To repay the debt, mathematical logic offers consequences to the arithmetic of elliptic curves over decidable rings. I will also discuss new results about diophantine stability.
Views: 3732 princetonmathematics
Solving Discrete Logarithm Problems: Baby-step, Giant-step
 
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Code: http://asecuritysite.com/encryption/baby
Views: 596 Bill Buchanan OBE
Elliptic Curves as Abelian Groups
 
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Math 706 Section 10.5 Elliptic Curves as Abelian Groups
Views: 272 Todd Cochrane
Asymptotics of elliptic curves I - Manjul Bhargava [2011]
 
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Asymptotics of elliptic curves I Introductory Workshop: Arithmetic Statistics January 31, 2011 - February 04, 2011 February 02, 2011 (09:30 AM PST - 10:30 AM PST) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/566
MMUSSL - Elliptic Curves
 
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The Michigan Math Undergraduate Summer Seminar Lunch (MMUSSL) is a mini course series organized by, given by, and aimed at undergraduate math concentrators at the University of Michigan, with the goal of giving students a chance to share their knowledge of mathematics that interest them. All of the speakers are currently or recently graduated students at the University of Michigan. Sorry for the poor video quality. -------------------- Title: Elliptic Curves (1/1) Speaker: Gwyn Moreland Date: 6/11/14 Description: Elliptic curves arise in many problems in mathematics as a useful tool. This is much in part due to their structure and the multitude of theorems about them, especially their torsion groups. Not only that, they also generate some fun math on their own, such as the open problem of finding elliptic curves of arbitrarily high rank. The first talk will serve as an abridged introduction to elliptic curves. We will discuss their origin (parametrizations of integrands) and give a definition of an elliptic curve. We will also introduce some of the important theorems surrounding them (Nagell-Lutz, Mordell-Weil, Mazur) and then lastly look at some of their applications and where they appear in math today (BSD, cryptography).
Views: 913 Juliette Bruce
Discrete Log Problem - Applied Cryptography
 
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This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
Views: 13821 Udacity
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: 740 UConn Mathematics
Scalable Zero Knowledge via Cycles of Elliptic Curves
 
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Speaker: Alessandro Chiesa, ETH Zurich 'The First Greater Tel Aviv Area Symposium' School of Computer Science Tel-Aviv University, 13.11.14
Views: 1180 TAUVOD
Complex Analysis  and algebraic geometry
 
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In many ways, the modern revival of algebraic geometry resulted from investigations in complex function theory. In this video, we show how Weierstrass's p-function can be used to relate cubic curves and 2-tori. We see in particular that cubic curves have an abelian group structure. The material in this video and the other in the playlist can be found in Kirwan's "Complex algebraic curves".
Views: 2237 DanielChanMaths
Asymptotics of Elliptic Curves (Part 2)
 
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This was a lecture given by Manjul Bhargava in the Introductory Workshop on Arithmetic Statistics at MSRI.
Views: 233 MathSciResInst
Galois Field Part 2
 
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Multiplication and addition tables for GF(2^3), concept of generator in GF and operations using generator.
Views: 5556 DrVikasThada
(Fundamental Group of an Elliptic Curve) = (Tate Module)
 
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Here we talk about how the abelianization of the geometric algebraic fundmental group is really the Tate module.
Solving Diophantine equations using elliptic curves + Introduction to SAGE by Chandrakant Aribam
 
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12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An elliptic curve, say E, can be represented by points on a cubic equation as below with certain A, B ∈ Q: y2 = x3 + Ax +B A Theorem of Mordell says that that E(Q), the set of rational points of E, is a finitely generated abelian group, and thus, E(Q) = Zr ⊕ T, for some non-negative integer r and a finite group T. Here, r is called the algebraic rank of E. The Birch and Swinnerton-Dyer conjecture relates the algebraic rank of E to the value of the L-function, L(E, s), attached to E at s = 1. Further theoretical understanding, corroborated by computations lead to a stronger version of the BSD conjecture. This refined version of the BSD conjecture provides a very precise formula for the leading term of L(E, s) at s = 1, the coefficient of (s − 1)r, in terms of various arithmetical data attached to E. Thus, the computational side of the BSD conjecture goes hand in hand with the advanced concepts in the theory of Elliptic curves. In this program, the computational aspects of the BSD conjecture with various illustrative examples, as well as p-adic L-functions, which are the p-adic analogues of the L-functions and other theoretical aspects which are important for the BSD conjecture will be discussed. CONTACT US: [email protected] PROGRAM LINK: https://www.icts.res.in/program/bsdtc2016
Modular Arithmetic & Modulus Function (Part 4 Crashcourse Cryptography)
 
