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Elliptic curve cryptography explained

Elliptic-curve cryptography - Wikipedi

  1. Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks
  2. read. Recently, I am learning how Elliptic Curve Cryptography works. I searched around the internet,.
  3. Elliptic Curve Cryptography (ECC) is one of the most powerful but least understood types of cryptography in wide use today. At CloudFlare, we make extensive use of ECC to secure everything from our customers' HTTPS connections to how we pass data between our data centers.. Fundamentally, we believe it's important to be able to understand the technology behind any security system in order to.
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Elliptic Curve Cryptography Explained by Fang-Pen Lin

Elliptic Curve Cryptography Explained # cryptography # ellipticcurve. Fang-Pen Lin Oct 7, 2019 ・2 min read. Recently, I am learning how Elliptic Curve Cryptography works. I searched around the internet, found so many articles and videos explaining it. Most of them are. Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in Andrew Wiles's proof of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization I think it would be more precise to say The best way to understand elliptic curve cryptography is to study discrete log cryptography, not to study elliptic curves. There is a tremendous amount of ECC tutorials that walk people mechanically through the group law, I think I've seen a dozen new ones posted on HN in the past year

A (Relatively Easy To Understand) Primer on Elliptic Curve

Elliptic curve cryptography (ECC) is a public key encryption technique based on an elliptic curve theory that can be used to create faster, smaller, and more efficient cryptographic keys 26 thoughts on Understanding Elliptic Curve Cryptography And Embedded Security Canuckfire says: July 4, 2019 at 8:41 pm I like IoTs. (IoT-secure) Kinda.

elliptic curve cryptography explained

Elliptic curves are a very important new area of mathematics which has been greatly explored over the past few decades. They have shown tremendous potential as a tool for solving complicated number problems and also for use in cryptography. In 1994 Andrew Wiles, together with his former student Richard Taylor, solved one of the most famous maths problems of the last 400 years John Wagnon discusses the basics and benefits of Elliptic Curve Cryptography (ECC) in this episode of Lightboard Lessons. Check out this article on DevCentra.. Elliptic curve cryptography is the backbone behind bitcoin technology and other crypto currencies, especially when it comes to to protecting your digital ass.. Elliptic curve cryptography Matthew England MSc Applied Mathematical Sciences Heriot-Watt University Summer 2006. Abstract This project studies the mathematics of elliptic curves, starting with their derivation and the proof of how points upon them form an additive abelian group

Elliptic Curve Cryptography (ECC) The History and Benefits of ECC Certificates The constant back and forth between hackers and security researchers, coupled with advancements in cheap computational power, results in the need for continued evaluation of acceptable encryption algorithms and standards Elliptic Curve Cryptography as a Billiards Game. Digital Signing Algorithm) equations are R = k×G, s = (h(m)+r⋅d)/k where k is a random number and the full process is explained below <br>In other words, how many times we've jumped from \\(P\\) to \\(NP\\), like the following diagram: I can tell you the answer \\(N\\) of the \\(NP\\) point on the diagram above is \\(13\\). With that in mind, I would like to write a post explaining Elliptic Curve Cryptography, cover from the basics to key exchange, encryption, and decryption. In the end, I didn't find an article that. Guide to Elliptic Curve Cryptography Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo. Darrel Hankerson Alfred Menezes Scott Vanstone Guide to Elliptic Curve Cryptography With 38 Illustrations Springer. Darrel Hankcrsnn Department of Mathematics Auburn Universit

Elliptic Curve Cryptography (ECC) - Concepts. The Elliptic Curve Cryptography (ECC) is modern family of public-key cryptosystems, which is based on the algebraic structures of the elliptic curves over finite fields and on the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP).. ECC implements all major capabilities of the asymmetric cryptosystems: encryption, signatures and. Implementing Curve25519/X25519: A Tutorial on Elliptic Curve Cryptography 3 2.2 Groups An abelian group is a set E together with an operation •. The operation combines two elements of the set, denoted a •

