CINXE.COM

May 2015 – Cryptography & Payments

<!doctype html> <html lang="en"> <head> <meta charset="UTF-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <link rel="profile" href="https://gmpg.org/xfn/11" /> <title>May 2015 &#8211; Cryptography &amp; Payments</title> <script type="text/javascript"> WebFontConfig = {"google":{"families":["Source+Sans+Pro:r,i,b,bi:latin,latin-ext"]},"api_url":"https:\/\/fonts-api.wp.com\/css"}; (function() { var wf = document.createElement('script'); wf.src = 'https://s0.wp.com/wp-content/plugins/custom-fonts/js/webfont.js'; wf.type = 'text/javascript'; wf.async = 'true'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(wf, s); })(); </script><style id="jetpack-custom-fonts-css"></style> <meta name='robots' content='max-image-preview:large' /> <meta name="google-site-verification" content="Zw5b22p04kGoy8Ch3FcgAxEamB26jLd3FALtlnOF6RA" /> <!-- Async WordPress.com Remote Login --> <script id="wpcom_remote_login_js"> var wpcom_remote_login_extra_auth = ''; function wpcom_remote_login_remove_dom_node_id( element_id ) { var dom_node = document.getElementById( element_id ); if ( dom_node ) { dom_node.parentNode.removeChild( dom_node ); } } function wpcom_remote_login_remove_dom_node_classes( class_name ) { var dom_nodes = document.querySelectorAll( '.' + class_name ); for ( var i = 0; i < dom_nodes.length; i++ ) { dom_nodes[ i ].parentNode.removeChild( dom_nodes[ i ] ); } } function wpcom_remote_login_final_cleanup() { wpcom_remote_login_remove_dom_node_classes( "wpcom_remote_login_msg" ); wpcom_remote_login_remove_dom_node_id( "wpcom_remote_login_key" ); wpcom_remote_login_remove_dom_node_id( "wpcom_remote_login_validate" ); wpcom_remote_login_remove_dom_node_id( "wpcom_remote_login_js" ); wpcom_remote_login_remove_dom_node_id( "wpcom_request_access_iframe" ); wpcom_remote_login_remove_dom_node_id( "wpcom_request_access_styles" ); } // Watch for messages back from the remote login window.addEventListener( "message", function( e ) { if ( e.origin === "https://r-login.wordpress.com" ) { var data = {}; try { data = JSON.parse( e.data ); } catch( e ) { wpcom_remote_login_final_cleanup(); return; } if ( data.msg === 'LOGIN' ) { // Clean up the login check iframe wpcom_remote_login_remove_dom_node_id( "wpcom_remote_login_key" ); var id_regex = new RegExp( /^[0-9]+$/ ); var token_regex = new RegExp( /^.*|.*|.*$/ ); if ( token_regex.test( data.token ) && id_regex.test( data.wpcomid ) ) { // We have everything we need to ask for a login var script = document.createElement( "script" ); script.setAttribute( "id", "wpcom_remote_login_validate" ); script.src = '/remote-login.php?wpcom_remote_login=validate' + '&wpcomid=' + data.wpcomid + '&token=' + encodeURIComponent( data.token ) + '&host=' + window.location.protocol + '//' + window.location.hostname + '&postid=138' + '&is_singular='; document.body.appendChild( script ); } return; } // Safari ITP, not logged in, so redirect if ( data.msg === 'LOGIN-REDIRECT' ) { window.location = 'https://wordpress.com/log-in?redirect_to=' + window.location.href; return; } // Safari ITP, storage access failed, remove the request if ( data.msg === 'LOGIN-REMOVE' ) { var css_zap = 'html { -webkit-transition: margin-top 1s; transition: margin-top 1s; } /* 9001 */ html { margin-top: 0 !important; } * html body { margin-top: 0 !important; } @media screen and ( max-width: 782px ) { html { margin-top: 0 !important; } * html body { margin-top: 0 !important; } }'; var style_zap = document.createElement( 'style' ); style_zap.type = 'text/css'; style_zap.appendChild( document.createTextNode( css_zap ) ); document.body.appendChild( style_zap ); var e = document.getElementById( 'wpcom_request_access_iframe' ); e.parentNode.removeChild( e ); document.cookie = 'wordpress_com_login_access=denied; path=/; max-age=31536000'; return; } // Safari ITP if ( data.msg === 'REQUEST_ACCESS' ) { console.log( 'request access: safari' ); // Check ITP iframe enable/disable knob if ( wpcom_remote_login_extra_auth !== 'safari_itp_iframe' ) { return; } // If we are in a "private window" there is no ITP. var private_window = false; try { var opendb = window.openDatabase( null, null, null, null ); } catch( e ) { private_window = true; } if ( private_window ) { console.log( 'private window' ); return; } var iframe = document.createElement( 'iframe' ); iframe.id = 'wpcom_request_access_iframe'; iframe.setAttribute( 'scrolling', 'no' ); iframe.setAttribute( 'sandbox', 'allow-storage-access-by-user-activation allow-scripts allow-same-origin allow-top-navigation-by-user-activation' ); iframe.src = 'https://r-login.wordpress.com/remote-login.php?wpcom_remote_login=request_access&origin=' + encodeURIComponent( data.origin ) + '&wpcomid=' + encodeURIComponent( data.wpcomid ); var css = 'html { -webkit-transition: margin-top 1s; transition: margin-top 1s; } /* 9001 */ html { margin-top: 46px !important; } * html body { margin-top: 46px !important; } @media screen and ( max-width: 660px ) { html { margin-top: 71px !important; } * html body { margin-top: 71px !important; } #wpcom_request_access_iframe { display: block; height: 71px !important; } } #wpcom_request_access_iframe { border: 0px; height: 46px; position: fixed; top: 0; left: 0; width: 100%; min-width: 100%; z-index: 99999; background: #23282d; } '; var style = document.createElement( 'style' ); style.type = 'text/css'; style.id = 'wpcom_request_access_styles'; style.appendChild( document.createTextNode( css ) ); document.body.appendChild( style ); document.body.appendChild( iframe ); } if ( data.msg === 'DONE' ) { wpcom_remote_login_final_cleanup(); } } }, false ); // Inject the remote login iframe after the page has had a chance to load // more critical resources window.addEventListener( "DOMContentLoaded", function( e ) { var iframe = document.createElement( "iframe" ); iframe.style.display = "none"; iframe.setAttribute( "scrolling", "no" ); iframe.setAttribute( "id", "wpcom_remote_login_key" ); iframe.src = "https://r-login.wordpress.com/remote-login.php" + "?wpcom_remote_login=key" + "&origin=aHR0cHM6Ly9hcnRodXJ2YW5kZXJtZXJ3ZS5jb20%3D" + "&wpcomid=70204527" + "&time=1732380575"; document.body.appendChild( iframe ); }, false ); </script> <link rel='dns-prefetch' href='//s1.wp.com' /> <link rel='dns-prefetch' href='//s2.wp.com' /> <link rel='dns-prefetch' href='//s0.wp.com' /> <link rel='dns-prefetch' href='//fonts-api.wp.com' /> <link rel='dns-prefetch' href='//s.pubmine.com' /> <link rel='dns-prefetch' href='//x.bidswitch.net' /> <link rel='dns-prefetch' href='//static.criteo.net' /> <link rel='dns-prefetch' href='//ib.adnxs.com' /> <link rel='dns-prefetch' href='//aax.amazon-adsystem.com' /> <link rel='dns-prefetch' href='//bidder.criteo.com' /> <link rel='dns-prefetch' href='//cas.criteo.com' /> <link rel='dns-prefetch' href='//gum.criteo.com' /> <link rel='dns-prefetch' href='//ads.pubmatic.com' /> <link rel='dns-prefetch' href='//gads.pubmatic.com' /> <link rel='dns-prefetch' href='//tpc.googlesyndication.com' /> <link rel='dns-prefetch' href='//ad.doubleclick.net' /> <link rel='dns-prefetch' href='//googleads.g.doubleclick.net' /> <link rel='dns-prefetch' href='//www.googletagservices.com' /> <link rel='dns-prefetch' href='//cdn.switchadhub.com' /> <link rel='dns-prefetch' href='//delivery.g.switchadhub.com' /> <link rel='dns-prefetch' href='//delivery.swid.switchadhub.com' /> <link rel='dns-prefetch' href='//a.teads.tv' /> <link rel='dns-prefetch' href='//prebid.media.net' /> <link rel='dns-prefetch' href='//adserver-us.adtech.advertising.com' /> <link rel='dns-prefetch' href='//fastlane.rubiconproject.com' /> <link rel='dns-prefetch' href='//prebid-server.rubiconproject.com' /> <link rel='dns-prefetch' href='//hb-api.omnitagjs.com' /> <link rel='dns-prefetch' href='//mtrx.go.sonobi.com' /> <link rel='dns-prefetch' href='//apex.go.sonobi.com' /> <link rel='dns-prefetch' href='//u.openx.net' /> <link rel="alternate" type="application/rss+xml" title="Cryptography &amp; Payments &raquo; Feed" href="https://arthurvandermerwe.com/feed/" /> <link rel="alternate" type="application/rss+xml" title="Cryptography &amp; Payments &raquo; Comments Feed" href="https://arthurvandermerwe.com/comments/feed/" /> <script type="text/javascript"> /* <![CDATA[ */ function addLoadEvent(func) { var oldonload = window.onload; if (typeof window.onload != 'function') { window.onload = func; } else { window.onload = function () { oldonload(); func(); } } } /* ]]> */ </script> <script> window._wpemojiSettings = {"baseUrl":"https:\/\/s0.wp.com\/wp-content\/mu-plugins\/wpcom-smileys\/twemoji\/2\/72x72\/","ext":".png","svgUrl":"https:\/\/s0.wp.com\/wp-content\/mu-plugins\/wpcom-smileys\/twemoji\/2\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/s2.wp.com\/wp-includes\/js\/wp-emoji-release.min.js?m=1719498190i&ver=6.8-alpha-59438"}}; /*! This file is auto-generated */ !function(i,n){var o,s,e;function c(e){try{var t={supportTests:e,timestamp:(new Date).valueOf()};sessionStorage.setItem(o,JSON.stringify(t))}catch(e){}}function p(e,t,n){e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(t,0,0);var t=new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data),r=(e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(n,0,0),new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data));return t.every(function(e,t){return e===r[t]})}function u(e,t,n){switch(t){case"flag":return n(e,"\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!n(e,"\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!n(e,"\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!n(e,"\ud83d\udc26\u200d\u2b1b","\ud83d\udc26\u200b\u2b1b")}return!1}function f(e,t,n){var r="undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?new OffscreenCanvas(300,150):i.createElement("canvas"),a=r.getContext("2d",{willReadFrequently:!0}),o=(a.textBaseline="top",a.font="600 32px Arial",{});return e.forEach(function(e){o[e]=t(a,e,n)}),o}function t(e){var t=i.createElement("script");t.src=e,t.defer=!0,i.head.appendChild(t)}"undefined"!