57 skills found · Page 1 of 2
Naereen / Nginx Fancyindex ThemeA :iphone: responsive theme for Nginx Fancyindex module :wrench:. Minimal, modern and simple. ☀ Light & 😎 Dark themes. Comes with a search form :mag_right:, aims to handle thousands of files without any problems :open_file_folder:
petrhruby97 / Learning MinimalLearning to Solve Hard Minimal Problems
hovren / Minimal Ceres SophusMinimal example showing problem with Ceres and Sophus
sanusanth / Javascript Basic ProgramWhat is JavaScript and what does it do? Before you start learning something new, it’s important to understand exactly what it is and what it does. This is especially useful when it comes to mastering a new programming language. In simple terms, JavaScript is a programming language used to make websites interactive. If you think about the basic makeup of a website, you have HTML, which describes and defines the basic content and structure of the website, then you have CSS, which tells the browser how this HTML content should be displayed—determining things like color and font. With just HTML and CSS, you have a website that looks good but doesn’t actually do much. JavaScript brings the website to life by adding functionality. JavaScript is responsible for elements that the user can interact with, such as drop-down menus, modal windows, and contact forms. It is also used to create things like animations, video players, and interactive maps. Nowadays, JavaScript is an all-purpose programming language—meaning it runs across the entire software stack. The most popular application of JavaScript is on the client side (aka frontend), but since Node.js came on the scene, many people run JavaScript on the server side (aka backend) as well. When used on the client side, JavaScript code is read, interpreted, and executed in the user’s web browser. When used on the server side, it is run on a remote computer. You can learn more about the difference between frontend and backend programming here. JavaScript isn’t only used to create websites. It can also be used to build browser-based games and, with the help of certain frameworks, mobile apps for different operating systems. The creation of new libraries and frameworks is also making it possible to build backend programs with JavaScript, such as web apps and server apps. Is it still worth learning JavaScript in 2021? The world of web development is constantly moving. With so many new tools popping up all the time, it can be extremely difficult to know where you should focus your efforts. As an aspiring developer, you’ll want to make sure that what you’re learning is still relevant in today’s industry. If you’re having doubts about JavaScript, it’s important to know that, since its creation in 1995, JavaScript is pretty much everywhere on the web—and that’s not likely to change any time soon. According to the 2020 StackOverflow developer survey, JavaScript is the most commonly used programming language for the eighth year in a row. It is currently used by 94.5% of all websites and, despite originally being designed as a client-side language, JavaScript has now made its way to the server-side of websites (thanks to Node.js), mobile devices (thanks to React Native and Ionic) and desktop (courtesy of Electron). As long as people are interacting with the web, you can assume that JavaScript is highly relevant—there’s no doubt that this is a language worth knowing! With that in mind, let’s look at some of the key benefits of becoming a JavaScript expert. Why learn JavaScript? The most obvious reason for learning JavaScript is if you have hopes of becoming a web developer. Even if you haven’t got your heart set on a tech career, being proficient in JavaScript will enable you to build websites from scratch—a pretty useful skill to have in today’s job market! If you do want to become a web developer, here are some of the main reasons why you should learn JavaScript: JavaScript experts are versatile JavaScript is an extremely versatile language. Once you’ve mastered it, the possibilities are endless: you can code on the client-side (frontend) using Angular and on the server-side (backend) using Node.js. You can also develop web, mobile, and desktop apps using React, React Native, and Electron, and you can even get involved in machine learning. If you want to become a frontend developer, JavaScript is a prerequisite. However, that’s not the only career path open to you as a JavaScript expert. Mastering this key programming language could see you go on to work in full-stack development, games development, information security software engineering, machine learning, and artificial intelligence—to name just a few! Ultimately, if you want any kind of development or engineering career, proficiency in JavaScript is a must. JavaScript experts are in-demand (and well-paid) JavaScript is the most popular programming language in the world, so it’s no wonder that JavaScript is one of the most sought-after skills in the web development