A (relatively easy to understand) primer on elliptic curve

Recently, I am learning how Elliptic Curve Cryptography works. I searched around the internet, found so many articles and video Av Fred Piper - Låga priser & snabb leverans

What is Elliptic Curve Cryptography? - Tutorialspoin

<p>Using some more formal and mathematical terms, d is called the private key, while Q is called the public key. Join the DZone community and get the full member experience. It allows us to get to the desired multiple times of point jumping on an elliptic curve pretty fast. Elliptic Curve Cryptography Explained # cryptography # ellipticcurve. We also don't want to dig too deep into the. elliptic curve cryptography explained. elliptic curve cryptography explained. Posted On : October 27, 2020 Published By : Early public-key systems, such as the RSA algorithm, are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors elliptic curve cryptography explained. Posted by on October 27, 2020. When it hits the curve, the ball bounces either straight up (if it's below the x-axis) or straight down (if it's above the x-axis) to the other side of the curve and this is the result C <br>In other words, how many times we've jumped from \\(P\\) to \\(NP\\), like the following diagram: I can tell you the answer \\(N\\) of the \\(NP\\) point on the diagram above is \\(13\\). With that in mind, I would like to write a post explaining Elliptic Curve Cryptography, cover from the basics to key exchange, encryption, and decryption. In the end, I didn't find an article that.

An Attack on Elliptic Curve Cryptography. Elliptic curve pairings were introduced by French mathematician André Weil in 1940 as a tool for solving an analogue of the Riemann Hypothesis for finite fields. Pairings were later used as an attack on elliptic curve cryptography Workshop on Elliptic Curve Cryptography ECC 2020 28 - 30 October 2020, online Announcements. Latest update: 31 Oct. The Curated list of talks is now posted. Many of them have links to slides and videos Cryptography Stack Exchange is a question and answer site for software developers, There is an encryption scheme using elliptic curves given by @tylo explained here: @tylo's answer on ElGamal with elliptic curves and here: ElGamal with elliptic curves I Introduction to Elliptic Curve Cryptography Elisabeth Oswald Institute for Applied Information Processing and Communication A-8010 Inffeldgasse 16a,Graz,Austria Elisabeth.Oswald@iaik.at July 3,2002 Abstract This document should be considered as a tutorial to elliptic curve cryptography. It i Elliptic curve cryptography is a modern public-key encryption technique based on mathematical elliptic curves. Elliptic curve crypto often creates smaller, faster, and more efficient cryptographic keys. In this introduction, our goal will be to focus on the high-level principles of what makes ECC work. For the purposes of keeping this article easy to digest, we'll omit implementation details.

Elliptic curve encryption algorithm: Elliptic curve cryptography can be used to encrypt plaintext message, M, into ciphertexts. The plaintext message M is encoded into a point P M from the finite set of points in the elliptic group, E p (a, b) To do elliptic curve cryptography properly, rather than adding two arbitrary points together, we specify a base point on the curve and only add that point to itself. For example, let's say we have the following curve with base point P: Initially, we have P, or 1•P

