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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: 181601 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: 55663 CSBreakdown
Elliptic Curve Cryptography Tutorial - Understanding ECC through the Diffie-Hellman Key Exchange
 
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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 build off of the Diffie-Hellman encryption scheme and show how we can change the Diffie-Hellman procedure with elliptic curve equations. Watch this video to learn: - The basics of Elliptic Curve Cryptography - Why Elliptic Curve Cryptography is an important trend - A comparison between Elliptic Curve Cryptography and the Diffie-Hellman Key Exchange
Views: 24561 Fullstack Academy
Elliptic Curve Point Addition
 
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This was for the MAO Math Presentation Competition. I won! :D
Views: 32737 Riverninj4
Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
 
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For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
Elliptic Curves - Computerphile
 
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Just what are elliptic curves and why use a graph shape in cryptography? Dr Mike Pound explains. Mike's myriad Diffie-Hellman videos: https://www.youtube.com/playlist?list=PLzH6n4zXuckpoaxDKOOV26yhgoY2S-xYg https://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: https://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Views: 178218 Computerphile
Elliptic Integrals and cubic curves
 
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Elliptic integrals arise naturally in computing arc lengths of ellipses. In this video, we re-interpret them as integrals on cubic curves. We then show how the group structure on the cubic curve gives a wonderful formula regarding elliptic integrals called the addition law.
Views: 4611 DanielChanMaths
The Beauty of Elliptic Curves
 
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Talk at the MathSoc at UCT in Cape Town, October 26, 2017.
Views: 1657 Linda Frey
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: 31175 nptelhrd
Elliptic Curve Cryptography (ECC) - Public Key Cryptography w/ JAVA   (tutorial 08)
 
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Website + download source code @ http://www.zaneacademy.com | derive equations For point addition & point doubling @ https://youtu.be/ImEIf-9LQwg | Elliptic Curve Digital Signature Algorithm (ECDSA) - Public Key Cryptography w/ JAVA (tutorial 10) @ https://youtu.be/Kxt8bXFK6zg 00:05 demo prebuilt version of the application 01:05 find all points that satisfy elliptic curve equation 03:05 show cyclic behavior of a generator point in a small group 04:05 use double and add algorithm for fast point hopping 04:45 quick intro to elliptic curves 05:20 singular versus nonsingular elliptic curves 06:00 why use elliptic curve in cryptography 09:55 equations for elliptic curve point addition and doubling 12:02 what is a field 13:35 elliptic curve group operations 14:02 associativity proof for elliptic curve point addition 15:30 elliptic curve over prime fields 16:35 code the application 19:46 check if curve to be instantiated is singular 24:06 implement point addition and doubling 25:59 find all points that satisfy elliptic curve equation 28:00 check if 2 points are inverse of each other 29:15 explain elliptic curve order, subgroup size n, and cofactor h 32:53 implement double and add algorithm 35:09 test run the application 40:20 what does 'Points on elliptic curve + O have cyclic subgroups' mean 40:45 when do all points on an elliptic curve form a cyclic group
Views: 324 zaneacademy
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: 13611 nptelhrd
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: 13079 Fullstack Academy
Defn Elliptic Curve
 
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Views: 2164 Harpreet Bedi
Elliptic Curves: Facts, Conjectures and Applications
 
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Elliptic curves E can be given by plane projective cubic curves and so seem to be very simple objects. A first hint for more structure is that there is an algebraic addition law for the rational points. In fact, there is a natural isomorphism of E with its Jacobian variety, and so E is at the same time a curve of low degree and an abelian variety of smallest possible dimension. This is the reason for a very rich and deep theory behind making elliptic curves to ideal objects for both theoretical and experimental investigations, always with a strong algorithmic aspect. As outcome we find an abundance of key conjectures of arithmetic geometry inspired (and even proven) by elliptic curves. It will be the purpose of the talk to explain some of these conjectures and results and, as important and rather astonishing side effect, state why these properties of elliptic curves make them to a most efficient and secure tool for public key crypto systems based on discrete logarithms.
Views: 435 Microsoft Research
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: 3472 UConn Mathematics
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: 36058 Learn Math Tutorials
Barry Mazur -  Logic, Elliptic curves, and Diophantine stability
 
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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: 3806 princetonmathematics
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: 1131 MathSciResInst
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: 924 Juliette Bruce
Elliptic curves and modular forms
 