industry today. According to the Devskiller IT Skills and Hiring Report 2020, 72% of companies are looking to hire JavaScript experts. Enter the search term “JavaScript” on job site Indeed and you’ll find over 40,000 jobs requiring this skill (in the US). Run the same search on LinkedIn and the results are in excess of 125,000. At the same time, the global demand for JavaScript seems to outweigh the expertise available on the market. According to this 2018 HackerRank report, 48% of employers worldwide need developers with JavaScript skills, while only 42% of student developers claim to be proficient in JavaScript. And, in their most recent report for 2020, HackerRank once again reports that JavaScript is the most popular language that hiring mangers look for in a web developer candidate. Not only are JavaScript experts in demand—they are also well-paid. In the United States, JavaScript developers earn an average yearly salary of $111,953 per year. We’ve covered this topic in more detail in our JavaScript salary guide, but as you can see, learning JavaScript can really boost your earning potential as a developer. JavaScript is beginner-friendly Compared to many other programming languages, JavaScript offers one of the more beginner-friendly entry points into the world of coding. The great thing about JavaScript is that it comes installed on every modern web browser—there’s no need to set up any kind of development environment, which means you can start coding with JavaScript right away! Another advantage of learning JavaScript as your first programming language is that you get instant feedback; with a minimal amount of JavaScript code, you’ll immediately see visible results. There’s also a huge JavaScript community on sites like Stack Overflow, so you’ll find plenty of support as you learn. Not only is JavaScript beginner-friendly; it will also set you up with some extremely valuable transferable skills. JavaScript supports object-oriented, functional, and imperative styles of programming—skills which can be transferred to any new language you might learn later on, such as Python, Java, or C++. JavaScript provides a crucial introduction to key principles and practices that you’ll take with you throughout your career as a developer. Should you learn plain JavaScript first or can you skip to frameworks and libraries? When deciding whether or not to learn JavaScript, what you’re really asking is whether or not you should learn “vanilla” JavaScript. Vanilla JavaScript just means plain JavaScript without any libraries or frameworks. Let’s explore what this means in more detail now. What is meant by vanilla JavaScript, libraries, and frameworks? If you research the term “vanilla JavaScript”, you might run into some confusion; however, all you need to know is that vanilla JavaScript is used to refer to native, standards-based, non-extended JavaScript. There is no difference between vanilla JavaScript and JavaScript—it’s just there to emphasize the usage of plain JavaScript without the use of libraries and frameworks. So what are libraries and frameworks? JavaScript libraries and frameworks both contain sets of prewritten, ready-to-use JavaScript code—but they’re not the same thing. You can think of a framework as your blueprint for building a website: it gives you a structure to work from, and contains ready-made components and tools that help you to build certain elements much quicker than if you were to code them from scratch. Some popular JavaScript frameworks include Angular, React, Vue, and Node.js. Frameworks also contain libraries. Libraries are smaller than frameworks, and tend to be used for more specific cases. A JavaScript library contains sets of JavaScript code which can be called upon to implement certain functions and features. Let’s imagine you want to code a particular element into your website. You could write, say, ten lines of JavaScript from scratch—or you could take the condensed, ready-made version from your chosen JavaScript library. Some examples of JavaScript libraries include jQuery, Lodash, and Underscore. The easiest way to understand how frameworks and libraries work together is to imagine you are building a house. The framework provides the foundation and the structure, while the library enables you to add in ready-made components (like furniture) rather than building your own from scratch. You can learn more about the relationship between languages and libraries in this post explaining the main differences between JavaScript and jQuery. For now, let’s go back to our original question: How important is it to learn vanilla JavaScript? Should you learn vanilla JavaScript first? When it comes to learning JavaScript, it can be tempting to skip ahead to those time-saving frameworks and libraries we just talked about—and many developers do. However, there are many compelling arguments for learning plain JavaScript first. While JavaScript frameworks may help you get the job done quicker, there’s