=typeof Promise&&(o="wpEmojiSettingsSupports",s=["flag","emoji"],n.supports={everything:!0,everythingExceptFlag:!0},e=new Promise(function(e){i.addEventListener("DOMContentLoaded",e,{once:!0})}),new Promise(function(t){var n=function(){try{var e=JSON.parse(sessionStorage.getItem(o));if("object"==typeof e&&"number"==typeof e.timestamp&&(new Date).valueOf()<e.timestamp+604800&&"object"==typeof e.supportTests)return e.supportTests}catch(e){}return null}();if(!n){if("undefined"!=typeof Worker&&"undefined"!=typeof OffscreenCanvas&&"undefined"!=typeof URL&&URL.createObjectURL&&"undefined"!=typeof Blob)try{var e="postMessage("+f.toString()+"("+[JSON.stringify(s),u.toString(),p.toString()].join(",")+"));",r=new Blob([e],{type:"text/javascript"}),a=new Worker(URL.createObjectURL(r),{name:"wpTestEmojiSupports"});return void(a.onmessage=function(e){c(n=e.data),a.terminate(),t(n)})}catch(e){}c(n=f(s,u,p))}t(n)}).then(function(e){for(var t in e)n.supports[t]=e[t],n.supports.everything=n.supports.everything&&n.supports[t],"flag"!==t&&(n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&n.supports[t]);n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&!n.supports.flag,n.DOMReady=!1,n.readyCallback=function(){n.DOMReady=!0}}).then(function(){return e}).then(function(){var e;n.supports.everything||(n.readyCallback(),(e=n.source||{}).concatemoji?t(e.concatemoji):e.wpemoji&&e.twemoji&&(t(e.twemoji),t(e.wpemoji)))}))}((window,document),window._wpemojiSettings); </script> <link crossorigin='anonymous' rel='stylesheet' id='all-css-0-1' href='https://s2.wp.com/wp-content/blog-plugins/wordads/global.css?m=1561495466i&cssminify=yes' type='text/css' media='all' /> <style id='wp-emoji-styles-inline-css'> img.wp-smiley, img.emoji { display: inline !important; border: none !important; box-shadow: none !important; height: 1em !important; width: 1em !important; margin: 0 0.07em !important; vertical-align: -0.1em !important; background: none !important; padding: 0 !important; } </style> <link crossorigin='anonymous' rel='stylesheet' id='all-css-2-1' href='https://s0.wp.com/_static/??-eJydzMsOwiAQheEXEibEXtKF8VmATggVgcwMNby91U13LlyenHw/vKryJQtmgZpaiJkhtGM6pHA8hLCbRU96ANdiWsGl4h8qRUeWOrD0hNozX+Bn6KsYNpRqP9z20kQFiuu/CbISc+CT3583M1/NMg6zGbc3O1tP4A==&cssminify=yes' type='text/css' media='all' /> <style id='wp-block-library-inline-css'> .has-text-align-justify { text-align:justify; } .has-text-align-justify{text-align:justify;} </style> <link crossorigin='anonymous' rel='stylesheet' id='all-css-4-1' href='https://s2.wp.com/_static/??-eJzTLy/QzcxLzilNSS3WzyrWz01NyUxMzUnNTc0rQeEU5CRWphbp5qSmJyZX6uVm5uklFxfr6OPTDpRD5sM02efaGpoZmFkYGRuZGmQBAHPvL0Y=&cssminify=yes' type='text/css' media='all' /> <style id='jetpack-sharing-buttons-style-inline-css'> .jetpack-sharing-buttons__services-list{display:flex;flex-direction:row;flex-wrap:wrap;gap:0;list-style-type:none;margin:5px;padding:0}.jetpack-sharing-buttons__services-list.has-small-icon-size{font-size:12px}.jetpack-sharing-buttons__services-list.has-normal-icon-size{font-size:16px}.jetpack-sharing-buttons__services-list.has-large-icon-size{font-size:24px}.jetpack-sharing-buttons__services-list.has-huge-icon-size{font-size:36px}@media print{.jetpack-sharing-buttons__services-list{display:none!important}}.editor-styles-wrapper .wp-block-jetpack-sharing-buttons{gap:0;padding-inline-start:0}ul.jetpack-sharing-buttons__services-list.has-background{padding:1.25em 2.375em} </style> <link crossorigin='anonymous' rel='stylesheet' id='all-css-6-1' href='https://s2.wp.com/wp-content/plugins/coblocks/2.18.1-simple-rev.4/dist/coblocks-style.css?m=1681832297i&cssminify=yes' type='text/css' media='all' /> <style id='classic-theme-styles-inline-css'> /*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} </style> <link crossorigin='anonymous' rel='stylesheet' id='all-css-8-1' href='https://s1.wp.com/_static/??/wp-content/mu-plugins/core-compat/wp-mediaelement.css,/wp-content/mu-plugins/wpcom-bbpress-premium-themes.css?m=1432920480j&cssminify=yes' type='text/css' media='all' /> <style id='global-styles-inline-css'> :root{--wp--preset--aspect-ratio--square: 1;--wp--preset--aspect-ratio--4-3: 4/3;--wp--preset--aspect-ratio--3-4: 3/4;--wp--preset--aspect-ratio--3-2: 3/2;--wp--preset--aspect-ratio--2-3: 2/3;--wp--preset--aspect-ratio--16-9: 16/9;--wp--preset--aspect-ratio--9-16: 9/16;--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #ffffff;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--color--primary: #000000;--wp--preset--color--secondary: #3C8067;--wp--preset--color--foreground: #333333;--wp--preset--color--tertiary: #FAFBF6;--wp--preset--color--background: #FFFFFF;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--gradient--hard-diagonal: linear-gradient(to bottom right, #3C8067 49.9%, #FAFBF6 50%);--wp--preset--gradient--hard-diagonal-inverted: linear-gradient(to top left, #3C8067 49.9%, #FAFBF6 50%);--wp--preset--gradient--hard-horizontal: linear-gradient(to bottom, #3C8067 50%, #FAFBF6 50%);--wp--preset--gradient--hard-horizontal-inverted: linear-gradient(to top, #3C8067 50%, #FAFBF6 50%);--wp--preset--gradient--diagonal: linear-gradient(to bottom right, #3C8067, #FAFBF6);--wp--preset--gradient--diagonal-inverted: linear-gradient(to top left, #3C8067, #FAFBF6);--wp--preset--gradient--horizontal: linear-gradient(to bottom, #3C8067, #FAFBF6);--wp--preset--gradient--horizontal-inverted: linear-gradient(to top, #3C8067, #FAFBF6);--wp--preset--gradient--stripe: linear-gradient(to bottom, transparent 20%, #3C8067 20%, #3C8067 80%, transparent 80%);--wp--preset--font-size--small: 16px;--wp--preset--font-size--medium: 20px;--wp--preset--font-size--large: 24px;--wp--preset--font-size--x-large: 42px;--wp--preset--font-size--tiny: 14px;--wp--preset--font-size--normal: 18px;--wp--preset--font-size--huge: 28px;--wp--preset--font-family--albert-sans: 'Albert Sans', sans-serif;--wp--preset--font-family--alegreya: Alegreya, serif;--wp--preset--font-family--arvo: Arvo, serif;--wp--preset--font-family--bodoni-moda: 'Bodoni Moda', serif;--wp--preset--font-family--bricolage-grotesque: 'Bricolage Grotesque', sans-serif;--wp--preset--font-family--cabin: Cabin, sans-serif;--wp--preset--font-family--chivo: Chivo, sans-serif;--wp--preset--font-family--commissioner: Commissioner, sans-serif;--wp--preset--font-family--cormorant: Cormorant, serif;--wp--preset--font-family--courier-prime: 'Courier Prime', monospace;--wp--preset--font-family--crimson-pro: 'Crimson Pro', serif;--wp--preset--font-family--dm-mono: 'DM Mono', monospace;--wp--preset--font-family--dm-sans: 'DM Sans', sans-serif;--wp--preset--font-family--dm-serif-display: 'DM Serif Display', serif;--wp--preset--font-family--domine: Domine, serif;--wp--preset--font-family--eb-garamond: 'EB Garamond', serif;--wp--preset--font-family--epilogue: Epilogue, sans-serif;--wp--preset--font-family--fahkwang: Fahkwang, sans-serif;--wp--preset--font-family--figtree: Figtree, sans-serif;--wp--preset--font-family--fira-sans: 'Fira Sans', sans-serif;--wp--preset--font-family--fjalla-one: 'Fjalla One', sans-serif;--wp--preset--font-family--fraunces: Fraunces, serif;--wp--preset--font-family--gabarito: Gabarito, system-ui;--wp--preset--font-family--ibm-plex-mono: 'IBM Plex Mono', monospace;--wp--preset--font-family--ibm-plex-sans: 'IBM Plex Sans', sans-serif;--wp--preset--font-family--ibarra-real-nova: 'Ibarra Real Nova', serif;--wp--preset--font-family--instrument-serif: 'Instrument Serif', serif;--wp--preset--font-family--inter: Inter, sans-serif;--wp--preset--font-family--josefin-sans: 'Josefin Sans', sans-serif;--wp--preset--font-family--jost: Jost, sans-serif;--wp--preset--font-family--libre-baskerville: 'Libre Baskerville', serif;--wp--preset--font-family--libre-franklin: 'Libre Franklin', sans-serif;--wp--preset--font-family--literata: Literata, serif;--wp--preset--font-family--lora: Lora, serif;--wp--preset--font-family--merriweather: Merriweather, serif;--wp--preset--font-family--montserrat: Montserrat, sans-serif;--wp--preset--font-family--newsreader: Newsreader, serif;--wp--preset--font-family--noto-sans-mono: 'Noto Sans Mono', sans-serif;--wp--preset--font-family--nunito: Nunito, sans-serif;--wp--preset--font-family--open-sans: 'Open Sans', sans-serif;--wp--preset--font-family--overpass: Overpass, sans-serif;--wp--preset--font-family--pt-serif: 'PT Serif', serif;--wp--preset--font-family--petrona: Petrona, serif;--wp--preset--font-family--piazzolla: Piazzolla, serif;--wp--preset--font-family--playfair-display: 'Playfair Display', serif;--wp--preset--font-family--plus-jakarta-sans: 'Plus Jakarta Sans', sans-serif;--wp--preset--font-family--poppins: Poppins, sans-serif;--wp--preset--font-family--raleway: Raleway, sans-serif;--wp--preset--font-family--roboto: Roboto, sans-serif;--wp--preset--font-family--roboto-slab: 'Roboto Slab', serif;--wp--preset--font-family--rubik: Rubik, sans-serif;--wp--preset--font-family--rufina: Rufina, serif;--wp--preset--font-family--sora: