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
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Elliptic Curve Cryptography(ECC) - GATE Computer Science - Unacademy

Views: 20848
Unacademy - GATE Preparation

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

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

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

This was for the MAO Math Presentation Competition. I won! :D

Views: 32737
Riverninj4

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com

Views: 117336
Introduction to Cryptography by Christof Paar

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 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

Views: 4334
Internetwork Security

Talk at the MathSoc at UCT in Cape Town, October 26, 2017.

Views: 1657
Linda Frey

Views: 4035
Internetwork Security

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

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

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

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

Views: 2164
Harpreet Bedi

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,” 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

In this tutorial, I demonstrate two different approaches to multiplying numbers in modular arithmetic.
Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm
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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

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

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
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

Views: 651
Graduate Mathematics

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

Help me keep making videos: http://paypal.me/mlbakermath

Views: 12506
mlbaker

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 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

This was a lecture given by Manjul Bhargava in the Introductory Workshop on Arithmetic Statistics at MSRI.

Views: 234
MathSciResInst

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

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)

Views: 722
Hausdorff Center for Mathematics

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.

Views: 829
princetonmathematics

Code: http://asecuritysite.com/encryption/baby

Views: 972
Bill Buchanan OBE

Solutions to some typical exam questions. See my other videos
https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.

Views: 40054
Randell Heyman

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com

Views: 82304
Introduction to Cryptography by Christof Paar

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

http://wstein.org/talks/2017-02-10-wing-rh_and_bsd/

Views: 332
William Stein

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 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

Discrete Logarithm Problem - modular arithmetic

Views: 48988
Art of the Problem

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

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

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...
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► Hardware Wallet: http://www.julianhosp.com/hardwallet
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Bitcoin: 3MNWaot64Fr1gRGxv4YzHCKAcoYTLXKxbc
Litecoin: MTaGwg5EhKooonoVjDktroiLqQF6Rvn8uE
---------------
► Completely NEW? What is Blockchain, Bitcoin and Co? Get this book from me: https://www.amazon.com/Cryptocurrenci...
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https://www.facebook.com/groups/crypt...
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► 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

Florian Sprung
151 Thayer Street
Box #1917
Providence, RI 02912
Email: [email protected]
Manuscript Number: JNT-D-10-00057R1

Views: 3871
JournalNumberTheory

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

Views: 1235
Jeff Suzuki