only so far you can go if you don’t understand the core concepts behind these frameworks. Frontend developer Abhishek Nagekar describes how not learning vanilla JavaScript came back to bite him when he started learning the JavaScript frameworks Node and Express: “As I went to write more and more code in Node and Express, I began to get stuck at even the tiniest problems. Suddenly, I was surrounded with words like callbacks, closures, event loop and prototype. It felt like I got a reintroduction to JavaScript, but this time, it was not a toddler playing in its cradle, it was something of a mysterious monster, challenging me on every other step for not having taken it seriously.” The above Tweet references a long-running joke within the developer community, and although it dates way back to 2015, it’s still highly relevant today. If you want to become a developer who can innovate, not just execute, you need to understand the underlying principles of the web—not just the shortcuts. This means learning vanilla JavaScript before you move on to frameworks. In fact, understanding plain JavaScript will help you later on when it comes to deciding whether to use a framework for a certain project, and if so, which framework to use. Why Study JavaScript? JavaScript is one of the 3 languages all web developers must learn: 1. HTML to define the content of web pages 2. CSS to specify the layout of web pages 3. JavaScript to program the behavior of web pages Learning Speed In this tutorial, the learning speed is your choice. Everything is up to you. If you are struggling, take a break, or re-read the material. Always make sure you understand all the "Try-it-Yourself" examples. The only way to become a clever programmer is to: Practice. Practice. Practice. Code. Code. Code ! Commonly Asked Questions How do I get JavaScript? Where can I download JavaScript? Is JavaScript Free? You don't have to get or download JavaScript. JavaScript is already running in your browser on your computer, on your tablet, and on your smart-phone. JavaScript is free to use for everyone.
rfabbri / MinusMinimal problem numerical continuation solver
prclibo / Relative PoseA Collection of Algorithms for Relative Pose Estimation of a Calibrated Camera
janvorisek / Minimal Latex CvMinimal resumé template written in LaTeX. Just black and white making it printable without problems.
PavelTrutman / Automatic GeneratorAutomatic generator of Groebner basis solvers.
prclibo / GapsGAPS: A Generator for Automatic Polynomial Solvers
thousandlemons / Database Normalization SolverA Java library to handle attributes and functional dependencies, and to solve database normalization related problems, including closure, minimal basis, projection, and decomposition to BCNF and 3NF, etc.
timduff35 / PLMPminimal problems with points, lines, and their incidences
rciorba / PidunuA very minimal docker init daemon to handle the zombie process problem.
subarnop / AMachineLearningWalkThroughThis repository contains programs that are often used in machine learning problems implemented with minimal dependencies.
N30nHaCkZ / LinuxLinux kernel release 3.x <http://kernel.org/> These are the release notes for Linux version 3. Read them carefully, as they tell you what this is all about, explain how to install the kernel, and what to do if something goes wrong. WHAT IS LINUX? Linux is a clone of the operating system Unix, written from scratch by Linus Torvalds with assistance from a loosely-knit team of hackers across the Net. It aims towards POSIX and Single UNIX Specification compliance. It has all the features you would expect in a modern fully-fledged Unix, including true multitasking, virtual memory, shared libraries, demand loading, shared copy-on-write executables, proper memory management, and multistack networking including IPv4 and IPv6. It is distributed under the GNU General Public License - see the accompanying COPYING file for more details. ON WHAT HARDWARE DOES IT RUN? Although originally developed first for 32-bit x86-based PCs (386 or higher), today Linux also runs on (at least) the Compaq Alpha AXP, Sun SPARC and UltraSPARC, Motorola 68000, PowerPC, PowerPC64, ARM, Hitachi SuperH, Cell, IBM S/390, MIPS, HP PA-RISC, Intel IA-64, DEC VAX, AMD x86-64, AXIS CRIS, Xtensa, Tilera TILE, AVR32 and Renesas M32R architectures. Linux is easily portable to most general-purpose 32- or 64-bit architectures as long as they have a paged memory management unit (PMMU) and a port of the GNU C compiler (gcc) (part of The GNU Compiler Collection, GCC). Linux has also been ported to a number of architectures without a PMMU, although functionality is then obviously somewhat limited. Linux has also been ported to itself. You can now run the kernel as a userspace application - this is called UserMode Linux (UML). DOCUMENTATION: - There is a lot of documentation available both in electronic form on the Internet and in books, both Linux-specific and pertaining to general UNIX questions. I'd recommend