Simple explanation for Elliptic Curve Cryptographic

  1. Elliptic Curve Cryptography (ECC) is a public key cryptography. In public key cryptography each user or the device taking part in the communication generally have a pair of keys, a public key and a private key, and a set of operations associated with the keys to do the cryptographic operations
  2. Elliptic Curve Cryptography: The Next Big Step For Dnssec - Surf Blog. Elliptic Curve Cryptography: the next big step for DNSSEC When SURFnet introduced DNSSEC-signing for its domains in 2010, we were one of the pioneers in the field. Our own main domain,surfnet.nlwas the first secure delegation under the.nlcountry-code top-level domain (ccTLD)
  3. Tweet New courses on distributed systems and elliptic curve cryptography. Published by Martin Kleppmann on 18 Nov 2020. I have just published new educational materials that might be of interest to computing people: a new 8-lecture course on distributed systems, and a tutorial on elliptic curve cryptography
  4. To understand ECC, ask the company that owns the patents. Certicom. (Elliptic Curve Cryptography) > Elliptic Curve Cryptography (ECC) was discovered in 1985 by Victor Miller (IBM) and Neil Koblitz (University of Washington) as an alternative mecha..
  5. Elliptic Curve Cryptography - An Implementation Tutorial 5 s = (3x J 2 + a) / (2y J) mod p, s is the tangent at point J and a is one of the parameters chosen with the elliptic curve If y J = 0 then 2J = O, where O is the point at infinity. 8. EC on Binary field F 2 m The equation of the elliptic curve on a binary field
  6. White Paper: Elliptic Curve Cryptography (ECC) Certificates Performance Analysis 7 To enable session resumption, the server such as an Apache Web Server, can be configured to host the session information per client or the client can cache the same . The latter approach is explained in RFC 507713. Older clients require that th
  7. Elliptic Curve Cryptography. It took us a long time, but finally here we are! Therefore, The principle behind the Diffie-Hellman problem is also explained in a great YouTube video by Khan Academy, which later explains the Diffie-Hellman algorithm applied to modular arithmetic.

Video: Basic explanation of Elliptic Curve Cryptography

ECC, RSA, DSA, Elliptic Curves, Elliptic Equations —————————— —————————— 1. Introduction lliptic curve cryptography was come into consideration by Victor Miller and Neal Koblitz in 1985. Elliptic curve cryptography is famous due to the determination that is based on a harder mathematical problem than. However, not all elliptic curves are suitable for cryptography, since in some cases the internal structure of an elliptic curve can be used to solve the discrete logarithm problem e ciently. The main question of this thesis is: In order to answer this question, rst elliptic curves have to be de ned and their basic properties explained

Elliptic curve cryptography explained - tigpsariadaha

Elliptic Curve Cryptography: Before we can understand cryptography, we first have to understand how to perform operations on points on an elliptic curve. An elliptic curve is a group, so it possesses all the characteristics of a group mentioned above. The formula for point addition is as follows: a 3 = (b 2 - b 1 / a 2 - a 1) 2 - a 1. In elliptic curve cryptography, the security assumption is based on the hardness of the discrete log problem. RSA and its modular-arithmetic-based friends are still important today and are often used alongside ECC. Rough implementations of the mathematics behind RSA can be built and explained rather easily Elliptic Curves and Cryptography Koblitz (1987) and Miller (1985) first recommended the use of elliptic-curve groups (over finite fields) in cryptosystems. Use of supersingular curves discarded after the proposal of the Menezes-Okamoto-Vanstone (1993) or Frey-R uck (1994) attack. The OpenSSL EC library provides support for Elliptic Curve Cryptography (ECC).It is the basis for the OpenSSL implementation of the Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic Curve Diffie-Hellman (ECDH).. Note: This page provides an overview of what ECC is, as well as a description of the low-level OpenSSL API for working with Elliptic Curves Elliptic curve cryptography is a branch of mathematics that deals with curves or functions that take the format. y 2 =x 3 +ax+b. These curves have some properties that are of interest and use in cryptography - where we define the addition of points as the reflection in the x axis of the third point that intersects the curve

I am working with PyECC - it is the only elliptic curve cryptography module for python that I can find. I was wondering if anyone had an example of how to use the module? I'll try reading the source, but I couldn't find anything on Stack Overflow on the topic regarding python 3. Elliptic Curve Cryptography 5 3.1. Elliptic Curve Fundamentals 5 3.2. Elliptic Curves over the Reals 5 3.3. Elliptic Curves over Finite Fields 8 3.4. Computing Large Multiples of a Point 9 3.5. Elliptic Curve Discrete Logarithm Problem 10 3.6. Elliptic Curve Di e-Hellman (ECDH) 10 3.7. ElGamal System on Elliptic Curves 11 3.8 7.4. The Group Law for Points on an Elliptic Curve 159 172; 7.5. A Formula for the Group Law on an Elliptic Curve 179 192; 7.6. The Number of Points on an Elliptic Curve 185 198; Chapter 8. Applications of Elliptic Curves 189 202; 8.1. Elliptic Curves and Factoring 190 203; 8.2. Elliptic Curves and Cryptography 196 209; 8.3 Elliptic Curve Cryptography Explained. Recently, I am learning how Elliptic Curve Cryptography works. I searched around the internet, found so many articles and videos explaining it. Most of them are covering only a portion of it, some of them skip many critical steps how you get from here to there

