Search results “Finite fields in elliptic curve cryptography example”

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

Views: 30484
Randell Heyman

Mapping smooth elliptic curve in simple Weierstrass form over a prime finite field and then discarding all but rational points. You can find the accompanying article at https://trustica.cz/en/2018/03/01/elliptic-curves-over-finite-fields/

Views: 662
Trustica

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

Views: 101319
Introduction to Cryptography by Christof Paar

Views: 2313
Internetwork Security

Much of the research in number theory, like mathematics as a whole, has been inspired by hard problems which are easy to state. A famous example is 'Fermat's Last Theorem'. Starting in the 1970's number theoretic problems have been suggested as the basis for cryptosystems, such as RSA and Diffie-Hellman. In 1985 Koblitz and Miller independently suggested that the discrete logarithm problem on elliptic curves might be more secure than the 'conventional' discrete logarithm on multiplicative groups of finite fields. Since then it has inspired a great deal of research in number theory and geometry in an attempt to understand its security. I'll give a brief historical tour concerning the elliptic curve discrete logarithm problem, and the closely connected Weil Pairing algorithm.

Views: 991
Microsoft Research

This is lecture 1 of a mini-course on "Elliptic curves over finite fields", taught by Erik Wallace, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

Views: 126
UConn Mathematics

Ring Theory: As an application of maximal ideals and residue fields, we give explicit constructions of fields with 4 and 8 elements. A key step is to find irreducible polynomials (quadratic and cubic).

Views: 7678
MathDoctorBob

Views: 1385
Jeff Suzuki

Vídeo original: https://youtu.be/iB3HcPgm_FI
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/blackboard1...
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/1JryT...
Here's the private key we use at the end:
42F615A574E9CEB29E1D5BD0FDE55553775A6AF0663D569D0A2E45902E4339DB
Public Address on Blockchain.info
https://blockchain.info/address/16iTd...
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: 5315
Fabio Carpi

This is episode one of the Math Behind Bitcoin. In an effort to understand the math behind bitcoin, I try to explain it to you guys. If there are any mistakes or suggestions, please put it in the comment section below. Thanks!
Resources
- https://www.coindesk.com/math-behind-bitcoin/
- https://eng.paxos.com/blockchain-101-foundational-math
- Mastering Bitcoin by Andreas Antonopoulos
- https://www.cryptocoinsnews.com/explaining-the-math-behind-bitcoin/
- https://en.wikipedia.org/wiki/Finite_field

Views: 896
Kevin Su

In this youtube channel "gate hack" we are going to teach you the basic concepts of Cryptography and Network Security.
In this lecture we are teaching about Ring and Field.

Views: 2493
Quick Trixx

Elliptic Curve Cryptography (ECC) is hot. Far better scalable than traditional encryption, more and more data and networks are being protected using ECC. Not many people know the gory details of ECC though, which given its increasing prevalence is a very bad thing. In this presentation I will turn all members of the audience into ECC experts who will be able to implement the relevant algorithms and also audit existing implementations to find weaknesses or backdoors. Actually, I won't. To fully understand ECC to a point where you could use it in practice, you would need to spend years inside university lecture rooms to study number theory, geometry and software engineering. And then you can probably still be fooled by a backdoored implementation. What I will do, however, is explain the basics of ECC. I'll skip over the gory maths (it will help if you can add up, but that's about the extent of it) and explain how this funny thing referred to as "point addition on curves" can be used to exchange a secret code between two entities over a public connection. I will also explain how the infamous backdoor in Dual_EC_DRGB (a random number generator that uses the same kind of maths) worked. At the end of the presentation, you'll still not be able to find such backdoors yourselves and you probably realise you never will. But you will be able to understand articles about ECC a little better. And, hopefully, you will be convinced it is important that we educate more people to become ECC-experts.

Views: 18911
Security BSides London

Visualization of point addition on elliptic curve in simple Weierstrass form over real numbers and finite field. The underlying math is explained in next article of our elliptic curves' series: https://trustica.cz/en/2018/03/15/elliptic-curves-point-addition/

Views: 182
Trustica

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
(Don't worry, I start in German but at minute 2:00 I am switiching to English for the remainder of the lecture :)

Views: 44721
Introduction to Cryptography by Christof Paar

A talk about the basics of Elliptic Curve Cryptography (ECC), its use and application today, strengths and weaknesses.