looking into the documentation subdirectories on any Linux FTP site for the LDP (Linux Documentation Project) books. This README is not meant to be documentation on the system: there are much better sources available. - There are various README files in the Documentation/ subdirectory: these typically contain kernel-specific installation notes for some drivers for example. See Documentation/00-INDEX for a list of what is contained in each file. Please read the Changes file, as it contains information about the problems, which may result by upgrading your kernel. - The Documentation/DocBook/ subdirectory contains several guides for kernel developers and users. These guides can be rendered in a number of formats: PostScript (.ps), PDF, HTML, & man-pages, among others. After installation, "make psdocs", "make pdfdocs", "make htmldocs", or "make mandocs" will render the documentation in the requested format. INSTALLING the kernel source: - If you install the full sources, put the kernel tarball in a directory where you have permissions (eg. your home directory) and unpack it: gzip -cd linux-3.X.tar.gz | tar xvf - or bzip2 -dc linux-3.X.tar.bz2 | tar xvf - Replace "X" with the version number of the latest kernel. Do NOT use the /usr/src/linux area! This area has a (usually incomplete) set of kernel headers that are used by the library header files. They should match the library, and not get messed up by whatever the kernel-du-jour happens to be. - You can also upgrade between 3.x releases by patching. Patches are distributed in the traditional gzip and the newer bzip2 format. To install by patching, get all the newer patch files, enter the top level directory of the kernel source (linux-3.X) and execute: gzip -cd ../patch-3.x.gz | patch -p1 or bzip2 -dc ../patch-3.x.bz2 | patch -p1 Replace "x" for all versions bigger than the version "X" of your current source tree, _in_order_, and you should be ok. You may want to remove the backup files (some-file-name~ or some-file-name.orig), and make sure that there are no failed patches (some-file-name# or some-file-name.rej). If there are, either you or I have made a mistake. Unlike patches for the 3.x kernels, patches for the 3.x.y kernels (also known as the -stable kernels) are not incremental but instead apply directly to the base 3.x kernel. For example, if your base kernel is 3.0 and you want to apply the 3.0.3 patch, you must not first apply the 3.0.1 and 3.0.2 patches. Similarly, if you are running kernel version 3.0.2 and want to jump to 3.0.3, you must first reverse the 3.0.2 patch (that is, patch -R) _before_ applying the 3.0.3 patch. You can read more on this in Documentation/applying-patches.txt Alternatively, the script patch-kernel can be used to automate this process. It determines the current kernel version and applies any patches found. linux/scripts/patch-kernel linux The first argument in the command above is the location of the kernel source. Patches are applied from the current directory, but an alternative directory can be specified as the second argument. - Make sure you have no stale .o files and dependencies lying around: cd linux make mrproper You should now have the sources correctly installed. SOFTWARE REQUIREMENTS Compiling and running the 3.x kernels requires up-to-date versions of various software packages. Consult Documentation/Changes for the minimum version numbers required and how to get updates for these packages. Beware that using excessively old versions of these packages can cause indirect errors that are very difficult to track down, so don't assume that you can just update packages when obvious problems arise during build or operation. BUILD directory for the kernel: When compiling the kernel, all output files will per default be stored together with the kernel source code. Using the option "make O=output/dir" allow you to specify an alternate place for the output files (including .config). Example: kernel source code: /usr/src/linux-3.X build directory: /home/name/build/kernel To configure and build the kernel, use: cd /usr/src/linux-3.X make O=/home/name/build/kernel menuconfig make O=/home/name/build/kernel sudo make O=/home/name/build/kernel modules_install install Please note: If the 'O=output/dir' option is used, then it must be used for all invocations of make. CONFIGURING the kernel: Do not skip this step even if you are only upgrading one minor version. New configuration options are added in each release, and odd problems will turn up if the configuration files are not set up as expected. If you want to carry your existing configuration to a new version with minimal work, use "make oldconfig", which will only ask you for the answers to new questions. - Alternative configuration commands are: "make config" Plain text interface. "make menuconfig" Text based color menus, radiolists & dialogs. "make nconfig" Enhanced text based color menus. "make xconfig" X windows (Qt) based configuration tool. "make gconfig" X windows (Gtk) based configuration