Sora, sans-serif;--wp--preset--font-family--source-sans-3: 'Source Sans 3', sans-serif;--wp--preset--font-family--source-serif-4: 'Source Serif 4', serif;--wp--preset--font-family--space-mono: 'Space Mono', monospace;--wp--preset--font-family--syne: Syne, sans-serif;--wp--preset--font-family--texturina: Texturina, serif;--wp--preset--font-family--urbanist: Urbanist, sans-serif;--wp--preset--font-family--work-sans: 'Work Sans', sans-serif;--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:where(.is-layout-flex){gap: 0.5em;}:where(.is-layout-grid){gap: 0.5em;}body .is-layout-flex{display: flex;}.is-layout-flex{flex-wrap: wrap;align-items: center;}.is-layout-flex > :is(*, div){margin: 0;}body .is-layout-grid{display: grid;}.is-layout-grid > :is(*, div){margin: 0;}:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;}.has-albert-sans-font-family{font-family: var(--wp--preset--font-family--albert-sans) !important;}.has-alegreya-font-family{font-family: var(--wp--preset--font-family--alegreya) !important;}.has-arvo-font-family{font-family: var(--wp--preset--font-family--arvo) !important;}.has-bodoni-moda-font-family{font-family: var(--wp--preset--font-family--bodoni-moda) !important;}.has-bricolage-grotesque-font-family{font-family: var(--wp--preset--font-family--bricolage-grotesque) !important;}.has-cabin-font-family{font-family: var(--wp--preset--font-family--cabin) !important;}.has-chivo-font-family{font-family: var(--wp--preset--font-family--chivo) !important;}.has-commissioner-font-family{font-family: var(--wp--preset--font-family--commissioner) !important;}.has-cormorant-font-family{font-family: var(--wp--preset--font-family--cormorant) !important;}.has-courier-prime-font-family{font-family: var(--wp--preset--font-family--courier-prime) !important;}.has-crimson-pro-font-family{font-family: var(--wp--preset--font-family--crimson-pro) !important;}.has-dm-mono-font-family{font-family: var(--wp--preset--font-family--dm-mono) !important;}.has-dm-sans-font-family{font-family: var(--wp--preset--font-family--dm-sans) !important;}.has-dm-serif-display-font-family{font-family: var(--wp--preset--font-family--dm-serif-display) !important;}.has-domine-font-family{font-family: var(--wp--preset--font-family--domine) !important;}.has-eb-garamond-font-family{font-family: var(--wp--preset--font-family--eb-garamond) !important;}.has-epilogue-font-family{font-family: var(--wp--preset--font-family--epilogue) !important;}.has-fahkwang-font-family{font-family: var(--wp--preset--font-family--fahkwang) !important;}.has-figtree-font-family{font-family: var(--wp--preset--font-family--figtree) !important;}.has-fira-sans-font-family{font-family: var(--wp--preset--font-family--fira-sans) !important;}.has-fjalla-one-font-family{font-family: var(--wp--preset--font-family--fjalla-one) !important;}.has-fraunces-font-family{font-family: var(--wp--preset--font-family--fraunces) !important;}.has-gabarito-font-family{font-family: var(--wp--preset--font-family--gabarito) !important;}.has-ibm-plex-mono-font-family{font-family: var(--wp--preset--font-family--ibm-plex-mono) !important;}.has-ibm-plex-sans-font-family{font-family: var(--wp--preset--font-family--ibm-plex-sans) !important;}.has-ibarra-real-nova-font-family{font-family: var(--wp--preset--font-family--ibarra-real-nova) !important;}.has-instrument-serif-font-family{font-family: var(--wp--preset--font-family--instrument-serif) !important;}.has-inter-font-family{font-family: var(--wp--preset--font-family--inter) !important;}.has-josefin-sans-font-family{font-family: var(--wp--preset--font-family--josefin-sans) !important;}.has-jost-font-family{font-family: var(--wp--preset--font-family--jost) !important;}.has-libre-baskerville-font-family{font-family: var(--wp--preset--font-family--libre-baskerville) !important;}.has-libre-franklin-font-family{font-family: var(--wp--preset--font-family--libre-franklin) !important;}.has-literata-font-family{font-family: var(--wp--preset--font-family--literata) !important;}.has-lora-font-family{font-family: var(--wp--preset--font-family--lora) !important;}.has-merriweather-font-family{font-family: var(--wp--preset--font-family--merriweather) !important;}.has-montserrat-font-family{font-family: var(--wp--preset--font-family--montserrat) !important;}.has-newsreader-font-family{font-family: var(--wp--preset--font-family--newsreader) !important;}.has-noto-sans-mono-font-family{font-family: var(--wp--preset--font-family--noto-sans-mono) !important;}.has-nunito-font-family{font-family: var(--wp--preset--font-family--nunito) !important;}.has-open-sans-font-family{font-family: var(--wp--preset--font-family--open-sans) !important;}.has-overpass-font-family{font-family: var(--wp--preset--font-family--overpass) !important;}.has-pt-serif-font-family{font-family: var(--wp--preset--font-family--pt-serif) !important;}.has-petrona-font-family{font-family: var(--wp--preset--font-family--petrona) !important;}.has-piazzolla-font-family{font-family: var(--wp--preset--font-family--piazzolla) !important;}.has-playfair-display-font-family{font-family: var(--wp--preset--font-family--playfair-display) !important;}.has-plus-jakarta-sans-font-family{font-family: var(--wp--preset--font-family--plus-jakarta-sans) !important;}.has-poppins-font-family{font-family: var(--wp--preset--font-family--poppins) !important;}.has-raleway-font-family{font-family: var(--wp--preset--font-family--raleway) !important;}.has-roboto-font-family{font-family: var(--wp--preset--font-family--roboto) !important;}.has-roboto-slab-font-family{font-family: var(--wp--preset--font-family--roboto-slab) !important;}.has-rubik-font-family{font-family: var(--wp--preset--font-family--rubik) !important;}.has-rufina-font-family{font-family: var(--wp--preset--font-family--rufina) !important;}.has-sora-font-family{font-family: var(--wp--preset--font-family--sora) !important;}.has-source-sans-3-font-family{font-family: var(--wp--preset--font-family--source-sans-3) !important;}.has-source-serif-4-font-family{font-family: var(--wp--preset--font-family--source-serif-4) !important;}.has-space-mono-font-family{font-family: var(--wp--preset--font-family--space-mono) !important;}.has-syne-font-family{font-family: var(--wp--preset--font-family--syne) !important;}.has-texturina-font-family{font-family: var(--wp--preset--font-family--texturina) !important;}.has-urbanist-font-family{font-family: var(--wp--preset--font-family--urbanist) !important;}.has-work-sans-font-family{font-family: var(--wp--preset--font-family--work-sans) !important;} :where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;} :root :where(.wp-block-pullquote){font-size: 1.5em;line-height: 1.6;} :where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;} </style> <link rel='stylesheet' id='seedlet-fonts-css' href='https://fonts-api.wp.com/css?family=Fira+Sans%3Aital%2Cwght%400%2C400%3B0%2C500%3B1%2C400%7CPlayfair+Display%3Aital%2Cwght%400%2C400%3B0%2C700%3B1%2C400&#038;subset=latin%2Clatin-ext' media='all' /> <link crossorigin='anonymous' rel='stylesheet' id='all-css-12-1' href='https://s0.wp.com/_static/??/wp-content/themes/pub/seedlet/style.css,/wp-content/themes/pub/seedlet/assets/css/style-navigation.css?m=1720456615j&cssminify=yes' type='text/css' media='all' /> <link crossorigin='anonymous' rel='stylesheet' id='print-css-13-1' href='https://s2.wp.com/wp-content/themes/pub/seedlet/assets/css/print.css?m=1603804565i&cssminify=yes' type='text/css' media='print' /> <link crossorigin='anonymous' rel='stylesheet' id='all-css-14-1' href='https://s0.wp.com/_static/??-eJx9y0EOwjAMRNELYQyiBbFAnKU1JgQ5dlQ7qnp7yq5s2M2X5uFcgUyDNTBeXNixthGd+SEcmJVwrmQFPBbhPbnvcENKgyotZXWceBRL60y4vjb5DyU2EKMhsulPwFOGPH3pvdyO/bU7dOdLf3p/AANwQOQ=&cssminify=yes' type='text/css' media='all' /> <style id='jetpack-global-styles-frontend-style-inline-css'> :root { --font-headings: unset; --font-base: unset; --font-headings-default: -apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,Oxygen-Sans,Ubuntu,Cantarell,"Helvetica Neue",sans-serif; --font-base-default: -apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,Oxygen-Sans,Ubuntu,Cantarell,"Helvetica Neue",sans-serif;} </style> <link crossorigin='anonymous' rel='stylesheet' id='all-css-16-1' href='https://s2.wp.com/wp-content/themes/h4/global.css?m=1420737423i&cssminify=yes' type='text/css' media='all' /> <script id="wpcom-actionbar-placeholder-js-extra"> var actionbardata = {"siteID":"70204527","postID":"0","siteURL":"https:\/\/arthurvandermerwe.com","xhrURL":"https:\/\/arthurvandermerwe.com\/wp-admin\/admin-ajax.php","nonce":"f1f7d771d3","isLoggedIn":"","statusMessage":"","subsEmailDefault":"instantly","proxyScriptUrl":"https:\/\/s0.wp.com\/wp-content\/js\/wpcom-proxy-request.js?ver=20211021","i18n":{"followedText":"New posts from this site will now appear in your <a href=\"https:\/\/wordpress.com\/read\">Reader<\/a>","foldBar":"Collapse this bar","unfoldBar":"Expand this bar"}}; </script> <script id="jetpack-mu-wpcom-settings-js-before"> var JETPACK_MU_WPCOM_SETTINGS = {"assetsUrl":"https:\/\/s1.wp.com\/wp-content\/mu-plugins\/jetpack-mu-wpcom-plugin\/sun\/vendor\/automattic\/jetpack-mu-wpcom\/src\/build\/"}; </script> <script crossorigin='anonymous' type='text/javascript' src='https://s1.wp.com/_static/??