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Help me keep making videos: http://paypal.me/mlbakermath
Views: 12506 mlbaker
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: 22495 CRI
Elliptic curves with complex multiplication: history and perspectives
 
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Elliptic curves with complex multiplication: history and perspectives The theory of complex multiplication on curves is very old and rich, going back at least to Klein. Since then, many authors have been developing the theory, in parallel with quite a heavy load of computations and formulas (by hand!). Soon after Schoof's 1985 major article, reduction of curves with complex multiplication over finite fields were used to prove the primality of special or general numbers, and the corresponding algorithms are still in use today. As a result, this led to the emergence of the so-called CM-method to build curves with prescribed properties. The talk will present some parts of this history, concentrating on explicit computations and applications of the CM theory to some old and new problems.
Views: 616 Microsoft Research
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: 234 MathSciResInst
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: 1211 TAUVOD
Massimo Bertolini: Beilinson Flach elements and the arithmetic of elliptic curves
 
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This talk explains a p-adic Beilinson formula relating the p-adic L-function associated to the Rankin convolution of two cusp forms to so-called Beilinson-Flach elements. It will then describe some applications to new cases of the Birch and Swinnerton-Dyer conjecture for elliptic curves. This is a report on work in progress with Henri Darmon and Victor Rotger.(6.2.2014)
Barry Mazur - Logic, Elliptic curves, and Diophantine stability
 
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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.
Solving Discrete Logarithm Problems: Baby-step, Giant-step
 
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Code: http://asecuritysite.com/encryption/baby
Views: 972 Bill Buchanan OBE
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: 40054 Randell Heyman
Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function & Euler's Theorem
 
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For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
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: 1337 Gideon Samid
RH and BSD -- counting primes and points on elliptic curves
 
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http://wstein.org/talks/2017-02-10-wing-rh_and_bsd/
Views: 332 William Stein
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
 
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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
Fermet Theorem and Eulers theorem - Cryptography lecture series
 
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In this lecture series, you will be learning about cryptography basic concepts and examples related to it. Detailed explanation of Fermet Theorem and Eulers theorem with example.
Views: 20319 Eezytutorials
RSA Algorithm Solved Example | Information and Cyber security | Encryption
 
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RSA Algorithm example explained. Subscribe to the channel for more videos in ICS. Notes of RSA can be referred for free https://drive.google.com/open?id=0B45NQkm1qd_3N1hlMlY3SVhvUzhWNXhlNk1teDF6OGNUcWdn
Views: 79 Dexter Labs
Igor Shparlinski: Group structures of elliptic curves #1
 
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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 We give a survey of results which address the following generic question: How does a random elliptic curve over a finite field look like. This question has a rich variety of specfic interpretations, which depend on how one defines a random curve and what properties which are of interest. The former may include randomisation of the coefficients of the Weierstrass equation or the prime power defining the field, or both. The latter may include studying the group structure, arithmetic structure of the number of points (primality, smoothness, etc.) and certain divisibility conditions. These questions are related to such celebrated problems as Lang-Trotter and Sato-Tate conjectures. More recently the interest to these questions was re-fueled by the needs of pairing based cryptography. In a series of talks we will describe the state of art in some of these directions, demonstrate the richness of underlying mathematics and pose some open questions. Recording during the thematic meeting: "Frobenius distribution on curves" the February 18, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
Discrete Logarithm Problem
 
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Discrete Logarithm Problem - modular arithmetic
Views: 48988 Art of the Problem
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: 2491 DanielChanMaths
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: 110 wolframmathematica
Number Theory: Finite Fields and Cyclic Groups | Part 6 Cryptography Crashcourse
 
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Crashcourse Playlist: https://www.youtube.com/playlist?list=PLjwO-iVuY1v1kxWtOsqKEuXDB4ijXSHIk 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: 1973 Dr. Julian Hosp
Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures
 
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Florian Sprung 151 Thayer Street Box #1917 Providence, RI 02912 Email: [email protected] Manuscript Number: JNT-D-10-00057R1
Views: 3871 JournalNumberTheory
Elliptic curves: point at infinity
 
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When summing or doubling points on an elliptic curve in simple Weierstrass form, sometimes, the straight line used to find the negative of the result does not cross such curve elsewhere. Then we say the result is the point at infinity and you can see a demonstration of this phenomenon in this video - both over the set of real numbers and over a finite field GF(23). More information is in the article: https://trustica.cz/2018/03/29/elliptic-curves-point-at-infinity/
Views: 591 Trustica