tool. "make oldconfig" Default all questions based on the contents of your existing ./.config file and asking about new config symbols. "make silentoldconfig" Like above, but avoids cluttering the screen with questions already answered. Additionally updates the dependencies. "make olddefconfig" Like above, but sets new symbols to their default values without prompting. "make defconfig" Create a ./.config file by using the default symbol values from either arch/$ARCH/defconfig or arch/$ARCH/configs/${PLATFORM}_defconfig, depending on the architecture. "make ${PLATFORM}_defconfig" Create a ./.config file by using the default symbol values from arch/$ARCH/configs/${PLATFORM}_defconfig. Use "make help" to get a list of all available platforms of your architecture. "make allyesconfig" Create a ./.config file by setting symbol values to 'y' as much as possible. "make allmodconfig" Create a ./.config file by setting symbol values to 'm' as much as possible. "make allnoconfig" Create a ./.config file by setting symbol values to 'n' as much as possible. "make randconfig" Create a ./.config file by setting symbol values to random values. "make localmodconfig" Create a config based on current config and loaded modules (lsmod). Disables any module option that is not needed for the loaded modules. To create a localmodconfig for another machine, store the lsmod of that machine into a file and pass it in as a LSMOD parameter. target$ lsmod > /tmp/mylsmod target$ scp /tmp/mylsmod host:/tmp host$ make LSMOD=/tmp/mylsmod localmodconfig The above also works when cross compiling. "make localyesconfig" Similar to localmodconfig, except it will convert all module options to built in (=y) options. You can find more information on using the Linux kernel config tools in Documentation/kbuild/kconfig.txt. - NOTES on "make config": - Having unnecessary drivers will make the kernel bigger, and can under some circumstances lead to problems: probing for a nonexistent controller card may confuse your other controllers - Compiling the kernel with "Processor type" set higher than 386 will result in a kernel that does NOT work on a 386. The kernel will detect this on bootup, and give up. - A kernel with math-emulation compiled in will still use the coprocessor if one is present: the math emulation will just never get used in that case. The kernel will be slightly larger, but will work on different machines regardless of whether they have a math coprocessor or not. - The "kernel hacking" configuration details usually result in a bigger or slower kernel (or both), and can even make the kernel less stable by configuring some routines to actively try to break bad code to find kernel problems (kmalloc()). Thus you should probably answer 'n' to the questions for "development", "experimental", or "debugging" features. COMPILING the kernel: - Make sure you have at least gcc 3.2 available. For more information, refer to Documentation/Changes. Please note that you can still run a.out user programs with this kernel. - Do a "make" to create a compressed kernel image. It is also possible to do "make install" if you have lilo installed to suit the kernel makefiles, but you may want to check your particular lilo setup first. To do the actual install, you have to be root, but none of the normal build should require that. Don't take the name of root in vain. - If you configured any of the parts of the kernel as `modules', you will also have to do "make modules_install". - Verbose kernel compile/build output: Normally, the kernel build system runs in a fairly quiet mode (but not totally silent). However, sometimes you or other kernel developers need to see compile, link, or other commands exactly as they are executed. For this, use "verbose" build mode. This is done by inserting "V=1" in the "make" command. E.g.: make V=1 all To have the build system also tell the reason for the rebuild of each target, use "V=2". The default is "V=0". - Keep a backup kernel handy in case something goes wrong. This is especially true for the development releases, since each new release contains new code which has not been debugged. Make sure you keep a backup of the modules corresponding to that kernel, as well. If you are installing a new kernel with the same version number as your working kernel, make a backup of your modules directory before you do a "make modules_install". Alternatively, before compiling, use the kernel config option "LOCALVERSION" to append a unique suffix to the regular kernel version. LOCALVERSION can be set in the "General Setup" menu. - In order to boot your new kernel, you'll need to copy the kernel image (e.g. .../linux/arch/i386/boot/bzImage after compilation) to the place where your regular bootable kernel is found. - Booting a kernel directly from a floppy without the assistance of a bootloader such as LILO, is no longer supported. If you boot Linux from the hard drive, chances are you use LILO, which uses the kernel image as specified in the file /etc/lilo.conf. The kernel image file is usually /vmlinuz, /boot/vmlinuz, /bzImage or /boot/bzImage. To use the new kernel, save a copy of the old image and copy the new image over the old one. Then, you MUST RERUN LILO to update the loading map!! If you don't, you won't be able to boot the new kernel image. Reinstalling LILO is usually a matter of running /sbin/lilo. You may wish to edit /etc/lilo.conf to specify an entry for your old kernel image (say, /vmlinux.old) in case the new one does not work. See the LILO docs for more information. After reinstalling LILO, you should be all set. Shutdown the system, reboot, and enjoy! If you ever need to change the default root device, video mode, ramdisk size, etc. in the kernel image, use the 'rdev' program (or alternatively the LILO boot options when appropriate). No need to recompile the kernel to change these parameters. - Reboot with the new kernel and enjoy. IF SOMETHING GOES WRONG: - If you have problems that seem to be due to kernel bugs, please check the file MAINTAINERS to see if there is a particular person associated with the part of the kernel that you are having trouble with. If there isn't anyone listed there, then the second best thing is to mail them to me (torvalds@linux-foundation.org), and possibly to any other relevant mailing-list or to the newsgroup. - In all bug-reports, *please* tell what kernel you are talking about, how to duplicate the problem, and what your setup is (use your common sense). If the problem is new, tell me so, and if the problem is old, please try to tell me when you first noticed it. - If the bug results in a message like unable to handle kernel paging request at address C0000010 Oops: 0002 EIP: 0010:XXXXXXXX eax: xxxxxxxx ebx: xxxxxxxx ecx: xxxxxxxx edx: xxxxxxxx esi: xxxxxxxx edi: xxxxxxxx ebp: xxxxxxxx ds: xxxx es: xxxx fs: xxxx gs: xxxx Pid: xx, process nr: xx xx xx xx xx xx xx xx xx xx xx or similar kernel debugging information on your screen or in your system log, please duplicate it *exactly*. The dump may look incomprehensible to you, but it does contain information that may help debugging the problem. The text above the dump is also important: it tells something about why the kernel dumped code (in the above example, it's due to a bad kernel pointer). More information on making sense of the dump is in Documentation/oops-tracing.txt - If you compiled the kernel with CONFIG_KALLSYMS you can send the dump as is, otherwise you will have to use the "ksymoops" program to make sense of the dump (but compiling with CONFIG_KALLSYMS is usually preferred). This utility can be downloaded from ftp://ftp.<country>.kernel.org/pub/linux/utils/kernel/ksymoops/ . Alternatively, you can do the dump lookup by hand: - In debugging dumps like the above, it helps enormously if you can look up what the EIP value means. The hex value as such doesn't help me or anybody else very much: it will depend on your particular kernel setup. What you should do is take the hex value from the EIP line (ignore the "0010:"), and look it up in the kernel namelist to see which kernel function contains the offending address. To find out the kernel function name, you'll need to find the system binary associated with the kernel that exhibited the symptom. This is the file 'linux/vmlinux'. To extract the namelist and match it against the EIP from the kernel crash, do: nm vmlinux | sort | less This will give you a list of kernel addresses sorted in ascending order, from which it is simple to find the function that contains the offending address. Note that the address given by the kernel debugging messages will not necessarily match exactly with the function addresses (in fact, that is very unlikely), so you can't just 'grep' the list: the list will, however, give you the starting point of each kernel function, so by looking for the function that has a starting address lower than the one you are searching for but is followed by a function with a higher address you will find the one you want. In fact, it may be a good idea to include a bit of "context" in your problem report, giving a few lines around the interesting one. If you for some reason cannot do the above (you have a pre-compiled kernel image or similar), telling me as much about your setup as possible will help. Please read the REPORTING-BUGS document for details. - Alternatively, you can use gdb on a running kernel. (read-only; i.e. you cannot change values or set break points.) To do this, first compile the kernel with -g; edit arch/i386/Makefile appropriately, then do a "make clean". You'll also need to enable CONFIG_PROC_FS (via "make config"). After you've rebooted with the new kernel, do "gdb vmlinux /proc/kcore". You can now use all the usual gdb commands. The command to look up the point where your system crashed is "l *0xXXXXXXXX". (Replace the XXXes with the EIP value.) gdb'ing a non-running kernel currently fails because gdb (wrongly) disregards the starting offset for which the kernel is compiled.