-eJyVzckOwjAMBNAfwriL2A6Ib0kbtyRyEytOt7+HiAvixmkOozeDq0AfQ6aQ0SsmziApbvvR6wG/uvykiRRl7lCJLFNGo0pZi+pVYTFJQWLYB8fc/MUd1TUMbvtFHccRhOfRBcU1JmusQs8Ffm4nwaUpASEGGK2k98RjuteXpjq11fl68y+6C1Fw'></script> <script id="rlt-proxy-js-after"> rltInitialize( {"token":null,"iframeOrigins":["https:\/\/widgets.wp.com"]} ); </script> <link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://arthurvandermerwe.wordpress.com/xmlrpc.php?rsd" /> <meta name="generator" content="WordPress.com" /> <!-- Jetpack Open Graph Tags --> <meta property="og:type" content="website" /> <meta property="og:title" content="May 2015 &#8211; Cryptography &amp; Payments" /> <meta property="og:site_name" content="Cryptography &amp; Payments" /> <meta property="og:image" content="https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=200" /> <meta property="og:image:width" content="200" /> <meta property="og:image:height" content="200" /> <meta property="og:image:alt" content="" /> <meta property="og:locale" content="en_US" /> <!-- End Jetpack Open Graph Tags --> <link rel='openid.server' href='https://arthurvandermerwe.com/?openidserver=1' /> <link rel='openid.delegate' href='https://arthurvandermerwe.com/' /> <link rel="search" type="application/opensearchdescription+xml" href="https://arthurvandermerwe.com/osd.xml" title="Cryptography &#38; Payments" /> <link rel="search" type="application/opensearchdescription+xml" href="https://s1.wp.com/opensearch.xml" title="WordPress.com" /> <style type="text/css"> .recentcomments a { display: inline !important; padding: 0 !important; margin: 0 !important; } table.recentcommentsavatartop img.avatar, table.recentcommentsavatarend img.avatar { border: 0px; margin: 0; } table.recentcommentsavatartop a, table.recentcommentsavatarend a { border: 0px !important; background-color: transparent !important; } td.recentcommentsavatarend, td.recentcommentsavatartop { padding: 0px 0px 1px 0px; margin: 0px; } td.recentcommentstextend { border: none !important; padding: 0px 0px 2px 10px; } .rtl td.recentcommentstextend { padding: 0px 10px 2px 0px; } td.recentcommentstexttop { border: none; padding: 0px 0px 0px 10px; } .rtl td.recentcommentstexttop { padding: 0px 10px 0px 0px; } </style> <meta name="application-name" content="Cryptography &amp; Payments" /><meta name="msapplication-window" content="width=device-width;height=device-height" /><meta name="msapplication-tooltip" content="Arthur Van Der Merwe" /><meta name="description" content="3 posts published by arthurvdmerwe during May 2015" /> <script> var wa_smart = { 'network_id': 3905, 'site_id': 560111, 'page_id': 1700829, 'blog_id': 70204527, 'post_id': null, 'theme': 'pub/seedlet', 'target': 'wp_blog_id=70204527;language=en', '_': { 'title': 'Advertisement', 'privacy_settings': 'Privacy Settings' }, 'top': { 'enabled': false, 'adflow_enabled': true, 'format_id': 135099 }, 'inline': { 'enabled': false, 'adflow_enabled': true, 'format_id': 110354, 'max_slots': 20, 'max_blaze_slots': 20 }, 'belowpost': { 'enabled': false, 'adflow_enabled': true, 'format_id': 134071 }, 'bottom_sticky': { 'enabled': false, 'adflow_enabled': true, 'format_id': 117571 }, 'sidebar': { 'enabled': false, 'adflow_enabled': true, 'format_id': 134686 }, 'sidebar_sticky_right': { 'enabled': false, 'adflow_enabled': true, 'format_id': 135281 }, 'gutenberg_rectangle': { 'enabled': false, 'adflow_enabled': true, 'format_id': 134788 }, 'gutenberg_leaderboard': { 'enabled': false, 'adflow_enabled': true, 'format_id': 135073 }, 'gutenberg_mobile_leaderboard': { 'enabled': false, 'adflow_enabled': true, 'format_id': 135098 }, 'gutenberg_skyscraper': { 'enabled': false, 'adflow_enabled': true, 'format_id': 135088 } }; wa_smart.cmd = []; </script> <script type="text/javascript"> function __ATA_CC() {var v = document.cookie.match('(^|;) ?personalized-ads-consent=([^;]*)(;|$)');return v ? 1 : 0;} var __ATA_PP = { 'pt': 3, 'ht': 1, 'tn': 'seedlet', 'uloggedin': 0, 'amp': false, 'consent': __ATA_CC(), 'gdpr_applies': false, 'ad': { 'label': { 'text': 'Advertisements' }, 'reportAd': { 'text': 'Report this ad' } }, 'disabled_slot_formats': [], 'siteid': 70204527, 'afp_ad_client': 'pub-6694573643007653' }; var __ATA = __ATA || {}; __ATA.cmd = __ATA.cmd || []; __ATA.criteo = __ATA.criteo || {}; __ATA.criteo.cmd = __ATA.criteo.cmd || []; </script> <script type="text/javascript"> (function(){var g=Date.now||function(){return+new Date};function h(a,b){a:{for(var c=a.length,d="string"==typeof a?a.split(""):a,e=0;e<c;e++)if(e in d&&b.call(void 0,d[e],e,a)){b=e;break a}b=-1}return 0>b?null:"string"==typeof a?a.charAt(b):a[b]};function k(a,b,c){c=null!=c?"="+encodeURIComponent(String(c)):"";if(b+=c){c=a.indexOf("#");0>c&&(c=a.length);var d=a.indexOf("?");if(0>d||d>c){d=c;var e=""}else e=a.substring(d+1,c);a=[a.substr(0,d),e,a.substr(c)];c=a[1];a[1]=b?c?c+"&"+b:b:c;a=a[0]+(a[1]?"?"+a[1]:"")+a[2]}return a};var l=0;function m(a,b){var c=document.createElement("script");c.src=a;c.onload=function(){b&&b(void 0)};c.onerror=function(){b&&b("error")};a=document.getElementsByTagName("head");var d;a&&0!==a.length?d=a[0]:d=document.documentElement;d.appendChild(c)}function n(a){var b=void 0===b?document.cookie:b;return(b=h(b.split("; "),function(c){return-1!=c.indexOf(a+"=")}))?b.split("=")[1]:""}function p(a){return"string"==typeof a&&0<a.length} function r(a,b,c){b=void 0===b?"":b;c=void 0===c?".":c;var d=[];Object.keys(a).forEach(function(e){var f=a[e],q=typeof f;"object"==q&&null!=f||"function"==q?d.push(r(f,b+e+c)):null!==f&&void 0!==f&&(e=encodeURIComponent(b+e),d.push(e+"="+encodeURIComponent(f)))});return d.filter(p).join("&")}function t(a,b){a||((window.__ATA||{}).config=b.c,m(b.url))}var u=Math.floor(1E13*Math.random()),v=window.__ATA||{};window.__ATA=v;window.__ATA.cmd=v.cmd||[];v.rid=u;v.createdAt=g();var w=window.__ATA||{},x="s.pubmine.com"; w&&w.serverDomain&&(x=w.serverDomain);var y="//"+x+"/conf",z=window.top===window,A=window.__ATA_PP&&window.__ATA_PP.gdpr_applies,B="boolean"===typeof A?Number(A):null,C=window.__ATA_PP||null,D=z?document.referrer?document.referrer:null:null,E=z?window.location.href:document.referrer?document.referrer:null,F,G=n("__ATA_tuuid");F=G?G:null;var H=window.innerWidth+"x"+window.innerHeight,I=n("usprivacy"),J=r({gdpr:B,pp:C,rid:u,src:D,ref:E,tuuid:F,vp:H,us_privacy:I?I:null},"","."); (function(a){var b=void 0===b?"cb":b;l++;var c="callback__"+g().toString(36)+"_"+l.toString(36);a=k(a,b,c);window[c]=function(d){t(void 0,d)};m(a,function(d){d&&t(d)})})(y+"?"+J);}).call(this); </script> <script> var sas_fallback = sas_fallback || []; sas_fallback.push( { tag: "&lt;div id=&quot;atatags-702045271-{{unique_id}}&quot;&gt;&lt;/div&gt;&lt;script&gt;__ATA.cmd.push(function() {__ATA.initDynamicSlot({id: \'atatags-702045271-{{unique_id}}\',location: 120,formFactor: \'001\',label: {text: \'Advertisements\',},creative: {reportAd: {text: \'Report this ad\',},privacySettings: {text: \'Privacy\',}}});});&lt;/script&gt;", type: 'belowpost' }, { tag: "&lt;div id=&quot;atatags-702045271-{{unique_id}}&quot;&gt;&lt;/div&gt;&lt;script&gt;__ATA.cmd.push(function() {__ATA.initDynamicSlot({id: \'atatags-702045271-{{unique_id}}\',location: 310,formFactor: \'001\',label: {text: \'Advertisements\',},creative: {reportAd: {text: \'Report this ad\',},privacySettings: {text: \'Privacy\',}}});});&lt;/script&gt;", type: 'inline' }, { tag: "&lt;div id=&quot;atatags-702045271-{{unique_id}}&quot;&gt;&lt;/div&gt;&lt;script&gt;__ATA.cmd.push(function() {__ATA.initDynamicSlot({id: \'atatags-702045271-{{unique_id}}\',location: 140,formFactor: \'003\',label: {text: \'Advertisements\',},creative: {reportAd: {text: \'Report this ad\',},privacySettings: {text: \'Privacy\',}}});});&lt;/script&gt;", type: 'sidebar' }, { tag: "&lt;div id=&quot;atatags-702045271-{{unique_id}}&quot;&gt;&lt;/div&gt;&lt;script&gt;__ATA.cmd.push(function() {__ATA.initDynamicSlot({id: \'atatags-702045271-{{unique_id}}\',location: 110,formFactor: \'002\',label: {text: \'Advertisements\',},creative: {reportAd: {text: \'Report this ad\',},privacySettings: {text: \'Privacy\',}}});});&lt;/script&gt;", type: 'top' } ); </script><link rel="icon" href="https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=32" sizes="32x32" /> <link rel="icon" href="https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=192" sizes="192x192" /> <link rel="apple-touch-icon" href="https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=180" /> <meta name="msapplication-TileImage" content="https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=270" /> </head> <body class="archive date wp-embed-responsive customizer-styles-applied hfeed has-main-navigation jetpack-reblog-enabled"> <div id="page" class="site"> <a class="skip-link screen-reader-text" href="#content">Skip to content</a> <header id="masthead" class="site-header header_classes has-title-and-tagline has-menu" role="banner"> <div class="site-branding"> <p class="site-title"><a href="https://arthurvandermerwe.com/" rel="home">Cryptography &amp; Payments</a></p> <p class="site-description"> Arthur Van Der Merwe </p> </div><!