Search results “Elliptic curve cryptography arithmetic mean formula”

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: 157346
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: 51231
CSBreakdown

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

Views: 30058
Riverninj4

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: 29794
nptelhrd

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: 12678
nptelhrd

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

Views: 1057
Linda Frey

Examples solving congruences with discrete logarithms.

Views: 1473
Cathy Frey

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

Views: 388
Bill Buchanan OBE

Math 706 Section 10.5
Elliptic Curves as Abelian Groups

Views: 242
Todd Cochrane

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

Views: 35506
Randell Heyman

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: 21228
CRI

Math 706, Section 10.1
Introduction to Elliptic Curves

Views: 1606
Todd Cochrane

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

Views: 30886
Learn Math Tutorials

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

Views: 306
William Stein

Speaker: Alessandro Chiesa, ETH Zurich
'The First Greater Tel Aviv Area Symposium'
School of Computer Science
Tel-Aviv University,
13.11.14

Views: 1134
TAUVOD

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: 3666
princetonmathematics

I will discuss creating (conjectural) tables of elliptic curves over Q(ΓêÜ5) ordered by conductor up to the first curve of rank 2. We computed these curves by first computing weight (2,2) Hilbert modular forms over Q(ΓêÜ5) using an algorithm of Lassina Demb├⌐l├⌐. Using various methods we constructed the (conjecturally) corresponding elliptic curves. I will also discuss newer work towards partially extending these results to the first curve of rank 3. This is joint work with Jonathan Bober, Joanna Gaski, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Sebastian Pancratz, Ashwath Rabindranath, Paul Sharaba, Ari Shnidman, William Stein, and Christelle Vincent.

Views: 232
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: 2955
UConn Mathematics

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: 667
Hausdorff Center for Mathematics

Views: 3121
Internetwork Security

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: 517
Microsoft Research

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: 898
Juliette Bruce

A Joint IAS/Princeton University Number Theory Seminar
Topic: Rational curves on elliptic surfaces
Speaker: Douglas Ulmer
Affiliation: Georgia Institute of Technology
Date: Thursday, May 5
Given a non-isotrivial elliptic curve EE over K=𝔽qt K=Fqt, there is always a finite extension LL of KK which is itself a rational function field such that ELEL has large rank. The situation is completely different over complex function fields: For "most" EE over K=ℂtK=Ct, the rank ELEL is zero for any rational function field L=ℂu L=Cu. The yoga that suggests this theorem leads to other remarkable statements about rational curves on surfaces generalizing a conjecture of Lang.
For more videos, visit http://video.ias.edu

Views: 473
Institute for Advanced Study

Views: 4397
Internetwork Security

“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: 719
UConn 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: 808
princetonmathematics

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

Views: 232
MathSciResInst

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: 3828
DanielChanMaths

MIT 6.046J Design and Analysis of Algorithms, Spring 2015
View the complete course: http://ocw.mit.edu/6-046JS15
Instructor: Srinivas Devadas
In this lecture, Professor Devadas covers the basics of cryptography, including desirable properties of cryptographic functions, and their applications to security.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 68986
MIT OpenCourseWare

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: 26588
Steven Wong

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: 1288
Gideon Samid

Joint IAS/Princeton University Number Theory Seminar
Topic: Elliptic curves of rank two and generalised Kato classes
Speaker: Francesc Castella
Affiliation: Princeton University
Date: October 24, 2017
For more videos, please visit http://video.ias.edu

Views: 467
Institute for Advanced Study

Explaining how modern cryptography is built on the 1936 Turing Machine which leads to the idea of 'hardness' -- a computation that can be done, but is hard to do. This 'hardness' underlies everything in modern cryptography. Alas, hardness is not guaranteed and every one of our popular ciphers today is vulnerable to an attacker smarter than its designer. Also Turing Machines are about to give way to Quantum computers, which will do to 'modern cryptography' what modern cryptography did to 'Pre-Turing Cryptography'. Cryptography of tomorrow will be user-centric, and randomness-reliant. First in a series.

Views: 283
Gideon Samid

Views: 2429
Internetwork Security

The history behind public key cryptography & the Diffie-Hellman key exchange algorithm.
We also have a video on RSA here: https://www.youtube.com/watch?v=wXB-V_Keiu8

Views: 613241
Art of the Problem

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: 129725
Khan Academy Labs

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)

Views: 1269
Hausdorff Center for Mathematics

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: 390
Microsoft Research

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
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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: 48146
PBS Infinite Series