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Book: Understanding Cryptography https://www.amazon.com/Understanding-Cryptography-Textbook-Students-Practitioners/dp/3642041000/ref=as_li_ss_tl?ie=UTF8&qid=1541146284&sr=8-1&keywords=Understanding+Cryptography:+A+Textbook+for+Students+and+Practitioners&linkCode=sl1&tag=julianhosp-20&linkId=8e14aad9056003d3eefcacb57c2e0b73&language=en_US ---------- New to cryptocurrencies? You might want to read this book first! http://cryptofit.community/cryptobook If you liked the video, subscribe to my channel, give a "thumbs up" and share this video to make the world together #cryptofit :) ► Subscribe: https://www.youtube.com/channel/UCseN... ► Cryptocurrency Exchange: https://www.binance.com/?ref=11272739 ► Hardware Wallet: http://www.julianhosp.com/hardwallet ► Ruben's Trinkgeld Adressen: Bitcoin: 3MNWaot64Fr1gRGxv4YzHCKAcoYTLXKxbc Litecoin: MTaGwg5EhKooonoVjDktroiLqQF6Rvn8uE --------------- ► Completely NEW? What is Blockchain, Bitcoin and Co? Get this book from me: https://www.amazon.com/Cryptocurrenci... ► Join our Facebook group: https://www.facebook.com/groups/crypt... ► iTunes Podcast: https://itunes.apple.com/sg/podcast/t... ► My website: http://www.julianhosp.com ---------------- My name is Dr. Julian Hosp or just Julian. My videos are about Bitcoin, Ethereum, Blockchain and crypto currencies in general, to avoid scam, rip-off and fraud especially in mining. I'm talking about how you can invest wisely and do it rationally and simply. My ultimate goal is to make people all around the world #CRYPTOFIT. I.E fit for this new wave of decentralization and blockchain. Have fun! ► Follow me here and stay in touch: Facebook: www.facebook.com/julianhosp/ Twitter: https://twitter.com/julianhosp Instagram: https://www.instagram.com/julianhosp/ Linkedin: https://www.linkedin.com/julianhosp
Views: 928 Dr. Julian Hosp
Discrete Logarithm Problem
 
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Discrete Logarithm Problem - modular arithmetic
Views: 48684 Art of the Problem
Asymmetry -- The Cryptographic Game Changer
 
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The most impactful innovation in cryptography in the last half century is the notion of asymmetry: using different keys for encryption and decryption, and finding the mathematics that would make it difficult (so we assume) for our adversary to derive one key from the other. The essence of this game changing innovation is described in this video.
Views: 1309 Gideon Samid
More on RSA
 
30:06
Views: 3224 Internetwork Security
Infinite Magic Elliptic Curves
 
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http://demonstrations.wolfram.com/InfiniteMagicEllipticCurves The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Can points representing integers be placed in the plane so that any triplet of integers summing to 0 lies on a straight line? It turns out the answer is yes. This Demonstration shows seven different ways to do it by placing the points on elliptic curves... Contributed by: Ed Pegg Jr Audio created with WolframTones: http://tones.wolfram.com
Views: 109 wolframmathematica
Andrew Sutherland: Computing the image of Galois representations attached to elliptic curves
 
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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 Let E be an elliptic curve over a number field K. For each integer n[greater than]1 the action of the absolute Galois group GK:=Gal(K/K) on the n-torsion subgroup E[n] induces a Galois representation ρE,n:GK→ Aut(E[n])⋍GL2(ℤ/nℤ). The representations ρE,n form a compatible system, and after taking inverse limits one obtains an adelic representation ρE:GK→GL2(ℤ̂ ). If E/K does not have CM, then Serre's open image theorem implies that the image of ρE has finite index in GL2(ℤ̂ ); in particular, ρE,ℓ is surjective for all but finitely many primes ℓ. I will present an algorithm that, given an elliptic curve E/K without CM, determines the image of ρE,ℓ in GL2(ℤ/ℓℤ) up to local conjugacy for every prime ℓ for which ρE,ℓ is non-surjective. Assuming the generalized Riemann hypothesis, the algorithm runs in time that is polynomial in the bit-size of the coefficients of an integral Weierstrass model for E. I will then describe a probabilistic algorithm that uses this information to compute the index of ρE in GL2(ℤ̂ ). Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Euler's totient function | Journey into cryptography | Computer Science | Khan Academy
 
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Measuring the divisibility of a number Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/rsa-encryption-part-4?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/rsa-encryption-step-3?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 131311 Khan Academy Labs
Index Arithmetic Examples
 
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Examples solving congruences with discrete logarithms.
Views: 1647 Cathy Frey
The Mathematics of Diffie-Hellman Key Exchange | Infinite Series
 
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Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Symmetric keys are essential to encrypting messages. How can two people share the same key without someone else getting a hold of it? Upfront asymmetric encryption is one way, but another is Diffie-Hellman key exchange. This is part 3 in our Cryptography 101 series. Check out the playlist here for parts 1 & 2: https://www.youtube.com/watch?v=NOs34_-eREk&list=PLa6IE8XPP_gmVt-Q4ldHi56mYsBuOg2Qw Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Topology vs. “a” Topology https://www.youtube.com/watch?v=tdOaMOcxY7U&t=13s Symmetric single-key encryption schemes have become the workhorses of secure communication for a good reason. They’re fast and practically bulletproof… once two parties like Alice and Bob have a single shared key in hand. And that’s the challenge -- they can’t use symmetric key encryption to share the original symmetric key, so how do they get started? Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!
Views: 51437 PBS Infinite Series
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
 