-- .site-branding --> <nav id="site-navigation" class="primary-navigation" role="navigation" aria-label="Main"> <button id="primary-close-menu" class="button close"> <span class="dropdown-icon close">Close <svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M12 10.9394L5.53033 4.46973L4.46967 5.53039L10.9393 12.0001L4.46967 18.4697L5.53033 19.5304L12 13.0607L18.4697 19.5304L19.5303 18.4697L13.0607 12.0001L19.5303 5.53039L18.4697 4.46973L12 10.9394Z" fill="currentColor"/></svg></span> <span class="hide-visually collapsed-text">collapsed</span> </button> <div class="primary-menu-container"><ul id="menu-financial-switching-1" class="menu-wrapper"><li class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-239"><a href="https://arthurvandermerwe.com/category/hsm/">HSM</a></li> <li class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-240"><a href="https://arthurvandermerwe.com/category/cryptography-2/">Cryptography</a></li> <li class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-241"><a href="https://arthurvandermerwe.com/category/financial-switching/">Financial Switching</a></li> <li class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-242"><a href="https://arthurvandermerwe.com/category/atm-tracing/">ATM Tracing</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-27"><a href="https://arthurvandermerwe.com/downloads/">Downloads</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-5"><a href="https://arthurvandermerwe.com/about/">About</a></li> </ul></div> </nav><!-- #site-navigation --> <div class="menu-button-container"> <button id="primary-open-menu" class="button open"> <span class="dropdown-icon open">Menu <svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M4.5 6H19.5V7.5H4.5V6ZM4.5 12H19.5V13.5H4.5V12ZM19.5 18H4.5V19.5H19.5V18Z" fill="currentColor"/></svg></span> <span class="hide-visually expanded-text">expanded</span> </button> </div> <div class="menu-button-container"> </div> </header><!-- #masthead --> <div id="content" class="site-content"> <section id="primary" class="content-area"> <main id="main" class="site-main" role="main"> <header class="page-header default-max-width"> <h1 class="page-title"><span class="archive-prefix">Monthly Archives: </span><span class="page-description">May 2015</span></h1> </header><!-- .page-header --> <article id="post-138" class="post-138 post type-post status-publish format-standard hentry category-financial-switching category-uncategorized tag-ans-x9-24 tag-bdk tag-desdecrypt tag-desencrypt tag-iksns tag-ipek tag-ksn tag-tripledesdecrypt tag-tripledesencrypt entry"> <header class="entry-header default-max-width"> <h2 class="entry-title"><a href="https://arthurvandermerwe.com/2015/05/30/dukpt-explained-with-examples/" rel="bookmark">DUKPT Explained with&nbsp;examples</a></h2> </header><!-- .entry-header --> <div class="entry-content"> <p>Derived Unique Key Per Transaction (DUKPT) process that&#8217;s described in Annex A of ANS X9.24-2004.</p> <p>It&#8217;s generally considered to be complex, but I&#8217;ve simplified it slightly with the help of online resources.</p> <h2>Key Management<br /> <a id="user-content-usage" class="anchor" href="#usage"></a></h2> <p>Here&#8217;s a basic outline of the technique:</p> <ol> <li>You&#8217;re given a Base Derivation Key (BDK), which you assign to a swiper (note that the same BDK <em>can</em> be assigned to multiple swipers).</li> <li>You&#8217;ll use the BDK along with the device&#8217;s own unique Key Serial Number (KSN) to generate an Initial PIN Encryption Key (IPEK) for the device.</li> <li>You&#8217;ll assign this IPEK to a swiper, which uses it to irreversibly generate a list of future keys, which it&#8217;ll use to encrypt its messages.</li> <li>The swiper&#8217;s KSN is used along with one of its future keys to encrypt a message, and after each swipe it&#8217;ll increment the value of its KSN.</li> <li>Whenever a swiper takes a card it formats the card&#8217;s information into a series of tracks, each track having a particular set of information (e.g. card number, holder&#8217;s name, expiration date).</li> <li>The swiper usually encrypts these tracks using one of its generated future keys (called the &#8220;Session Key&#8221;) along with its current KSN. It&#8217;ll then increment the value of its KSN and discard the future key it used.</li> <li>At this point you&#8217;ll probably have an encrypted track along with the KSN the swiper used to encrypt it.</li> <li>It&#8217;s your responsibility to determine what BDK was used to initialize this device, and from there you&#8217;ll use the BDK and KSN to rederive the IPEK, which is used to rederive the Session Key, which is finally used to decrypt the message.</li> </ol> <p>There&#8217;s a lot of technical information to be said about key management, but this isn&#8217;t the place for that. In some cases your provider/manufacturer (e.g. MagTek) will supply you with swipers that need to be initialized with an IPEK, and your supplier will usually have a manual that walks you through that process. If you&#8217;re doing encryption/decryption through a third party who also supplies swipers, they may have already loaded the devices with that information; what&#8217;s more is they may not even given you the BDK that belongs to your device in order to reduce the risk of security threats.</p> <hr /> <p><strong>Note:</strong> Key management is beyond the scope of this explanation. Whatever you do with your keys, just make sure it&#8217;s secure.</p> <hr /> <p>One methodology I&#8217;ve seen that&#8217;ll allow you to associate a particular KSN to a BDK is to take the current KSN you&#8217;ve been given, mask it to retrieve the Initial Key Serial Number (IKSN), and look up the BDK in a table that maps IKSNs to BDKs:</p> <p>Example:</p> <pre><code>ksn = FFFF9876543210E00008 iksn = ksn &amp; FFFFFFFFFFFFFFE00000 // FFFF9876543210E00000 </code></pre> <p>You&#8217;d then have a table that looks like:</p> <table> <thead> <tr> <th align="center">IKSN</th> <th align="center">BDK</th> </tr> </thead> <tbody> <tr> <td align="center">0xFFFF9876543210E00000</td> <td align="center">0123456789ABCDEFFEDCBA9876543210</td> </tr> <tr> <td align="center">&#8230;</td> <td align="center">&#8230;</td> </tr> </tbody> </table> <p>From which you could easily grab the BDK <code>0123456789ABCDEFFEDCBA9876543210</code>.</p> <h2><a id="user-content-algorithm" class="anchor" href="#algorithm"></a>Algorithm</h2> <hr /> <p><strong>Note:</strong> Assume that all numeric values are hexadecimal numbers, or the representation of a sequence of bytes as a hexadecimal number.</p> <hr /> <p>The following are the BDK, KSN, and encrypted track message (cryptogram) we&#8217;ve been given:</p> <pre><code>bdk = 0123456789ABCDEFFEDCBA9876543210 ksn = FFFF9876543210E00008 cryptogram = C25C1D1197D31CAA87285D59A892047426D9182EC11353C051ADD6D0F072A6CB3436560B3071FC1FD11D9F7E74886742D9BEE0CFD1EA1064C213BB55278B2F12 </code></pre> <p>Here&#8217;s an example of the unencrypted track 1 data (cryptogram above), and below that is its value in hex; this is what we&#8217;ll get after successfully decrypting the cryptogram:</p> <pre><code>%B5452300551227189^HOGAN/PAUL ^08043210000000725000000? 2542353435323330303535313232373138395E484F47414E2F5041554C2020202020205E30383034333231303030303030303732353030303030303F00000000 </code></pre> <hr /> <p><strong>Note:</strong> As you&#8217;re probably already aware, this algorithm is best described using big numbers, which can&#8217;t be represented as literals in some programming languages (like Java or C#). However, many languages have classes that allow you to represent big numbers in other ways (e.g., java.math.BigInteger, System.Numerics.BigInteger). It&#8217;s your job to adapt this algorithm so that it can be represented in your language of choice. Two small problems I encountered were ensuring the correct endianness and signedness were being used (this algorithm requires the byte order to be big endian and that unsigned integers are used). I made a utility class called BigInt to do this for me.</p> <hr /> <p>First, let&#8217;s define a few standard functions:</p> <ul> <li><a href="http://en.wikipedia.org/wiki/Data_Encryption_Standard">DES</a> and <a href="http://en.wikipedia.org/wiki/Triple_DES">Triple DES</a> refer to their respective cryptographic algorithms. Most programming languages have access to some implementation of these ciphers either through OpenSSL or Bouncy Castle. These ciphers are initialized with a zeroed out IV of 8 bytes, they&#8217;re zero-padded, and use Cipher-Block Chaining (CBC). Let&#8217;s define the signatures for these standard functions that&#8217;ll be used throughout this algorithm: <ul> <li><code>DesEncrypt(key, message) -&gt; returns cryptogram</code></li> <li><code>DesDecrypt(key, cryptogram) -&gt; returns message</code></li> <li><code>TripleDesEncrypt(key, message) -&gt; returns cryptogram</code></li> <li><code>TripleDesDecrypt(key, cryptogram) -&gt; returns message</code></li> </ul> </li> </ul> <p>First we must create the IPEK given then KSN and BDK:</p> <pre><code>CreateIpek(ksn, bdk) { return TripleDesEncrypt(bdk, (ksn &amp; KsnMask) &gt;&gt; 16) &lt;&lt; 64 | TripleDesEncrypt(bdk ^ KeyMask, (ksn &amp; KsnMask) &gt;&gt; 16) } </code></pre> <p>Now we can get the IPEK:</p> <pre><code>ipek = CreateIpek(ksn, bdk) = CreateIpek(FFFF9876543210E00008, 0123456789ABCDEFFEDCBA9876543210) = 6AC292FAA1315B4D858AB3A3D7D5933A </code></pre> <p>After that we need a way to get the Session Key (this one is more complicated):</p> <pre><code>CreateSessionKey(ipek, ksn) { return DeriveKey(ipek, ksn) ^ FF00000000000000FF } </code></pre> <p>The DeriveKey method finds the IKSN and generates session keys until it gets to the one that corresponds to the current KSN. We define this method as:</p> <pre><code>DeriveKey(ipek, ksn) { ksnReg = ksn &amp; FFFFFFFFFFE00000 curKey = ipek for (shiftReg = 0x100000; shiftReg &gt; 0; shiftReg &gt;&gt;= 1) if ((shiftReg &amp; ksn &amp; 1FFFFF) &gt; 0) curKey = GenerateKey(curKey, ksnReg |= shiftReg) return curKey } </code></pre> <p>Where the GenerateKey method looks like:</p> <pre><code>GenerateKey(key, ksn) { return EncryptRegister(key ^ KeyMask, ksn) &lt;&lt; 64 | EncryptRegister(key, ksn) } </code></pre> <p>And EncryptRegister looks like:</p> <pre><code>EncryptRegister(key, reg) { return (key &amp; FFFFFFFFFFFFFFFF) ^ DesEncrypt((key &amp; FFFFFFFFFFFFFFFF0000000000000000) &gt;&gt; 64, key &amp; FFFFFFFFFFFFFFFF ^ reg) } </code></pre> <p>Then you can generate the Session Key given the IPEK and KSN:</p> <pre><code>key = CreateSessionKey(ipek, ksn) = CreateSessionKey(6AC292FAA1315B4D858AB3A3D7D5933A, FFFF9876543210E00008) = 27F66D5244FF621EAA6F6120EDEB427F </code></pre> <p>Which can be used to decrypt the cryptogram:</p> <pre><code>message = TripleDesDecrypt(key, cryptogram) = TripleDesDecrypt(27F66D5244FF621EAA6F6120EDEB427F, C25C1D1197D31CAA87285D59A892047426D9182EC11353C051ADD6D0F072A6CB3436560B3071FC1FD11D9F7E74886742D9BEE0CFD1EA1064C213BB55278B2F12) = 2542353435323330303535313232373138395E484F47414E2F5041554C2020202020205E30383034333231303030303030303732353030303030303F00000000 = %B5452300551227189^HOGAN/PAUL ^08043210000000725000000? </code></pre> <p>That&#8217;s it, you&#8217;re done!