Search results “Finite fields in elliptic curve cryptography implementation”
Elliptic Curve (ECC) with example - Cryptography lecture series
In this lecture series, you will be learning about cryptography basic concepts and examples related to it. Elliptic Curve (ECC) with example (ECC) with example.
Views: 26280 Eezytutorials
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: 762 UConn Mathematics
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
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: 1394 Microsoft Research
C# 6.0 Tutorial - Advanced - 62. How to Implement ECDsaCng Cryptography Implementation
Learn more free at my blog http://www.manuelradovanovic.com If you have any question please feel free to ask. Subscribe me on YouTube, please! Thank You!
Views: 493 Manuel Radovanovic
Software implementation of Koblitz curves over quadratic fields
Thomaz Oliveira and Julio López and Francisco Rodríguez-Henríquez, CHES 2016. See http://www.iacr.org/cryptodb/data/paper.php?pubkey=27854
Views: 155 TheIACR
Pairings on Elliptic Curves - Parameter Selection and Efficient Computation
This talk is about efficient pairing computation on elliptic curves. I will discuss particularly implementation-friendly curves, the use of the polynomial parameter representation to compute pairings on BN curves, and reasons to use affine coordinates for pairings at high security levels. This contains joint work with P. Barreto, G. Pereira, M. Simplício Jr, P. Schwabe, R. Niederhagen, K. Lauter, and P. Montgomery.
Views: 817 Microsoft Research
AES Encryption 2: AddRoundKey, SubBytes and ShiftRows
In this vid we'll fill out the bodies to three of the steps in AES. These three steps are AddRoundKey, SubBytes and ShiftRows. The remaining steps to AES are rather fiddly, MixColumns and ExpandKey, so we'll look at those separately. I've also taken the opportunity to introduce Galois fields for the AddRoundKey section. AddRoundKey is really just a matter of performing XOR, but it helps to understand Galois fields before we come to the MixColumns step. Link to the S_Box on Wikipedia: https://en.wikipedia.org/wiki/Rijndael_S-box Link to the Finite Field/Galois Field Wikipedia page: https://en.wikipedia.org/wiki/Finite_field Become a patron and support What's a Creel programming vids on Patreon: www.patreon.com/whatsacreel Play Intergalactic Memory for Free: http://apps.microsoft.com/windows/en-us/app/intergalactic-memory-free/92c1094c-32f5-4730-86f3-c43c46affe52 Full version of Intergalactic Memory: http://apps.microsoft.com/windows/app/intergalactic-memory/ae9457e6-dbc1-468b-93cb-39f80835f19a FaceBook: www.facebook.com/pages/WhatsaCreel/167732956665435
Views: 40818 What's a Creel?
Elliptic Curve Cryptography: Points on Curves
Outline: https://asecuritysite.com/encryption/ecc_points2
Views: 180 Bill Buchanan OBE
elliptic curve addition
Views: 2591 Jeff Suzuki
Rational Points over Finite Field Part_II
Elliptic Curve Cryptography
Views: 1354 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: 24802 mrdoctorprofessorsir
Endomorphisms, isogeny graphs, and moduli
I will present a retrospective of aspects of my thesis, in light of applications in the last 14 years since its birth. In particular, I will focus on explicit isogenies, moduli of elliptic curves and CM structure, the 'local' Galois module structures of l-torsion and l-isogeny graphs, and 'global' structure of action visa class groups and isogenies. The focus will be directed principally towards ordinary elliptic curves over finite fields, but I will discuss briefly the supersingular case and generalizations to higher dimension.
Views: 602 Microsoft Research
EC_ rational_point_part_I.m4v
Rational Points over a Finite Field
Views: 929 Israel Reyes
Doubling a Point (Adding a point to itself)
Elliptic Curve Arithmetic
Views: 3169 Israel Reyes
Recovering elliptic curves from their p-torsion - Benjamin Bakker
Benjamin Bakker New York University May 2, 2014 Given an elliptic curve EE over a field kk, its p-torsion EpEp gives a 2-dimensional representation of the Galois group GkGk over 𝔽pFp. The Frey-Mazur conjecture asserts that for k=ℚk=Q and p13p13, EE is in fact determined up to isogeny by the representation EpEp. In joint work with J. Tsimerman, we prove a version of the Frey-Mazur conjecture over geometric function fields: for a complex curve CC with function field kCkC, any two elliptic curves over kCkC with isomorphic pp-torsion representations are isogenous, provided pp is larger than a constant only depending on the gonality of CC. The proof involves understanding the hyperbolic geometry of a modular surface. For more videos, visit http://video.ias.edu
CTNT 2018 - "Elliptic curves over finite fields" (Lecture 2) by Erik Wallace
This is lecture 2 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: 127 UConn Mathematics
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: 13572 nptelhrd
CTNT 2018 - "Elliptic curves over finite fields" (Lecture 3) by Erik Wallace
This is lecture 3 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: 94 UConn Mathematics
Igor Shparlinski: Group structures of elliptic curves #1
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)
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: 26262 Security BSides London
Details of Elliptic Curve Cryptography | Part 9 Cryptography Crashcourse
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... ► Cryptocurrency Exchange: https://www.binance.com/?ref=11272739 ► Hardware Wallet: http://www.julianhosp.com/hardwallet ► Ruben's Trinkgeld Adressen: Bitcoin: 3MNWaot64Fr1gRGxv4YzHCKAcoYTLXKxbc Litecoin: MTaGwg5EhKooonoVjDktroiLqQF6Rvn8uE --------------- ► Completely NEW? What is Blockchain, Bitcoin and Co? Get this book from me: https://www.amazon.com/Cryptocurrenci... ► Join our Facebook group: https://www.facebook.com/groups/crypt... ► iTunes Podcast: https://itunes.apple.com/sg/podcast/t... ► 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: 2551 Dr. Julian Hosp
