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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: 30484 Randell Heyman
Mapping elliptic curve over finite field
 
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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
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, Cryptography and Computation
 
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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
Rational Points over Finite Field Part_II
 
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Elliptic Curve Cryptography
Views: 1323 Israel Reyes
CTNT 2018 - "Elliptic curves over finite fields" (Lecture 1) by Erik Wallace
 
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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
José Felipe Voloch: Generators of elliptic curves over finite fields
 
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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
RNT2.1.1. Finite Fields of Orders 4 and 8
 
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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
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields
 
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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 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
Bitcoin 101   Elliptic Curve Cryptography   Part 4   Generating the Public Key in Python
 
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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
The Math Behind Bitcoin - Finite Fields
 
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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
Mathematics Of Cryptography | Lecture 4 - Ring & Field | CRNS | Cryptography Basics
 
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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
Martijn Grooten - Elliptic Curve Cryptography for those who are afraid of maths
 
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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
Point addition on elliptic curve
 
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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
Lecture 16: Introduction to Elliptic Curves by Christof Paar
 
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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 :)
A Look Into Elliptic Curve Cryptography (ECC)
 
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A talk about the basics of Elliptic Curve Cryptography (ECC), its use and application today, strengths and weaknesses.
Views: 21132 mrdoctorprofessorsir
elliptic curve addition
 
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Views: 1701 Jeff Suzuki
Lecture 17: Elliptic Curve Cryptography (ECC) by Christof Paar
 
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For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
Elliptic curve cryptography
 
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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 Curve Cryptography (ECC) Parameters and Types: secp256k1, Curve 25519, and NIST
 
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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
 
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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
Mod-01 Lec-10 Computations in Finite Fields
 
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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
Pairings in Cryptography
 
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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
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: 11748 nptelhrd
Elliptic Curve Cryptography Authentication by NXP Semiconductors
 
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NXP Semiconductors introduces A1006 Secure Authenticator, using ECC.
Views: 1032 Interface Chips
EC_ rational_point_part_I.m4v
 
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Rational Points over a Finite Field
Views: 910 Israel Reyes
Elliptic Curve ElGamal Cryptosystem
 
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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
Rational curves on elliptic surfaces - Douglas Ulmer
 
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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
Elliptic Curve Cryptography (EEC) -- Nick Gonella
 
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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
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: 28350 nptelhrd
Elliptic Curve Integrated Encryption Scheme (ECIES)
 
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https://asecuritysite.com/encryption/ecc3
Views: 400 Bill Buchanan OBE
Doubling a Point (Adding a point to itself)
 
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Elliptic Curve Arithmetic
Views: 2712 Israel Reyes
Elliptic Curve Cryptography, A very brief and superficial introduction
 
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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
Igor Shparlinski: Group structures of elliptic curves #3
 
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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 21, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
CS 463/680: Finite Field Arithmetic
 
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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
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)
Elliptic curve cryptography for SoC security - Project presentation
 
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Students - Marincas Maria, Lapusteanu Andrei Coordinating teacher - Stanciu Alexandra
Views: 234 Andrei Lapusteanu
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: 235 Trustica
A Mathematica Package for Elliptic Curves
 
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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