</p> <div id="atatags-702045271-6742079f24d96"></div> <script> __ATA.cmd.push(function() { __ATA.initDynamicSlot({ id: 'atatags-702045271-6742079f24d96', location: 120, formFactor: '001', label: { text: 'Advertisements', }, creative: { reportAd: { text: 'Report this ad', }, privacySettings: { text: 'Privacy', } } }); }); </script> </div><!-- .entry-content --> <footer class="entry-footer default-max-width"> <span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M15 7.5C15 9.15685 13.6569 10.5 12 10.5C10.3431 10.5 9 9.15685 9 7.5C9 5.84315 10.3431 4.5 12 4.5C13.6569 4.5 15 5.84315 15 7.5ZM16.5 7.5C16.5 9.98528 14.4853 12 12 12C9.51472 12 7.5 9.98528 7.5 7.5C7.5 5.01472 9.51472 3 12 3C14.4853 3 16.5 5.01472 16.5 7.5ZM19.5 19.5V16.245C19.5 14.729 18.271 13.5 16.755 13.5L7.245 13.5C5.72898 13.5 4.5 14.729 4.5 16.245L4.5 19.5H6L6 16.245C6 15.5574 6.5574 15 7.245 15L16.755 15C17.4426 15 18 15.5574 18 16.245V19.5H19.5Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://arthurvandermerwe.com/author/arthurvdmerwe/">arthurvdmerwe</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M19.5 7.5H4.5V19.0005C4.5 19.2764 4.72363 19.5 4.9995 19.5H19.0005C19.2764 19.5 19.5 19.2764 19.5 19.0005V7.5ZM3 7.5V4.9995V4.995C3 3.89319 3.89319 3 4.995 3H4.9995H19.0005H19.005C20.1068 3 21 3.89319 21 4.995V4.9995V7.5V19.0005C21 20.1048 20.1048 21 19.0005 21H4.9995C3.89521 21 3 20.1048 3 19.0005V7.5ZM7.5 10.5H9V12H7.5V10.5ZM9 15H7.5V16.5H9V15ZM11.25 10.5H12.75V12H11.25V10.5ZM12.75 15H11.25V16.5H12.75V15ZM15 10.5H16.5V12H15V10.5ZM16.5 15H15V16.5H16.5V15Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/30/dukpt-explained-with-examples/" rel="bookmark"><time class="entry-date published" datetime="2015-05-30T15:30:52+10:00">May 30, 2015</time><time class="updated" datetime="2015-05-30T15:37:00+10:00">May 30, 2015</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M12.1979 8.25L11.2098 6.27363C11.1259 6.10593 10.9545 6 10.767 6H4.995C4.72162 6 4.5 6.22162 4.5 6.495V17.505C4.5 17.7784 4.72162 18 4.995 18H19.0005C19.2764 18 19.5 17.7764 19.5 17.5005V8.7495C19.5 8.47363 19.2764 8.25 19.0005 8.25H12.1979ZM13.125 6.75H19.0005C20.1048 6.75 21 7.64521 21 8.7495V17.5005C21 18.6048 20.1048 19.5 19.0005 19.5H4.995C3.89319 19.5 3 18.6068 3 17.505V6.495C3 5.39319 3.89319 4.5 4.995 4.5H10.767C11.5227 4.5 12.2135 4.92693 12.5514 5.60281L13.125 6.75Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted in</span><a href="https://arthurvandermerwe.com/category/financial-switching/" rel="category tag">Financial Switching</a>, <a href="https://arthurvandermerwe.com/category/uncategorized/" rel="category tag">Uncategorized</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M3 12.2045C3 12.5941 3.15158 12.9684 3.42267 13.2482L9.71878 19.747C11.0769 21.1489 13.3201 21.1667 14.7003 19.7865L19.7873 14.6995C21.1677 13.319 21.1497 11.0753 19.7471 9.71731L13.2459 3.42238C12.9661 3.15147 12.5919 3 12.2025 3H4.5C3.67157 3 3 3.67157 3 4.5V12.2045ZM12.2025 4.5H4.5V12.2045L10.7961 18.7033C11.5714 19.5035 12.8518 19.5137 13.6396 18.7258L18.7266 13.6388C19.5146 12.8509 19.5043 11.5701 18.7037 10.7949L12.2025 4.5ZM8.4975 9.495C9.0484 9.495 9.495 9.0484 9.495 8.4975C9.495 7.9466 9.0484 7.5 8.4975 7.5C7.9466 7.5 7.5 7.9466 7.5 8.4975C7.5 9.0484 7.9466 9.495 8.4975 9.495Z" fill="currentColor"/></svg><span class="screen-reader-text">Tags:</span><a href="https://arthurvandermerwe.com/tag/ans-x9-24/" rel="tag">ANS X9.24</a>, <a href="https://arthurvandermerwe.com/tag/bdk/" rel="tag">BDK</a>, <a href="https://arthurvandermerwe.com/tag/desdecrypt/" rel="tag">DesDecrypt</a>, <a href="https://arthurvandermerwe.com/tag/desencrypt/" rel="tag">DesEncrypt</a>, <a href="https://arthurvandermerwe.com/tag/iksns/" rel="tag">IKSNs</a>, <a href="https://arthurvandermerwe.com/tag/ipek/" rel="tag">IPEK</a>, <a href="https://arthurvandermerwe.com/tag/ksn/" rel="tag">KSN</a>, <a href="https://arthurvandermerwe.com/tag/tripledesdecrypt/" rel="tag">TripleDesDecrypt</a>, <a href="https://arthurvandermerwe.com/tag/tripledesencrypt/" rel="tag">TripleDesEncrypt</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M10.0458 15.0001L5.99998 17.697L5.99999 6.49478C5.99999 6.22141 6.2216 5.99979 6.49498 5.99978L17.505 5.99951C17.7784 5.9995 18 6.22113 18 6.49451L18 14.5046C18 14.778 17.7784 14.9996 17.505 14.9996L10.0458 15.0001ZM10.5 16.5L17.5051 16.4996C18.6069 16.4995 19.5 15.6063 19.5 14.5046L19.5 6.49451C19.5 5.39268 18.6068 4.49948 17.5049 4.49951L6.49494 4.49978C5.39315 4.49981 4.49999 5.39299 4.49999 6.49478L4.49998 18.3483C4.49998 18.9842 5.01549 19.4997 5.6514 19.4997C5.8787 19.4997 6.10091 19.4324 6.29004 19.3063L10.5 16.5Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/30/dukpt-explained-with-examples/#comments">18 Comments<span class="screen-reader-text"> on DUKPT Explained with&nbsp;examples</span></a></span> </footer><!-- .entry-footer --> </article><!-- #post-${ID} --> <article id="post-131" class="post-131 post type-post status-publish format-standard hentry category-financial-switching tag-3574932 tag-1799144 tag-diy tag-kca tag-kek1 tag-kek2 tag-keks tag-ki tag-kia tag-kmach tag-management-information tag-pksp tag-pos-terminal tag-ppasn tag-ppid tag-rsa tag-sktcu tag-tcu tag-terminal-manufacturer entry"> <header class="entry-header default-max-width"> <h2 class="entry-title"><a href="https://arthurvandermerwe.com/2015/05/28/eftpos-initialisation-using-rsa-cryptography/" rel="bookmark">EFTPOS Initialisation using RSA&nbsp;Cryptography</a></h2> </header><!-- .entry-header --> <div class="entry-content"> <p>Before you start with RSA, you should generate a public and private key pair using your HSM. These can be group keys or specific to the terminal you need to connect. Your terminal manufacturer will also provide its public key and modulus. Using these keys you will be able to calculate the TMK1 and TMK2 and also your session keys. The process is in fact very simple.</p> <p>Here is an example of how to create these keys using a Thales HSM</p> <p>Generating an 1536 bit RSA Key</p> <p>Input</p> <pre><span style="color:#999999;"><em>001-EI2153601</em></span></pre> <p>Output</p> <pre><span style="color:#999999;">001-EJ00</span></pre> <pre><span style="color:#000000;">Public Key</span> <span style="color:#999999;">3081C80281C0A0FAFB1789B87F6F075B04FE60B5F20AC9D658E6C9B9B4E82AD41FD748A5A00CAF0A5691D2D01726AB073AFB7B91810430F240244E0D4737A397C747FC67C622B12E3654DCDF4F58EE29241616AE7EBA08A1E16DB79E09529FB6CA92213F2DFAB3F677793BF977D640107FBF9833842A0BFBF5F871709E78EE5A152E0BBBBBDDED80D193BAC3033FE412B3C420532A8B309942E76F7A9FB4475B8EDEFDDADC4C101FF02F74BEE0261C681E314124654C39411E2CE56FE719A45CA7592B8431D30203010001</span></pre> <pre><span style="color:#000000;">Private key length</span> <span style="color:#999999;">0488</span></pre> <pre><span style="color:#000000;">Private Key</span> <span style="color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span></pre> <p>Generate a <span style="color:#333333;">MAC</span> on 1536 RSA key</p> <p>Input</p> <pre><span style="color:#999999;">002-EO01&lt;3081C80281C0A0FAFB1789B87F6F075B04FE60B5F20AC9D658E6C9B9B4E82AD41FD748A5A00CAF0A5691D2D01726AB073AFB7B91810430F240244E0D4737A397C747FC67C622B12E3654DCDF4F58EE29241616AE7EBA08A1E16DB79E09529FB6CA92213F2DFAB3F677793BF977D640107FBF9833842A0BFBF5F871709E78EE5A152E0BBBBBDDED80D193BAC3033FE412B3C420532A8B309942E76F7A9FB4475B8EDEFDDADC4C101FF02F74BEE0261C681E314124654C39411E2CE56FE719A45CA7592B8431D30203010001&gt;</span></pre> <p>Output</p> <pre><span style="color:#999999;">002-EP00&lt;<span style="color:#333333;">C905141E</span>&gt;&lt;3081C80281C0A0FAFB1789B87F6F075B04FE60B5F20AC9D658E6C9B9B4E82AD41FD748A5A00CAF0A5691D2D01726AB073AFB7B91810430F240244E0D4737A397C747FC67C622B12E3654DCDF4F58EE29241616AE7EBA08A1E16DB79E09529FB6CA92213F2DFAB3F677793BF977D640107FBF9833842A0BFBF5F871709E78EE5A152E0BBBBBDDED80D193BAC3033FE412B3C420532A8B309942E76F7A9FB4475B8EDEFDDADC4C101FF02F74BEE0261C681E314124654C39411E2CE56FE719A45CA7592B8431D30203010101&gt;</span></pre> <p>This is a generic version of RSA encryption using POS pinheads, there are variations in the field. Please keep that in mind when reading this.</p> <p>Now when a POS terminal logs on for the first time it shall always logon using a 9820 message with a network management information code of 191, containing the TCU public key signed by the manufacturer&#8217;s secret key, and the un-enciphered PPID.