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 :)
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: 6263 Fabio Carpi
David Jao : Implementing Supersingular Isogeny Cryptography - Part 1
ECC 2018,19th November 2018,Day 1,Session 1,Talk 1 https://cy2sec.comm.eng.osaka-u.ac.jp/ecc2018/
Views: 163 Miyaji Lab
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: 11859 Simons Institute
Elliptic Curve Cryptography, A very brief and superficial introduction
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: 3664 Arthur Gleckler
Security Now 374: Elliptic Curve Crypto
Hosts: Steve Gibson with Leo Laporte UPEK fingerprint software, Oracle software patch, ECC, and more. Download or subscribe to this show at twit.tv/sn. We invite you to read, add to, and amend our show notes. You can submit a question to Security Now! at the GRC Feedback Page. For 16kpbs versions, transcripts, and note s (including fixes), visit Steve's site: grc.com, also the home of the best disk maintenance and recovery utility ever written Spinrite 6. Audio bandwidth is provided by Winamp, subscribe to TWiT and all your favorite podcasts with the ultimate media player, download it for free at Winamp.com. Running time: 1:23:41
Views: 2116 TWiT Netcast Network
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: 248 Trustica
Elliptic Curve Cryptography (ECC) - Public Key Cryptography w/ JAVA   (tutorial 08)
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: 316 zaneacademy
High-Performance Pipelined Architecture of Elliptic Curve Scalar Multiplication Over GF(2m)
High-Performance Pipelined Architecture of Elliptic Curve Scalar Multiplication Over GF(2m) To get this project in ONLINE or through TRAINING Sessions, Contact: JP INFOTECH, Old No.31, New No.86, 1st Floor, 1st Avenue, Ashok Pillar, Chennai -83.Landmark: Next to Kotak Mahendra Bank. Pondicherry Office: JP INFOTECH, #45, Kamaraj Salai,Thattanchavady, Puducherry -9.Landmark: Next to VVP Nagar Arch. Mobile: (0) 9952649690, Email: [email protected], web: www.jpinfotech.org, Blog: www.jpinfotech.blogspot.com This paper proposes an efficient pipelined architecture of elliptic curve scalar multiplication (ECSM) over GF(2m). The architecture uses a bit-parallel finite field (FF) multiplier accumulator (MAC) based on the Karatsuba–Ofman algorithm. The Montgomery ladder algorithm is modified for better sharing of execution paths. The data path in the architecture is well designed, so that the critical path contains few extra logic primitives apart from the FF MAC. In order to find the optimal number of pipeline stages, scheduling schemes with different pipeline stages are proposed and the ideal placement of pipeline registers is thoroughly analyzed. We implement ECSM over the five binary fields recommended by the National Institute of Standard and Technology on Xilinx Virtex-4 and Virtex-5 field-programmable gate arrays. The three-stage pipelined architecture is shown to have the best performance, which achieves a scalar multiplication over GF(2163) in 6.1µs using 7354 Slices on Virtex-4. Using Virtex-5, the scalar multiplication form=163, 233, 283, 409, and 571 can be achieved in 4.6, 7.9, 10.9, 19.4, and 36.5 µs, respectively, which are faster than previous results. The proposed architecture of this paper analysis the logic size, area and power consumption using Xilinx 14.2.
Lecture 17: Elliptic Curve Cryptography (ECC) by Christof Paar
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
Application of Elliptic Curves to 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: 10698 nptelhrd
Elliptic Curve Cryptography (EEC) - Nick Gonella
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: 6166 White Hat Cal Poly
The Math Behind Elliptic Curves in Koblitz Curves
Elliptic curve cryptography is the hottest topic in public key cryptography world. For example, bitcoin and blockchain is mainly based on elliptic curves. We can also do encryption / decryption, key exchange and digital signatures with elliptic curves. This video covers the proofs of addition laws for both point addition and doubling for Koblitz Curves introduced by Neal Koblitz. This curves mostly used in binary field studies. This is the preview video of Elliptic Curve Cryptography Masterclass online course. You can find the course content here: https://www.udemy.com/elliptic-curve-cryptography-masterclass/?couponCode=ECCMC-BLOG-201801 Documentation: https://sefiks.com/2016/03/13/the-math-behind-elliptic-curves-over-binary-field/
Elliptic curve cryptography
If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 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: 584 WikiAudio
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: 10624 Theoretically
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: 2956 Audiopedia
An Introduction to 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: 31139 nptelhrd
ECC2012 - Deterministic elliptic curve primality proving for special sequences
Session M2: Primality Testing Session chair: Victor Miller Speaker: Alice Silverberg. Monday, October 29th, 2012. 18:00 - 19:00
Views: 383 ECC2012staff
reedemed systolic finite field multiplier design for polynomial hardware implementation
G.JAYAPRIYA,REGISTER NO :113112431008,VEL TECH MULTITECH DR.RR & DR.SR ENGG COLLEGE. ABSTRACT : Our project is to provide area efficient and low complex multiplier for GF (2m) on all one polynomial.Multiplier designing is done for irreducible all one polynomial.A reducing technique is been used to reduce the registers in the systolic structure.Finally we are going to implement our multiplier in a RS encoder used in cryptographic application.Using FPGA we can find our proposed technique can provide less area complexity and low latency.
Elliptic Curve Method of Factorization, Section 10.6
Math 706, Section 10.6 Elliptic Curve Method of Factorization
Views: 501 Todd Cochrane