Elliptic Curve Cryptography Explained CryptoCoins Info Clu

Using elliptic curve cryptography, the processes of key generation, encryption, and decryption become dramatically faster. That saves processing power (allowing you to log in and load emails faster), memory (freeing up space for other apps to work), and energy (giving you longer battery life). Elliptic curve cryptography is very secur Elliptic curve cryptography works with points on a curve. The security of this type of public key cryptography depends on the elliptic curve discrete logarithm problem. Introduction. Elliptic curve cryptography was invented by Neil Koblitz in 1987 and by Victor Miller in 1986. The principles of elliptic curve cryptography can be used to adapt. This Abelian group over a discrete elliptic curve can be used for cryptography similarly to the previous blog post, which will be explained in the following section. Elliptic Curve Diffie-Hellman (ECDH) Like exponentiation on integers, multiplication 4 on elliptic curves is a one-way function and therefore can be used for the Diffie-Hellman key. In the last 25 years, Elliptic Curve Cryptography (ECC) has become a mainstream primitive for cryptographic protocols and applications. ECC has been standardized for use in key exchange and digital signatures. This project focuses on efficient generation of parameters and implementation of ECC and pairing-based crypto primitives, across architectures and platforms Elliptic curve cryptography, or ECC, is a powerful approach to cryptography and an alternative method from the well known RSA. It is an approach used for public key encryption by utilizing the mathematics behind elliptic curves in order to generate security between key pairs

Algorithms on Flipboard by Tom Falk

Elliptic Curve Cryptography: a gentle introduction

Elliptic Curve Cryptography? Acknowledgments This paper and the accompanying presentation are both largely drawn from a nal project I put together for an Algebraic Geometry course in the fall of 2014. My sincere thanks are due to the instructor of th Elliptic Curve Cryptography (ECC) ECC depends on the hardness of the discrete logarithm problem Let P and Q be two points on an elliptic curve such that kP = Q, where k is a scalar. Given P and Q, it is hard to compute k k is the discrete logarithm of Q to the base P. The main operation is point multiplication Multiplication of scalar k * p to achieve anothe Over a period of sixteen years elliptic curve cryptography went from being an approach that many people mistrusted or mis- understood to being a public key technology that enjoys almost unquestioned acceptance. We describe the sometimes surprising twists and turns in this paradigm shift,.

In elliptic curve cryptography, it's necessary to specify another point, a base point, which is the generator for a subgroup. This post gives an example, specifying the base point on secp256k1, a curve used in the implementation of Bitcoin. Categories : Math Firstly, Intro to Cryptography Elliptic Curve Cryptography Brit Cruise Does excellent series on Cryptography Open.. Elliptic Curves and Cryptography Aleksandar Juri si c Alfred J. Menezesy March 23, 2005 Elliptic curves have been intensively studied in number theory and algebraic geome-try for over 100 years and there is an enormous literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves

Elliptic Curves and Cryptography Aleksandar Jurisic* Alfred J. Menezes† Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not. What it is: Elliptic Curve Cryptography (ECC) is a variety of asymmetric cryptography (see below).Asymmetric cryptography has various applications, but it is most often used in digital communication to establish secure channels by way of secure passkeys Elliptic Curve Cryptography (ECC) is a public key cryptography method, which evolved form Diffie Hellman. To understanding how ECC works, lets start by understanding how Diffie Hellman works. The Diffie Hellman key exchange protocol, and the Digital Signature Algorithm (DSA) which is based on it, is an asymmetric cryptographic systems in general use today Prime factorisation over elliptic curves: The study of elliptic curve is an old branch of mathematics based on some of the elliptic functions of Weierstrass [32], [2]. The applications of Elliptic Curve to cryptography, was independently discovered by Koblitz and Miller (1985) [15] and [17] Elliptic-curve cryptography explained. 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-EC cryptography (based on plain Galois fields) to provide equivalent security.. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random.

