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: 21823 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: 558 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
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: 97 UConn Mathematics
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: 6050 Fabio Carpi
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: 1311 Microsoft Research
Elliptic Curve Integrated Encryption Scheme (ECIES)
Views: 1068 Bill Buchanan OBE
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: 74 UConn Mathematics
Martijn Grooten  -- Getting ahead of the elliptic curve
Elliptic curves are relatively obscure mathematical objects: you can get a PhD in maths without ever having come across them. Yet these objects play an important role in modern cryptography and as such are found in most HTTPS connections, in Bitcoin, and in a large number of other places. To really understand elliptic curve cryptography (ECC) to the point that you can implement algorithms, you'd have to study the maths behind it. This talk assumes that you haven't studied the maths, but just want to understand what ECC is about, how is works and how it is implemented. It will discuss how 'point addition' works and how the Elliptic Curve Diffie-Hellman algorithm is used, for example in HTTPS - and how you can find it using Wireshark. It will explain how to use elliptic curve for digital signatures and why you don't want to be like Sony when it comes to implementing them. It will discuss how ECC was used in an infamous random number generator and, finally, will take a brief look at the use of elliptic curves in post-quantum algorithms. The goal of this talk is to keep things simple and understandable and no knowledge of maths is assumed. The talk won't make you an expert on ECC -- that would take years of studying. But it might help you understand the context a bit better when you come across them in your research. And hopefully it will also be a little bit fun. -- Martijn Grooten is a lapsed mathematician who by chance ended up working in security - and loved it. He's spend more than a decade testing security software but his interest in security is broad and he has a weak spot for cryptography. He currently is Editor of Virus Bulletin.
Views: 83 NorthSec
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: 521 WikiAudio
Elliptic Curve Cayley Diagram in 3D (Ubigraph)
Used SAGE and Ubigraph. This is a group isomorphic to Z/26 + Z/26 of points on Elliptic Curve defined by y^2 = x^3 + 673*x over Finite Field of size 677 Ubigraph's layout can't seem to sort out a perfect torus in this diagram, but the group structure says that's what it should be. There are 676 points total, including two small torsion E[r], r=13 suitable for Weil pairing which hopefully will be in a future video.
Views: 7872 Andrew L
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: 24173 Security BSides London
Rational Points over Finite Field Part_II
Elliptic Curve Cryptography
Views: 1348 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: 23859 mrdoctorprofessorsir
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: 149 TheIACR
Lecture 17: Elliptic Curve Cryptography (ECC) by Christof Paar
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com
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: 418 Manuel Radovanovic
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.
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: 13168 nptelhrd
elliptic curve addition
Views: 2293 Jeff Suzuki
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 :)
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: 3482 Arthur Gleckler
CS 463/680: Finite Field Arithmetic
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: 210 Orion Lawlor
The Beauty of Elliptic Curves
Talk at the MathSoc at UCT in Cape Town, October 26, 2017.
Views: 1268 Linda Frey
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 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: 9902 Theoretically
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: 6134 White Hat Cal Poly
Bugs in Crypto Implementations
Whether it’s by email, text, or social media platform, the average person will send over 60 messages per day—that's 22,000 messages per year. With billions of messages sent around the world each day, how can you be sure that your messages are safe and secure? Join professor Dan Boneh, one of the world’s leading experts of applied cryptography and network security, in this breakdown of vulnerabilities in WEP and iMessage. This presentation is brought to you by the Stanford Computer Forum and the Stanford Advanced Computer Security Program. If you would like information on how to join the forum and attend the next meeting, see our website: http://forum.stanford.edu/about/howtojoin.php.
Views: 1709 stanfordonline
Bitcoin 101 - Elliptic Curve Cryptography - Part 5 - The Magic of Signing vesves Verifying
There is nothing more magical in Bitcoin, or all of cryptography than digital signatures. And the most magical step of all is the verification. This is the step we . Vídeo original: Welcome to part four in our series on Elliptic Curve Cryptography. I this episode we dive into the development of . Congress can and should reflect the will of the people. Our research strives to achieve this goal by focusing on the institutional design of legislatures. A beginners guide to all things bitcoin.