</p> <p>The Financial Switch shall respond with a 9830 message with the same network management information code, communicating the public key of the sponsor host (PKsp), and a random number.</p> <p>The PIN Pad shall then generate the KI and send a 9820 message with a network management information code of 192 to the Financial Switch, containing the KI, PPID, date &amp; time stamp, the random number and user data enciphered under the Financial Switch&#8217;s public key (PKsp) and signed by the TCU&#8217;s secret key (SKtcu). You will need to extract this information using your HSM H8 command, example below:</p> <p>Input Data:</p> <pre><span style="color:#999999;"><em>001-H801&lt;FDC694A6&gt;</em></span> <span style="color:#999999;"><em>&lt;30550250AB378F98E373BBC6FA5E698F4F095A6D693A851E53C35CC9633947399C09D70932776DBEA5F2F0F0C4DAB4693CACB4D07B19242FF0435C55E3D4E28EFD563457F7EBA31BE1123DEA78CEC1573716130B020103&gt;</em></span> <span style="color:#999999;"><em>;990192</em></span> <span style="color:#999999;"><em>&lt;99658789F42672E7C51CB6ECAF3F061BBABCD954D4113E1CD9BD7BD4DF1BD94E6CBC10F497E9AE68265E87F77BFF293AA2D9FDE9C1A8F12A04D9B4D8DB9F5EAEE4690883838DEF670174E70C79E674F97E2457DD85EEEB346A17DD1F39CB3E8B2D69949436051994F8687F0FEE6558F28180D5A63946CD60604B1C82F6AE14454F5824CBFDCEE07478D2F0239299B64CD900DFF7559423E98F0C7AB8229933E4DD5A5E0BD736F8172668676949493577E323FC8EC592437F6DF20EDB5FBB6E92&gt;</em></span> <span style="color:#999999;"><em>;0080</em></span> <span style="color:#999999;"><em>&lt;7C9DDD3AEFF1D50BAFD11DBAF240BE827BAA156F9E8BB555CC019E183B3708F26EBE6C94702A9AD7CC1D2159CF587437532969D113C70BD622EB81AFC06E9408F1B69F3ED838A9EADFB41FB0E6E4202E&gt;</em></span> <span style="color:#999999;"><em>;1234567890123456;000</em></span></pre> <p>Response:</p> <pre><span style="color:#999999;"><em>001-H900</em></span> <span style="color:#999999;"><em>H604A678C8C78E1B9CFD415220D418E76</em></span> <span style="color:#999999;"><em>U9912C5D8B113B5E9D6787D57EE9E43BA</em></span> <span style="color:#999999;"><em>1122334455</em></span> <span style="color:#999999;"><em>9876543210987654</em></span></pre> <p>&nbsp;</p> <p>The Financial Switch shall check the PPID and random number. If the check fails, it will respond with a 9830 with a response code of &#8220;63&#8221;.</p> <p>Where the Financial Switch is satisfied with the contents of the second 9820 message, it shall respond with the KCA and the KMACH enciphered under KI and its AIIC in the clear. When the PIN Pad has deciphered KCA and KMACH, it shall erase KI.</p> <p>At this time the PIN Pad shall calculate the KIA. When the KIA has been calculated, the PIN Pad shall erase KCA.</p> <p>The POS terminal shall then generate a 9820 message with a network management information code of 193 to the Financial Switch containing the PPID and the Financial Switch shall respond with a 9830 response containing the two initial KEKs and the PPASN.</p> <p>You can generate this using the C0/C1 HSM command.</p> <p>The POS terminal shall validate the MAC on the two KEKs and the PPASN and, if the MAC is valid, shall install KEK1, KEK2 and the PPASN and shall calculate the single length DES key KMACI. These keys are the terminal initial keys, that will updated in the season key exchange.</p> <p>Once this has been carried out, the PIN Pad shall erase the KIA.</p> <p>When these tasks have been completed, the POS terminal shall carry out its normal logon and session key installation with the Financial Switch. As the processing (initial logon then normal logon and session key installation) completes, the POS terminal will move into the &#8220;Ready&#8221; state.</p> <p>easy as pie!</p> <div id="atatags-702045275-6742079f260b0"> <script type="text/javascript"> __ATA.cmd.push(function() { __ATA.initVideoSlot('atatags-702045275-6742079f260b0', { sectionId: '702045275', format: 'inread' }); }); </script> </div> </div><!-- .entry-content --> <footer class="entry-footer default-max-width"> <span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M15 7.5C15 9.15685 13.6569 10.5 12 10.5C10.3431 10.5 9 9.15685 9 7.5C9 5.84315 10.3431 4.5 12 4.5C13.6569 4.5 15 5.84315 15 7.5ZM16.5 7.5C16.5 9.98528 14.4853 12 12 12C9.51472 12 7.5 9.98528 7.5 7.5C7.5 5.01472 9.51472 3 12 3C14.4853 3 16.5 5.01472 16.5 7.5ZM19.5 19.5V16.245C19.5 14.729 18.271 13.5 16.755 13.5L7.245 13.5C5.72898 13.5 4.5 14.729 4.5 16.245L4.5 19.5H6L6 16.245C6 15.5574 6.5574 15 7.245 15L16.755 15C17.4426 15 18 15.5574 18 16.245V19.5H19.5Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://arthurvandermerwe.com/author/arthurvdmerwe/">arthurvdmerwe</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M19.5 7.5H4.5V19.0005C4.5 19.2764 4.72363 19.5 4.9995 19.5H19.0005C19.2764 19.5 19.5 19.2764 19.5 19.0005V7.5ZM3 7.5V4.9995V4.995C3 3.89319 3.89319 3 4.995 3H4.9995H19.0005H19.005C20.1068 3 21 3.89319 21 4.995V4.9995V7.5V19.0005C21 20.1048 20.1048 21 19.0005 21H4.9995C3.89521 21 3 20.1048 3 19.0005V7.5ZM7.5 10.5H9V12H7.5V10.5ZM9 15H7.5V16.5H9V15ZM11.25 10.5H12.75V12H11.25V10.5ZM12.75 15H11.25V16.5H12.75V15ZM15 10.5H16.5V12H15V10.5ZM16.5 15H15V16.5H16.5V15Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/28/eftpos-initialisation-using-rsa-cryptography/" rel="bookmark"><time class="entry-date published" datetime="2015-05-28T13:04:40+10:00">May 28, 2015</time><time class="updated" datetime="2015-05-28T13:24:54+10:00">May 28, 2015</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M12.1979 8.25L11.2098 6.27363C11.1259 6.10593 10.9545 6 10.767 6H4.995C4.72162 6 4.5 6.22162 4.5 6.495V17.505C4.5 17.7784 4.72162 18 4.995 18H19.0005C19.2764 18 19.5 17.7764 19.5 17.5005V8.7495C19.5 8.47363 19.2764 8.25 19.0005 8.25H12.1979ZM13.125 6.75H19.0005C20.1048 6.75 21 7.64521 21 8.7495V17.5005C21 18.6048 20.1048 19.5 19.0005 19.5H4.995C3.89319 19.5 3 18.6068 3 17.505V6.495C3 5.39319 3.89319 4.5 4.995 4.5H10.767C11.5227 4.5 12.2135 4.92693 12.5514 5.60281L13.125 6.75Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted in</span><a href="https://arthurvandermerwe.com/category/financial-switching/" rel="category tag">Financial Switching</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M3 12.2045C3 12.5941 3.15158 12.9684 3.42267 13.2482L9.71878 19.747C11.0769 21.1489 13.3201 21.1667 14.7003 19.7865L19.7873 14.6995C21.1677 13.319 21.1497 11.0753 19.7471 9.71731L13.2459 3.42238C12.9661 3.15147 12.5919 3 12.2025 3H4.5C3.67157 3 3 3.67157 3 4.5V12.2045ZM12.2025 4.5H4.5V12.2045L10.7961 18.7033C11.5714 19.5035 12.8518 19.5137 13.6396 18.7258L18.7266 13.6388C19.5146 12.8509 19.5043 11.5701 18.7037 10.7949L12.2025 4.5ZM8.4975 9.495C9.0484 9.495 9.495 9.0484 9.495 8.4975C9.495 7.9466 9.0484 7.5 8.4975 7.5C7.9466 7.5 7.5 7.9466 7.5 8.4975C7.5 9.0484 7.9466 9.495 8.4975 9.495Z" fill="currentColor"/></svg><span class="screen-reader-text">Tags:</span><a href="https://arthurvandermerwe.com/tag/9820/" rel="tag">9820</a>, <a href="https://arthurvandermerwe.com/tag/9830/" rel="tag">9830</a>, <a href="https://arthurvandermerwe.com/tag/diy/" rel="tag">DIY</a>, <a href="https://arthurvandermerwe.com/tag/kca/" rel="tag">KCA</a>, <a href="https://arthurvandermerwe.com/tag/kek1/" rel="tag">KEK1</a>, <a href="https://arthurvandermerwe.com/tag/kek2/" rel="tag">KEK2</a>, <a href="https://arthurvandermerwe.com/tag/keks/" rel="tag">KEKs</a>, <a href="https://arthurvandermerwe.com/tag/ki/" rel="tag">KI</a>, <a href="https://arthurvandermerwe.com/tag/kia/" rel="tag">KIA</a>, <a href="https://arthurvandermerwe.com/tag/kmach/" rel="tag">KMACH</a>, <a href="https://arthurvandermerwe.com/tag/management-information/" rel="tag">management information</a>, <a href="https://arthurvandermerwe.com/tag/pksp/" rel="tag">PKsp</a>, <a href="https://arthurvandermerwe.com/tag/pos-terminal/" rel="tag">POS terminal</a>, <a href="https://arthurvandermerwe.com/tag/ppasn/" rel="tag">PPASN</a>, <a href="https://arthurvandermerwe.com/tag/ppid/" rel="tag">PPID</a>, <a href="https://arthurvandermerwe.com/tag/rsa/" rel="tag">RSA</a>, <a href="https://arthurvandermerwe.com/tag/sktcu/" rel="tag">SKtcu</a>, <a href="https://arthurvandermerwe.com/tag/tcu/" rel="tag">TCU</a>, <a href="https://arthurvandermerwe.com/tag/terminal-manufacturer/" rel="tag">terminal manufacturer</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M10.0458 15.0001L5.99998 17.697L5.99999 6.49478C5.99999 6.22141 6.2216 5.99979 6.49498 5.99978L17.505 5.99951C17.7784 5.9995 18 6.22113 18 6.49451L18 14.5046C18 14.778 17.7784 14.9996 17.505 14.9996L10.0458 15.0001ZM10.5 16.5L17.5051 16.4996C18.6069 16.4995 19.5 15.6063 19.5 14.5046L19.5 6.49451C19.5 5.39268 18.6068 4.49948 17.5049 4.49951L6.49494 4.49978C5.39315 4.49981 4.49999 5.39299 4.49999 6.49478L4.49998 18.3483C4.49998 18.9842 5.01549 19.4997 5.6514 19.4997C5.8787 19.4997 6.10091 19.4324 6.29004 19.3063L10.5 16.5Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/28/eftpos-initialisation-using-rsa-cryptography/#comments">1 Comment<span class="screen-reader-text"> on EFTPOS Initialisation using RSA&nbsp;Cryptography</span></a></span> </footer><!-- .entry-footer --> </article><!-- #post-${ID} --> <article id="post-121" class="post-121 post type-post status-publish format-standard hentry category-atm-tracing category-financial-switching tag-3des tag-atm tag-thales tag-tmk tag-tpk entry"> <header class="entry-header default-max-width"> <h2 class="entry-title"><a href="https://arthurvandermerwe.com/2015/05/20/atm-pin-encryption-using-3des/" rel="bookmark">ATM Pin encryption using&nbsp;3DES</a></h2> </header><!