Search results “Finite fields in elliptic curve cryptography example”
Finite fields made easy
Solutions to some typical exam questions. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Views: 33025 Randell Heyman
Elliptic Curves, Cryptography and Computation
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: 1087 Microsoft Research
Mapping elliptic curve over finite field
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: 761 Trustica
Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
CTNT 2018 - "Elliptic curves over finite fields" (Lecture 1) by Erik Wallace
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: 207 UConn Mathematics
Galois Field Part 2
Multiplication and addition tables for GF(2^3), concept of generator in GF and operations using generator.
Views: 2419 DrVikasThada
Finite Fields
Views: 1081 Harpreet Bedi
Prime Fields Part 3
In this video we construct the prime fields.
Views: 1040 Ben1994
Rational Points over Finite Field Part_II
Elliptic Curve Cryptography
Views: 1334 Israel Reyes
Pairings in Cryptography
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: 10064 Simons Institute
Galois Fields Part 4
From the Paar Lectures on cryptography
Views: 947 Project Rhea
Elliptic Curve Cryptography(ECC) - GATE Computer Science
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
The Math Behind Bitcoin - Finite Fields
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: 997 Kevin Su
EC_ rational_point_part_I.m4v
Rational Points over a Finite Field
Views: 917 Israel Reyes
A Look Into Elliptic Curve Cryptography (ECC)
A talk about the basics of Elliptic Curve Cryptography (ECC), its use and application today, strengths and weaknesses.
Views: 21901 mrdoctorprofessorsir
Elliptic Curve Arithmetic and Bitcoin | Nathan Dalaklis
Bitcoin is a cryptocurrency that uses elliptic curves in the ECDSA. Since cryptosystems often require some form of arithmetic to encode and decode information we have a couple questions to ask; What are elliptic curves? And how can we do arithmetic on an elliptic curve? ________ Standards for Efficent Cryptography Group: http://www.secg.org Elliptic Curve Addition Modulo p Applet: https://cdn.rawgit.com/andreacorbellini/ecc/920b29a/interactive/modk-add.html ________ Last video: http://bit.ly/2Ms3VCr The CHALKboard: http://www.youtube.com/c/CHALKboard Find the CHALKboard on Facebook: http://bit.ly/CHALKboard _____________________ Interested in the person behind the camera? See what Nathan's up to on these platforms! Instagram: http://bit.ly/INSTAnatedlock Twitter: http://bit.ly/TWITTnatedlock _____________________ ---------------------------------- #CHALK #Bitcoin #EllipticCurves _____________________ ----------------------------------
Views: 101 CHALK
Breakthrough Junior Challange | Elliptic Curve Cryptography
Breakthrough Junior Challange | Elliptic Curve Cryptography. #breakthroughjuniorchallange
Views: 2893 Oliver Pelly
Elliptic curves: scalar multiplication
Explanation of the underlying math is in the accompanying article https://trustica.cz/2018/04/12/elliptic-curves-multiplication-by-scalar Although the stereographic projection of the projective plane is mostly useful for explaining the point at infinity, it can actually be used for depicting any operation over real numbers in the projective plane. This video shows the scalar multiplication of chosen point on an elliptic curve in simple Weierstrass form both using euclidean grid and stereographic projection onto a sphere.