01:14:53
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An elliptic curve, say E, can be represented by points on a cubic equation as below with certain A, B ∈ Q: y2 = x3 + Ax +B A Theorem of Mordell says that that E(Q), the set of rational points of E, is a finitely generated abelian group, and thus, E(Q) = Zr ⊕ T, for some non-negative integer r and a finite group T. Here, r is called the algebraic rank of E. The Birch and Swinnerton-Dyer conjecture relates the algebraic rank of E to the value of the L-function, L(E, s), attached to E at s = 1. Further theoretical understanding, corroborated by computations lead to a stronger version of the BSD conjecture. This refined version of the BSD conjecture provides a very precise formula for the leading term of L(E, s) at s = 1, the coefficient of (s − 1)r, in terms of various arithmetical data attached to E. Thus, the computational side of the BSD conjecture goes hand in hand with the advanced concepts in the theory of Elliptic curves. In this program, the computational aspects of the BSD conjecture with various illustrative examples, as well as p-adic L-functions, which are the p-adic analogues of the L-functions and other theoretical aspects which are important for the BSD conjecture will be discussed. CONTACT US: [email protected] PROGRAM LINK: https://www.icts.res.in/program/bsdtc2016
Diffie hellman key exchange - Primitive root - Cryptography lecture series
 
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In this lecture series, you will be learning about cryptography basic concepts and examples related to it. Diffie hellman key exchange - Primitive root
Views: 575 Eezytutorials
Special Class - Strategy to Crack Arithmetic with Practice Questions for CAT 2018 - Bharat Gupta
 
01:04:58
Follow Bharat Gupta on Unacademy here: https://unacademy.com/user/Bharat_gupta?utm_source=Youtube_Main_SpecialClass&utm_medium=BharatGupta_21_09_18&utm_campaign=BharatGupta For more Special Classes click here: https://unacademy.com/plus?utm_source=Youtube_Main_SpecialClass&utm_medium=Youtube_21_09_18&utm_campaign=YoutubeQRbjSC Strategy to Crack Arithmetic with Practice Questions for CAT 2018: In this course, Bharat Sir, (20 years teaching experience) will conduct a Revision course covering the most important topics of Strategy to Crack Arithmetic with Practice Questions and explain topics with his unique shortcut trick and option elimination approach. Target audience comprises of primarily CAT 2018 and other MBA Exams aspirants. The course will be conducted in English and the notes and practice sheet will also be provided in English. You can go to the Plus tab on Unacademy app or website at 12 noon every day to register for special classes conducted by Top Educators of Unacademy. Download the Unacademy Learning App here: Android: https://goo.gl/02OhYI iOS: https://goo.gl/efbytP Download the Unacademy Educator App here: Android: https://goo.gl/H4LGHE iOS: https://goo.gl/1FkFHp Do Subscribe and be a part of the community for more such lessons here: https://goo.gl/gycFVs
Views: 1445 Unacademy
Victor Rotger -- Elliptic curves and the Birch and Swinnerton-Dyer conjecture Part 1
 
01:10:10
Это видео создано с помощью видеоредактора YouTube (http://www.youtube.com/editor)
Views: 623 Mathematics at HSE
Minimal Discriminants and Minimal Weiestrass Forms For Elliptic Curves
 
36:03
This goes over the basic invariants I'm going to need for Elliptic curves for Szpiro's Conjecture.
Primitive Roots
 
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This video shows you the method to look for the primitive roots which are useful in to be used in cryptosystem of Discrete Logarithm.
Views: 28529 Steven Wong
Matteo Longo: Half weight modular forms and rational points on elliptic curves
 
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Let E be an elliptic curve, defined over the field of rational numbers, of conductor Np, where N is a positive integer and p is a prime which does not divide N. Let f be the weight 2 newform attached to E. We consider the Hida family passing through f. One can lift each classical form in the Hida family to a half-weight modular forms, by means of a generalized Kohnen-Shintani correspondence (Baruch-Mao). The resulting Fourier coefficients can be p-adically interpolated by rigid analytic functions defined over the weight space. Extending a previous work by Darmon-Tornaria, I will propose a relation between the coefficients of this formal series and certain global points on the elliptic curve E. This is a work in progress with Zhengyu Mao. The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (4.2.2014)
Barry Mazur - Logic, Elliptic curves, and Diophantine stability
 
59:42
This is the third lecture of the 2014 Minerva Lecture series at the Princeton University Mathematics Department. October 17, 2014 An introduction to aspects of mathematical logic and the arithmetic of elliptic curves that make these branches of mathematics inspiring to each other. Specifically: algebraic curves - other than the projective line - over number fields tend to acquire no new rational points over many extension fields. This feature (which I call 'diophantine stability') makes elliptic curves, in particular, useful as vehicles to establish diophantine unsolvability for many large rings. To repay the debt, mathematical logic offers consequences to the arithmetic of elliptic curves over decidable rings. I will also discuss new results about diophantine stability.