Views: 56 Samantha Russell
EC_ rational_point_part_I.m4v
Rational Points over a Finite Field
Views: 928 Israel Reyes
ShmooCon 2014: SafeCurves: Choosing Safe Curves for Elliptic-Curve Cryptography
There are several different standards covering selection of curves for use in elliptic-curve cryptography (ECC). Each of these standards tries to ensure that the elliptic-curve discrete-logarithm problem (ECDLP) is difficult. ECDLP is the problem of finding an ECC user's secret key, given the user's public key. Unfortunately, there is a gap between ECDLP difficulty and ECC security. None of these standards do a good job of ensuring ECC security. There are many attacks that break real-world ECC without solving ECDLP. The core problem is that if you implement the standard curves, chances are you're doing it wrong: Your implementation produces incorrect results for some rare curve points. Your implementation leaks secret data when the input isn't a curve point. Your implementation leaks secret data through branch timing. Your implementation leaks secret data through cache timing. These problems are exploitable by real attackers, taking advantage of the gaps between ECDLP and real-world ECC. Secure implementations of the standard curves are theoretically possible but very hard. Most of these attacks would have been ruled out by better choices of curves that allow simple implementations to be secure implementations. This is the primary motivation for SafeCurves, http://safecurves.cr.yp.to/. The SafeCurves criteria are designed to ensure ECC security, not just ECDLP security. We're researchers in both constructive and destructive aspects of elliptic-curve cryptography. We started issuing warnings about the security dangers of the NIST elliptic curves before it became fashionable to do so. We've proposed alternatives that are faster and stronger, including Curve25519, Ed25519, and Curve3617. Curve25519 is now the go-to alternative curve for people wanting speed and implementation security; it's also not tainted by NIST/NSA. In 2007 we pointed out that Edwards curves are faster and easier to implement securely than standard Weierstrass curves. Edwards curves are also mathematically simpler, allowing a much friendlier introduction to ECC. We've done some other things in crypto as well.
Views: 878 HackersOnBoard
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: 2856 Audiopedia
Elliptic Curves in Sage
Sage (http://sagemath.org) is the most feature rich general purpose free open source software for computing with elliptic curves. In this talk, I'll describe what Sage can compute about elliptic curves and how it does some of these computation, then discuss what Sage currently can't compute but should be able to (e.g., because Magma can).
Views: 887 Microsoft Research
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: 554 Microsoft Research
Elliptic curves: discrete logarithm problem
Described in https://trustica.cz/2018/05/10/elliptic-curves-discrete-logarithm-problem/ this video shows the difference of performing fast scalar multiplication of points on elliptic curve in simple Weierstrass form y²=x³-2x+15 over GF(23) using the double-and-add algorithm and the toughness of reversing this operation - called the Elliptic Curve Discrete Logarithm Problem. Please subscribe to our YouTube channel and remember to follow us on Twitter: https://twitter.com/trusticacz
Views: 264 Trustica
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: 30474 nptelhrd
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: 765 Microsoft Research
Elliptic Curve Method of Factorization, Section 10.6
Math 706, Section 10.6 Elliptic Curve Method of Factorization
Views: 465 Todd Cochrane
High-Speed and Low-Latency ECC Processor Implementation Over GF(2m)on FPGA
High-Speed and Low-Latency ECC Processor Implementation Over GF(2m)on FPGA 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, #37, Kamaraj Salai,Thattanchavady, Puducherry -9.Landmark: Next to VVP Nagar Arch. Mobile: (0) 9952649690, Email: [email protected], web: http://www.jpinfotech.org In this paper, a novel high-speed elliptic curve cryptography (ECC) processor implementation for point multiplication (PM) on field-programmable gate array (FPGA) is proposed. A new segmented pipelined full-precision multiplier is used to reduce the latency, and the Lopez-Dahab Montgomery PM algorithm is modified for careful scheduling to avoid data dependency resulting in a drastic reduction in the number of clock cycles (CCs) required. The proposed ECC architecture has been implemented on Xilinx FPGAs’ Virtex4, Virtex5, and Virtex7 families. To the best of our knowledge, our single- and three-multiplier-based designs show the fastest performance to date when compared with reported works individually. Our one-multiplier-based ECC processor also achieves the highest reported speed together with the best reported area-time performance on Virtex4 (5.32 µs at 210 MHz), on Virtex5 (4.91µs at 228 MHz), and on the more advanced Virtex7 (3.18 µsat 352 MHz). Finally, the proposed three-multiplier-based ECC implementation is the first work reporting the lowest number of CCs and the fastest ECC processor design on FPGA (450 CCs to get 2.83 µs on Virtex7). The proposed architecture of this paper analysis the logic size, area and power consumption using Xilinx 14.2.
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: 10454 nptelhrd
CTNT 2018 - "Factoring with Elliptic Curves" by Jeremy Teitelbaum
This is lecture on "Factoring with Elliptic Curves", by Jeremy Teitelbaum, 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: 118 UConn Mathematics
Breaking ECC2K-130
ECC2K-130 is the smallest unsolved Certicom discrete-logarithm challenge. Certicom originally stated that breaking ECC2K-130 was 'infeasible' and would require 2700000000 machine days. This talk reports on an ongoing joint project by researchers from 12 different universities to break ECC2K-130. The project has increased our knowledge of the mathematical speedups for attacking elliptic-curve cryptosystems, has led to a new representation for finite fields in 'optimal polynomial bases', and has led to a better understanding of the randomness of pseudorandom walks used in Pollard's rho method. The project has produced optimized implementations of a highly tuned iteration function for different platforms ranging from standard CPUs to customized FPGA clusters. These optimizations have moved the ECC2K-130 computation to the range of feasibility. The computation would finish in only two years using 1595 standard PCs, or 1231 PlayStation 3 game consoles, or 534 GTX 295 graphics cards, or 308 XC3S5000 FPGAs, or any combination of the above. We are now actively performing the computations. See our twitter page for updates.
Views: 270 Microsoft Research