Views: 397 Trustica
Lecture 17: Elliptic Curve Cryptography (ECC) by Christof Paar
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
Lecture 16: Introduction to Elliptic Curves by Christof Paar
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 :)
José Felipe Voloch: Generators of elliptic curves over finite fields
Abstract: We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin's conjecture for primitive roots. Recording during the thematic meeting: "Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects" the March 31, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent 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
Point addition on elliptic curve
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: 236 Trustica
Martijn Grooten - Elliptic Curve Cryptography for those who are afraid of maths
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: 20344 Security BSides London
Elliptic curves: scalar multiplication revisited
Scalar multiplication of points on elliptic curves over finite fields explained in article https://trustica.cz/2018/04/19/elliptic-curves-scalar-multiplication2/ is shown in this video. Subscribe to our channel and follow us on Twitter: https://twitter.com/trusticacz
Views: 128 Trustica
Implementation of Elliptic Curve Cryptography
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: 12160 nptelhrd
Elliptic Curve ElGamal Cryptosystem
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: 8855 Theoretically
Elliptic Curve Cryptography - Breakthrough Junior Challenge 2017
Views: 166 Miles05 Tullo04
Elliptic Curve Cryptography (ECC) Parameters and Types: secp256k1, Curve 25519, and NIST
Elliptic Curves: https://asecuritysite.com/comms/plot05 Key gen: https://asecuritysite.com/encryption/ecc EC Types: https://asecuritysite.com/encryption/ecdh3
Views: 537 Bill Buchanan OBE
elliptic curve addition
Views: 1847 Jeff Suzuki
Elliptic curve cryptography
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: 436 WikiAudio
Elliptic Curve Diffie Hellman
A short video I put together that describes the basics of the Elliptic Curve Diffie-Hellman protocol for key exchanges.
Views: 105797 Robert Pierce
Elliptic curve cryptography
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: 2609 Audiopedia
Elliptic Curve Automation
This shows how mechanical computers can be assembled to guide the joints of a two link serial chain to draw an elliptic cubic curve. This is an example of Kempe's universality theorem and is the work of Yang Liu.
Views: 800 mechanicaldesign101
Mathematics Of Cryptography | Lecture 4 - Ring & Field | CRNS | Cryptography Basics
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: 2964 Quick Trixx
Bitcoin 101   Elliptic Curve Cryptography   Part 4   Generating the Public Key in Python
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: 5551 Fabio Carpi
Doubling a Point (Adding a point to itself)
Elliptic Curve Arithmetic
Views: 2809 Israel Reyes
Dev++ 01-01-EN | Foundational Math, ECDSA and Transactions - Jimy Song
Jimmy Song explains the basics of cryptography that serves as a foundation for Bitcoin transactions. This course provides in-depth coverage of Elliptic Curve Digital Signature Algorithm (ECDSA), how ECDSA functions and how it is used to provide signing and verification of Bitcoin transactions. After covering the basics, Jimmy dives into and explains Bitcoin transaction data structure, including Bitcoin scripting opcodes - how these transactions are formed and interpreted by Bitcoin nodes. This session contains multiple sections at following timestamps: Finite Fields - https://youtu.be/e6voIwB-An4?t=4m50s Elliptic Curves - https://youtu.be/e6voIwB-An4?t=21m11s Elliptic Curves over Finite Fields - https://youtu.be/e6voIwB-An4?t=32m32s Mathematical Group - https://youtu.be/e6voIwB-An4?t=37m59s Bitcoin Addresses - https://youtu.be/e6voIwB-An4?t=50m08s ECDSA - https://youtu.be/e6voIwB-An4?t=57m42s Bitcoin Transactions - https://youtu.be/e6voIwB-An4?t=1h10m14s Bitcoin Scripts - https://youtu.be/e6voIwB-An4?t=1h17m27s Transaction Validation - https://youtu.be/e6voIwB-An4?t=1h25m Pay to Script Hash - https://youtu.be/e6voIwB-An4?t=1h29m27s To complete tasks in this course, you will need to setup the appropriate python environment as follows: Install python3, virtualenv, git $ git clone http://github.com/bitcoinedge/devplusplus $ cd devplusplus $ virtualenv -p python3 .venv $ . .venv/bin/activate $ pip install -r requirements.txt $ jupyter notebook Your browser should open up a jupyter notebook For additional information, please visit http://bitcoinedge.org
Views: 2298 Bitcoin Edge
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields
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 construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type GL(r) over finite rings (r≥3) instead of GL(2). In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational points/genus". The construction relies on higher-rank Drinfeld modular varieties and the supersingular trick and uses mainly rigid-analytic techniques. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 19, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

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