Jeongyong-park / Poly Split JsSolving the problem of cutting a given polygon into any number of areas of given squares with a lines of minimal length
Erfaniaa / TestsazTestsaz is a fast, minimal test-case generator system for ICPC style and IOI style problems.
Brown-LEMS / Homotopy Continuation Tracker On GPU[CVPR 2022] GPU-HC solving minimal problems in computer vision
uvhw / Bitcoin FoundationBitcoin: A Peer-to-Peer Electronic Cash System Satoshi Nakamoto satoshin@gmx.com www.bitcoin.org Abstract. A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone. 1. Introduction Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non- reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party. What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers. In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes. 1 2. Transactions We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership. Transaction Hash Transaction Hash Transaction Hash Owner 1's Public Key Owner 2's Public Key Owner 3's Public Key Owner 0's Signature Owner 1's Signature The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank. We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced [1], and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received. 3. Timestamp Server The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post [2-5]. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it. Hash Hash Owner 2's Signature Owner 1's Private Key Owner 2's Private Key Owner 3's Private Key Block Item Item ... 2 Block Item Item ... Verify Verify Sign Sign 4. Proof-of-Work To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof- of-work system similar to Adam Back's Hashcash [6], rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash. For our timestamp network, we implement the proof-of-work by incrementing a nonce in the block until a value is found that gives the block's hash the required zero bits. Once the CPU effort has been expended to make it satisfy the proof-of-work, the block cannot be changed without redoing the work. As later blocks are chained after it, the work to change the block would include redoing all the blocks after it. The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added. To compensate for increasing hardware speed and varying interest in running nodes over time, the proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. If they're generated too fast, the difficulty increases. 5. Network The steps to run the network are as follows: 1) New transactions are broadcast to all nodes. 2) Each node collects new transactions into a block. 3) Each node works on finding a difficult proof-of-work for its block. 4) When a node finds a proof-of-work, it broadcasts the block to all nodes. 5) Nodes accept the block only if all transactions in it are valid and not already spent. 6) Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash. Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof- of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one. 3 Block Nonce Tx Tx ... Block Nonce Tx Tx ... Prev Hash Prev Hash New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one. 6. Incentive By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended. The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free. The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth. 7. Reclaiming Disk Space Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block's hash, transactions are hashed in a Merkle Tree [7][2][5], with only the root included in the block's hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored. Block Hash0 Hash1 Hash2 Hash3 Tx0 Tx1 Tx2 Tx3 Block Header (Block Hash) Prev Hash Nonce Root Hash Hash01 Hash23 Block Block Header (Block Hash) Prev Hash Nonce Root Hash Hash01 Hash23 Hash2 Hash3 Tx3 Transactions Hashed in a Merkle Tree After Pruning Tx0-2 from the Block A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory. 4 8. Simplified Payment Verification It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it. Longest Proof-of-Work Chain Block Header Block Header Block Header Prev Hash Nonce Prev Hash Nonce Prev Hash Nonce Merkle Root Merkle Root Merkle Root Hash01 Hash23 Merkle Branch for Tx3 Hash2 Hash3 Tx3 As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification. 9. Combining and Splitting Value Although it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To allow value to be split and combined, transactions contain multiple inputs and outputs. Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender. It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. There is never the need to extract a complete standalone copy of a transaction's history. 