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

Views: 3822
JournalNumberTheory

lecture notes: https://drive.google.com/file/d/1VLucSK53-iLrVUbPAanNZ6Lb7nAAgaQ1/view?usp=sharing
Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"
survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Göttingen. Intended for graduate students and recent Ph.D.'s, this volume will introduce readers to modern techniques and outstanding conjectures at the interface of number theory and algebraic geometry.
The main focus is rational points on algebraic varieties over non-algebraically closed fields. Do they exist? If not, can this be proven efficiently and algorithmically? When rational points do exist, are they finite in number and can they be found effectively? When there are infinitely many rational points, how are they distributed?
For curves, a cohesive theory addressing these questions has emerged in the last few decades. Highlights include Faltings' finiteness theorem and Wiles's proof of Fermat's Last Theorem. Key techniques are drawn from the theory of elliptic curves, including modular curves and parametrizations, Heegner points, and heights.
The arithmetic of higher-dimensional varieties is equally rich, offering a complex interplay of techniques including Shimura varieties, the minimal model program, moduli spaces of curves and maps, deformation theory, Galois cohomology, harmonic analysis, and automorphic functions. However, many foundational questions about the structure of rational points remain open, and research tends to focus on properties of specific classes of varieties.
Contents
About the cover: Rational points on a K3 surface
Noam Elkies
Curves
Rational points on curves
Henri Darmon
Non-abelian descent and the generalized Fermat equation
Hugo Chapdelaine
Merel's theorem on the boundedness of the torsion of elliptic curves
Marusia Rebolledo
Generalized Fermat equations
Pierre Charollois
Heegner points and Sylvester's conjecture
Samit Dasgupta and John Voight
Shimura curve computations
John Voight
Computing Heegner points arising from Shimura curve parametrizations
Matthew Greenberg
The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points
Matthew Greenberg
Lectures on modular symbolsLectures on modular symbols
Yuri I. Manin
Surfaces
Rational surfaces over nonclosed fields
Brendan Hassett
Non-abelian descent
David Harari
Mordell-Weil Problem for Cubic Surfaces, Numerical Evidence
Bogdan Vioreanu
Higher-dimensional varieties
Algebraic varieties with many rational points
Yuri Tschinkel
Birational geometry for number theorists
Dan Abramovich
Arithmetic over function fields
Jason Starr
Galois + Equidistribution=Manin-Mumford
Nicolas Ratazzi and Emmanuel Ullmo
The Andre-Oort conjecture for products of modular curves
Emmanuel Ullmo and Andrei Yafaev
Moduli of abelian varieties and p-divisible groups
Ching-Li Chai and Frans Oort
Cartier isomorphism and Hodge Theory in the non-commutative case
Dmitry Kaledin
http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/

Views: 452
Graduate Mathematics

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

Views: 1523
Udacity

ICTP has awarded the 2018 Ramanujan Prize for Young Mathematicians from Developing Countries to Ritabrata Munshi of the Indian Statistical Institute, Kolkata, India and the Tata Institute of Fundamental Research, Mumbai, India. The prize is in recognition of Munshi's outstanding work in number theory, a branch of pure mathematics that studies properties of integers, or numbers that do not have a fractional part. In particular, the Prize cites Munshi's profound contributions to the study of analytic properties of L-functions and automorphic forms. The focus of his work is central to modern number theory, one that links arithmetic geometry, representation theory and complex analysis in many profound ways. Munshi has developed an ingenious method which produced a breakthrough in the field, going significantly beyond what was known before. ICTP administers the Ramanujan Prize jointly with the Department of Science and Technology (DST, Government of India), and the International Mathematical Union (IMU). The Prize Ceremony is scheduled to take place on Friday 9 November starting at 14.00 hrs. The programme will include a talk by Professor Munshi, a lecture by Professor Brian Conrey, and a special screening of the film "Salam - the first ..... Nobel Laureate" in conjunction with the "World Science Day for Peace and Development" (10 November 2018).

Views: 526
Int'l Centre for Theoretical Physics

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

Views: 2379
MathSciResInst

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© 2019 Public finance in theory and practice musgrave

Bring Your Own Encryption. Learn about customer-managed encryption, and why businesses should stay in control of their encrypted content in the cloud. Securing Business Information in the Cloud. Explore how a new generation of secure, enterprise cloud services mitigates security risks by centralizing documents in one platform. Design Thinking and Enterprise Security. How to Protect Content in the Age of Distributed Computing. Adapting security controls to protect sensitive content has proven difficult in the mobile workplace. Learn how you can secure your content and prevent data loss. Bridging The Cloud Encryption Gap. Learn how you can bridge the cloud encryption gap with customer-managed encryption keys. 10 Lessons from Tech Leaders on Digital Transformation. 4 Ways to Build Better Apps with Secure Content Services. 5 Counterintuitive Mistakes Made by Companies Going Digital. Learn how to make the right decisions upfront while building your digital business. Whitepapers. Explore the four key points you should consider when deciding between cloud versus hybrid for your business. The Future of Security.