Elliptic Curve Cryptography Explained - DE

Elliptic curve - Wikipedi

ECC stands for Elliptic Curve Cryptography, and is an approach to public key cryptography based on elliptic curves over finite fields (here is a great series of posts on the math behind this). How does ECC compare to RSA? The biggest differentiator between ECC and RSA is key size compared to cryptographic strength Monero's curve: The elliptic curve cryptography used by Monero [8] relies on a particular Twisted Edward curve known as [3]. It has the following attributes: is the prime number given by explaining the suffix in the curve's name So you've heard of Elliptic Curve Cryptography. Maybe you know it's supposed to be better than RSA. Maybe you know that all these cool new decentralized protocols use it. Maybe you've seen the landslide of acronyms that go along with it: ECC, ECDSA, ECDH, EdDSA, Ed25519, etc. Maybe you've seen some cool looking graphs but don't know how those translate to working cryptography in this guide for a level of understanding of Elliptic Curve cryptography that is sufficient to be able to explain the entire process to a computer. This is guide is mainly aimed at computer scientists with some mathematical background who are interested in learning more about Elliptic Curve cryptography The Magic of Elliptic Curve Cryptography. Finite fields are one thing and elliptic curves another. We can combine them by defining an elliptic curve over a finite field. All the equations for an elliptic curve work over a finite field

Elliptic-curve cryptography (ECC) is a public-key cryptography system, very powerful but yet widely unknown, although being massively used for the past decade. Elliptic curves have been studied extensively for the past century and from these studies has emerged a rich and deep theory 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.. Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks With elliptic-curve cryptography, Alice and Bob can arrive at a shared secret by moving around an elliptic curve. Alice and Bob first agree to use the same curve and a few other parameters, and then they pick a random point G on the curve. Both Alice and Bob choose secret numbers (α, β) Referensi: 1. Andreas Steffen, Elliptic Curve Cryptography, Zürcher Hochschule Winterthur. 2. Debdeep Mukhopadhyay, Elliptic Curve Cryptography, Dept of Computer Sc and Engg IIT Madras. 3. Anoop MS , Elliptic Curve Cryptography, an Implementation Guide Bahan Kuliah IF3058 Kriptografi Curves Over Finite Fields 14.9 Elliptic Curves Over Galois Fields GF(2n) 52 14.10 Is b 6= 0 a Sufficient Condition for the Elliptic 62 Curve y2 +xy = x3 + ax2 +b to Not be Singular 14.11 Elliptic Curves Cryptography — The Basic Idea 65 14.12 Elliptic Curve Diffie-Hellman Secret Key 67 Exchange 14.13 Elliptic Curve Digital Signature Algorithm.

An Introduction to the Theory of Elliptic Curves The Discrete Logarithm Problem Fix a group G and an element g 2 G.The Discrete Logarithm Problem (DLP) for G is: Given an element h in the subgroup generated by g, flnd an integer m satisfying h = gm: The smallest integer m satisfying h = gm is called the logarithm (or index) of h with respect to g, and is denote Elliptic curves cryptography (ECC) is a newer approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields, with a novelty of low key size for the user, and hard exponential time challenge for an intruder to break into the system, In the ECC a 160 bits key Since their introduction to cryptography in 1985, elliptic curves have sparked a lot of research and interest in public key cryptography. In this essay, we present an overview of public key. Elliptic Curve Cryptography support z/OS Cryptographic Services System SSL Programming SC14-7495-00 System SSL uses ICSF callable services for Elliptic Curve Cryptography (ECC) algorithm support. For ECC support through ICSF, ICSF must be initialized with PKCS #11 support 2 Elliptic Curve Cryptography 2.1 Introduction. If you're first getting started with ECC, there are two important things that you might want to realize before continuing: Elliptic is not elliptic in the sense of a oval circle. Curve is also quite misleading if we're operating in the field F p