5 Transaction In Out In ... ... 10. Privacy The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were. Traditional Privacy Model Identities Transactions New Privacy Model Identities Transactions As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner. 11. Calculations We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent. The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker's chain being extended by one block, reducing the gap by -1. The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows [8]: p = probability an honest node finds the next block q = probability the attacker finds the next block qz = probability the attacker will ever catch up from z blocks behind Trusted Third Party q ={ 1 if p≤q} z q/pz if pq 6 Counterparty Public Public Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind. We now consider how long the recipient of a new transaction needs to wait before being sufficiently certain the sender can't change the transaction. We assume the sender is an attacker who wants to make the recipient believe he paid him for a while, then switch it to pay back to himself after some time has passed. The receiver will be alerted when that happens, but the sender hopes it will be too late. The receiver generates a new key pair and gives the public key to the sender shortly before signing. This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is lucky enough to get far enough ahead, then executing the transaction at that moment. Once the transaction is sent, the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction. The recipient waits until the transaction has been added to a block and z blocks have been linked after it. He doesn't know the exact amount of progress the attacker has made, but assuming the honest blocks took the average expected time per block, the attacker's potential progress will be a Poisson distribution with expected value: = z qp To get the probability the attacker could still catch up now, we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point: ∞ ke−{q/pz−k ifk≤z} ∑k=0 k!⋅ 1 ifkz Rearranging to avoid summing the infinite tail of the distribution... z ke− z−k 1−∑k=0 k! 1−q/p Converting to C code... #include <math.h> double AttackerSuccessProbability(double q, int z) { double p = 1.0 - q; double lambda = z * (q / p); double sum = 1.0; int i, k; for (k = 0; k <= z; k++) { double poisson = exp(-lambda); for (i = 1; i <= k; i++) poisson *= lambda / i; sum -= poisson * (1 - pow(q / p, z - k)); } return sum; } 7 Running some results, we can see the probability drop off exponentially with z. q=0.1 z=0 P=1.0000000 z=1 P=0.2045873 z=2 P=0.0509779 z=3 P=0.0131722 z=4 P=0.0034552 z=5 P=0.0009137 z=6 P=0.0002428 z=7 P=0.0000647 z=8 P=0.0000173 z=9 P=0.0000046 z=10 P=0.0000012 q=0.3 z=0 P=1.0000000 z=5 P=0.1773523 z=10 P=0.0416605 z=15 P=0.0101008 z=20 P=0.0024804 z=25 P=0.0006132 z=30 P=0.0001522 z=35 P=0.0000379 z=40 P=0.0000095 z=45 P=0.0000024 z=50 P=0.0000006 Solving for P less than 0.1%... P < 0.001 q=0.10 z=5 q=0.15 z=8 q=0.20 z=11 q=0.25 z=15 q=0.30 z=24 q=0.35 z=41 q=0.40 z=89 q=0.45 z=340 12. Conclusion We have proposed a system for electronic transactions without relying on trust. We started with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power. The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism. 8 References [1] W. Dai, "b-money," http://www.weidai.com/bmoney.txt, 1998. [2] H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements," In 20th Symposium on Information Theory in the Benelux, May 1999. [3] S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991. [4] D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping," In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993. [5] S. Haber, W.S. Stornetta, "Secure names for bit-strings," In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997. [6] A. Back, "Hashcash - a denial of service counter-measure," http://www.hashcash.org/papers/hashcash.pdf, 2002. [7] R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980. [8] W. Feller, "An introduction to probability theory and its applications," 1957. 9
AhmadYahya97 / CrosswordsGenerationCrosswords puzzle generator and publisher using Constraints Satisfaction Problem (CSP) technique. With minimal backtracks.
mahaveer-rulaniya / Healthify AgriTechThe project is based on the Idea of Addressing real-life problems in the Agricultural sector and Healthcare sector. It can be also considered as the Minimal Viable Product.