Views: 21132
mrdoctorprofessorsir

Views: 1701
Jeff Suzuki

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

Views: 25788
Introduction to Cryptography by Christof Paar

Elliptic curve cryptography
Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC requires smaller keys compared to non-ECC cryptography (based on plain Galois fields) to provide equivalent security.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=UTJ2jxuyL7g

Views: 409
WikiAudio

Elliptic Curves: https://asecuritysite.com/comms/plot05
Key gen: https://asecuritysite.com/encryption/ecc
EC Types: https://asecuritysite.com/encryption/ecdh3

Views: 389
Bill Buchanan OBE

Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC cryptography is the same level of security provided by keys of smaller size.
Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 2462
Audiopedia

Views: 799
Harpreet Bedi

Coding Theory by Dr. Andrew Thangaraj, Department of Electronics & Communication Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 7179
nptelhrd

Dan Boneh, Stanford University
Historical Papers in Cryptography Seminar Series
http://simons.berkeley.edu/crypto2015/historical-papers-seminar-series/Dan-Boneh-2015-07-13

Views: 9509
Simons Institute

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: 11748
nptelhrd

NXP Semiconductors introduces A1006 Secure Authenticator, using ECC.

Views: 1032
Interface Chips

Views: 2191
Internetwork Security

In this video I primarily do through the Elliptic Curve ElGamal crytposystem (Bob's variables/computations, Alice's variables/computations, what is sent, and how it is decrypted by Bob). In addition, I go over the basics of elliptic curves such as their advantages and how they are written.
Digital Signatures - ElGamal: https://www.youtube.com/watch?v=Jo3wHnIH4y832,rpd=4,rpg=7,rpgr=0,rpm=t,rpr=d,rps=7
Reference:
Trappe, W., & Washington, L. (2006). Introduction to cryptography: With coding theory (2nd ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.

Views: 8483
Theoretically

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: 432
Institute for Advanced Study

Nick Gonella, officer of White Hat, talks about Elliptic Curve Cryptography (ECC), a cutting edge encryption method that is taking the cryptography world by storm. Learn the machinery behind this new technology and how it's being used today.
Recommended read on ECC: https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/

Views: 5527
White Hat Cal Poly

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: 28350
nptelhrd

https://asecuritysite.com/encryption/ecc3

Views: 400
Bill Buchanan OBE

by Ron Garret
Bay Area Lisp and Scheme Meetup
http://balisp.org/
Sat 30 Apr 2016
Hacker Dojo
Mountain View, CA
Abstract
This will be a beginner’s introduction to elliptic curve cryptography using Lisp as a pedagogical tool. Cryptography generally relies heavily on modular arithmetic. Lisp’s ability to change the language syntax and define generic functions provides opportunities to implement modular arithmetic operations much more cleanly than other languages.
Video notes
The audio for the introduction and for the questions from the audience is hard to hear. I will try to improve on that in the next batch of talks. — Arthur

Views: 2931
Arthur Gleckler

Arithmetic in finite integer fields.
Course lecture for CS 463/680, Cryptography and Data Security
https://www.cs.uaf.edu/courses/cs463/2015-spring/

Views: 192
Orion Lawlor

Views: 953
Jeff Suzuki

Students - Marincas Maria, Lapusteanu Andrei
Coordinating teacher - Stanciu Alexandra

Views: 234
Andrei Lapusteanu

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: 235
Trustica

For the latest information, please visit:
http://www.wolfram.com
Speaker: John McGee
Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and more.

Views: 1159
Wolfram

© 2018 International currency exchange

Better Than Any Blockchain. Built on the most advanced blockchain technology that is scalable, secure and interoperates different networks. Growing Global Network. Banks, payment providers and digital asset exchanges process and provide liquidity for payments on RippleNet, creating new, competitive cross-border payments services for their customers. Buy Ripple. How to buy Ripple. The payment is easily completed online in minutes by POLi Payments a business from Australia Post and after payment is complete the coins will be sent to your CoinSpot online wallet immediately. Ripple is a technology that acts as both a cryptocurrency and a digital payment network for financial transactions. Ripple was released in 2012 and co-founded by Chris Larsen and Jed McCaleb. The coin for the cryptocurrency is premined and labeled XRP. Ripple Swell. Digital Copy. Bitcoin Dust.