Elliptic Curve Cryptography Explained Hacker New

Fang-Pen&#39;s coding note

including elliptic curves, which are probably unfamiliar and we introduce in Section 5. Finally, we come to a conclusion of which is most secure and begin to discuss how to implement these systems in Section 6. We thus provide only a brief introduction to elliptic curve cryptography, leaving out such topics as pairings. 2 Though we are mostly an essay writing service, Thesis On Elliptic Curve Cryptography this still doesn't mean that we specialize on essays only. Sure, we can write you a top-quality essay, be it admission, persuasive or description one, but if Thesis On Elliptic Curve Cryptography you have a more challenging paper to write, don't worry. We can help with that too, crafting a course paper, a. The most of cryptography resources mention elliptic curve cryptography, but they often ignore the math behind elliptic curve cryptography and directly start with the addition formula. This approach could be very confusing for beginners. In this post, proven of the addition formula would be illustrated We'll start by showing how Elliptic Curve Cryptography works at a high level, then create a list of questions about how/why Elliptic Curve Cryptography works and how it is useful to cryptogrpahy. Once those questions are answered we will end with a recap. Hopefully we will zero in on what Elliptic Curves are and what Elliptic Curve Cryptography is

To date many papers in Elliptic Curve Cryptography have been published by researchers all cwer the worlct as earl he viewed in the refs. However, the idea of using elliptic curves In cryptography is sull considered R difficult concept and neither wv:lely accepteclnor understood by typical technical people Tb Elliptic curve cryptography, or ECC, builds upon the complexity of the elliptic curve discrete logarithm problem to provide strong security that is not dependent upon the factorization of prime numbers. Quantum computing attempts to use quantum mechanics for the same purpose. In this video, learn how cryptographers make use of these two algorithms Elliptic curve cryptography is far from being supported as a standard option in most cryptographic deployments. Despite three NIST curves having been standardized, at the 128-bit security level or higher, the smallest curve size, secp256r1, is by far the most commonly used We're a couple of amateurs in cryptography. We have to implement different algorithms related to Elliptic curve cryptography in Java. So far, we have been able to identify some key algorithms like ECDH, ECIES, ECDSA, ECMQV from the Wikipedia page on elliptic curve cryptography.. Now, we are at a loss in trying to understand how and where to start implementing these algorithms Library for elliptic curves cryptography. Contribute to ANSSI-FR/libecc development by creating an account on GitHub

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SafeCurves: choosing safe curves for elliptic-curve cryptography. https://safecurves.cr.yp.to, accessed 1 December 2014. Replace 1 December 2014 by your download date. Acknowledgments. This work was supported by the U.S. National Science Foundation under grant 1018836 Neal Koblitz and Victor S. Miller independently suggested the use of elliptic curves in cryptography in 1985, and a wide performance was gained in 2004 and 2005. It differs from DSA due to that fact that it is applicable not over the whole numbers of a finite field but to certain points of elliptic curve to define Public/Private Keys pair Elliptic curves over finite fields. Efficient implementation of basic operations on elliptic curves. Elliptic curves over the field of characteristic 2. Algorithms for cumputing the order of the group of points on elliptic curves. Public key cryptography. The idea of the public key Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size, thereby. Elliptic Curve Cryptography & Online Voting Elliptic Curve Cryptography, or ECC, is the kind of cryptography most widely used for blockchains . It is used to validate new transactions to the blockchain and ensure that the transactions are authorized to execute

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