-- .entry-header --> <div class="entry-content"> <h2>Introduction</h2> <p>Most modern ATM&#8217;s use a Triple Des algorithm to encrypt the pin and send it to a host server for processing. Once the host system receives the pin, it does a translation of the pin from one encryption key to another, and sends it to a bank. In this post I will attempt to explain the process and how it is done in the real world.</p> <h2>Overview of the Triple Data Encryption Standard</h2> <p>What we all call Triple DES is EDE (encrypt, decrypt, encrypt). The way that it works is that you take three 56-bit keys, and encrypt with K1, decrypt with K2 and encrypt with K3. There are two-key and three-key versions. Think of the two-key version as merely one where K1=K3. Note that if K1=K2=K3, then Triple DES is really Single DES.</p> <p>Triple DES was created back when DES was getting a bit weaker than people were comfortable with. As a result, they wanted an easy way to get more strength. In a system dependent on DES, making a composite function out of multiple DESes is likely to be easier than bolting in a new cipher and sidesteps the political issue of arguing that the new cipher is better than DES.</p> <p>As it turns out, when you compose a cipher into a new one, you can&#8217;t use a double enciphering. There is a class of attacks called meet-in-the-middle attacks, in which you encrypt from one end, decrypt from the other, and start looking for collisions (things that give you the same answer). With sufficient memory, Double DES (or any other cipher) would only be twice as strong as the base cipher &#8212; or one bit more in strength.</p> <p>There&#8217;s more to it. If the cipher forms a group, then encrypting twice with two keys is equivalent to encrypting once with some key. Now, it&#8217;s not trivial to know what that other key is, but it means that a brute-force attack would find that third key as it tried all possible single-keys. So if the cipher&#8217;s a group, then multiple-ciphering is merely a waste of time.</p> <p>Applying this encryption in Python is trivial as there are plenty of tested libraries that can provide the functionality like pyDes and Crypto :</p> <pre>import os from Crypto.Cipher import DES3 def encrypt_file(in_filename, out_filename, chunk_size, key, iv): des3 = DES3.new(key, DES3.MODE_CFB, iv) with open(in_filename, 'r') as in_file: with open(out_filename, 'w') as out_file: while True: chunk = in_file.read(chunk_size) if len(chunk) == 0: break elif len(chunk) % 16 != 0: chunk += ' ' * (16 - len(chunk) % 16) out_file.write(des3.encrypt(chunk)) def decrypt_file(in_filename, out_filename, chunk_size, key, iv): des3 = DES3.new(key, DES3.MODE_CFB, iv) with open(in_filename, 'r') as in_file: with open(out_filename, 'w') as out_file: while True: chunk = in_file.read(chunk_size) if len(chunk) == 0: break out_file.write(des3.decrypt(chunk))</pre> <p>&nbsp;</p> <h2>ATM Internals and how they calculate the keys</h2> <p>When you have an ATM, you typically need to provide it with a set of encryption keys from your host, or HSM. These keys are clear text keys and it&#8217;s not encrypted in any way. Your host will link them to your terminal number, and when the ATM encrypts the pin; the host will know what keys are used so it can decrypt / translate them to the bank. The clear keys are never stored by the host, only the LMK encrypted keys.</p> <p>Lets assume your host provides the following keys to you as the &#8216;ATM Encryption Key&#8217; :</p> <pre>Clear component A: <strong>67C4 A719 1ADA FD08 6432 CE0D D638 4AB</strong></pre> <pre>Key check value: 20D40B</pre> <pre>Clear component B: <strong>8A89 6D4C 4625 5E2A 1A75 2002 07A7 D35E</strong></pre> <pre>Key check value: 4EC801</pre> <pre>Combined Check Value: <strong>2B547D</strong></pre> <p>Now typically you would enter the clear components into the ATM, as Encryption keys, and the ATM will combine them (Basically XOR Them) and derive the check value. If the check value match, then all is good.</p> <p>What happens at your host end is the following:</p> <p>Your host will also combine the keys and encrypt them under the LMK (Local Master Key). It will then use this key to encrypt all other keys that are sent to the ATM.</p> <p>Now the ATM have a Terminal Master Key that it can use to decrypt all keys that are sent to it from the host.</p> <h2>ATM Configuration Request (Key Exchange)</h2> <p>Now when an ATM starts up, the first thing it does it send a configuration request to the host. This request is to get the Third key used in Triple DES.  The Host will generate a random Terminal Pin Key and encrypt it under the Terminal Master Key (TMK). Since the ATM has the Terminal Master Key, it can decrypt the encrypted TPK, and use all 3 Keys now for the Triple DES operations. (it actually uses 2)</p> <p>The Host would generally execute the A0 Thales command to get this key. He would store the key in the key database to do the decryption / translation later.</p> <p>&nbsp;</p> <h2>Pin Encryption / Decryption</h2> <p>When a ATM gets ready to transmit a transaction it does the 3DES operation on the Pin only. the cypher text is now transmitted to the host. The host never knows the pin code, and only does a translation of the pin from the terminal keys to the bank keys.</p> <blockquote><p>The Host will have the following:</p> <p>(ZPK) Zone Pin Key &#8211; from the Bank during Host to Bank Key exchange</p> <p>(TPK) Terminal Pin Key &#8211; from Terminal using Terminal Configuration Request</p> <p>(PAN) Account Number &#8211;  from Transaction transmitted.</p></blockquote> <p>With these values, the Host can translate the pin using a HSM, below is an example of the D4 Command.</p> <pre> Res = KeyGenerator.TranslatePIN_TDES(TerminalPINKey=self.Crypto["TPK_LMK"], PINEncryptionKey=self.HostKeys["ZPK_LMK"], PINBlock=self.iso.getBit(52), AccountNumber=track2["PAN"][-13:-1]) def get_commandTPKPinBlock(self, TerminalPINKey, PINEncryptionKey, PINBlock, AccountNumber): command_code = 'D4' KTP = TerminalPINKey KPE = PINEncryptionKey PinBlock = PINBlock PAN = AccountNumber message = command_code message += KTP message += KPE message += PinBlock message += PAN return message #transmit to HSM</pre> <p>The transaction can now be transmitted to the acquiring bank with the translated pin for processing.</p> <p>Sometimes the ATM requires a Message Authentication Code, this will be covered in another post.</p> <p>easy as pie</p> <p>&nbsp;</p> <p>&nbsp;</p> </div><!-- .entry-content --> <footer class="entry-footer default-max-width"> <span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M15 7.5C15 9.15685 13.6569 10.5 12 10.5C10.3431 10.5 9 9.15685 9 7.5C9 5.84315 10.3431 4.5 12 4.5C13.6569 4.5 15 5.84315 15 7.5ZM16.5 7.5C16.5 9.98528 14.4853 12 12 12C9.51472 12 7.5 9.98528 7.5 7.5C7.5 5.01472 9.51472 3 12 3C14.4853 3 16.5 5.01472 16.5 7.5ZM19.5 19.5V16.245C19.5 14.729 18.271 13.5 16.755 13.5L7.245 13.5C5.72898 13.5 4.5 14.729 4.5 16.245L4.5 19.5H6L6 16.245C6 15.5574 6.5574 15 7.245 15L16.755 15C17.4426 15 18 15.5574 18 16.245V19.5H19.5Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://arthurvandermerwe.com/author/arthurvdmerwe/">arthurvdmerwe</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M19.5 7.5H4.5V19.0005C4.5 19.2764 4.72363 19.5 4.9995 19.5H19.0005C19.2764 19.5 19.5 19.2764 19.5 19.0005V7.5ZM3 7.5V4.9995V4.995C3 3.89319 3.89319 3 4.995 3H4.9995H19.0005H19.005C20.1068 3 21 3.89319 21 4.995V4.9995V7.5V19.0005C21 20.1048 20.1048 21 19.0005 21H4.9995C3.89521 21 3 20.1048 3 19.0005V7.5ZM7.5 10.5H9V12H7.5V10.5ZM9 15H7.5V16.5H9V15ZM11.25 10.5H12.75V12H11.25V10.5ZM12.75 15H11.25V16.5H12.75V15ZM15 10.5H16.5V12H15V10.5ZM16.5 15H15V16.5H16.5V15Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/20/atm-pin-encryption-using-3des/" rel="bookmark"><time class="entry-date published" datetime="2015-05-20T11:30:55+10:00">May 20, 2015</time><time class="updated" datetime="2015-05-20T11:54:32+10:00">May 20, 2015</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M12.1979 8.25L11.2098 6.27363C11.1259 6.10593 10.9545 6 10.767 6H4.995C4.72162 6 4.5 6.22162 4.5 6.495V17.505C4.5 17.7784 4.72162 18 4.995 18H19.0005C19.2764 18 19.5 17.7764 19.5 17.5005V8.7495C19.5 8.47363 19.2764 8.25 19.0005 8.25H12.1979ZM13.125 6.75H19.0005C20.1048 6.75 21 7.64521 21 8.7495V17.5005C21 18.6048 20.1048 19.5 19.0005 19.5H4.995C3.89319 19.5 3 18.6068 3 17.505V6.495C3 5.39319 3.89319 4.5 4.995 4.5H10.767C11.5227 4.5 12.2135 4.92693 12.5514 5.60281L13.125 6.75Z" fill="currentColor"/></svg><span class="screen-reader-text">Posted in</span><a href="https://arthurvandermerwe.com/category/atm-tracing/" rel="category tag">ATM Tracing</a>, <a href="https://arthurvandermerwe.com/category/financial-switching/" rel="category tag">Financial Switching</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M3 12.2045C3 12.5941 3.15158 12.9684 3.42267 13.2482L9.71878 19.747C11.0769 21.1489 13.3201 21.1667 14.7003 19.7865L19.7873 14.6995C21.1677 13.319 21.1497 11.0753 19.7471 9.71731L13.2459 3.42238C12.9661 3.15147 12.5919 3 12.2025 3H4.5C3.67157 3 3 3.67157 3 4.5V12.2045ZM12.2025 4.5H4.5V12.2045L10.7961 18.7033C11.5714 19.5035 12.8518 19.5137 13.6396 18.7258L18.7266 13.6388C19.5146 12.8509 19.5043 11.5701 18.7037 10.7949L12.2025 4.5ZM8.4975 9.495C9.0484 9.495 9.495 9.0484 9.495 8.4975C9.495 7.9466 9.0484 7.5 8.4975 7.5C7.9466 7.5 7.5 7.9466 7.5 8.4975C7.5 9.0484 7.9466 9.495 8.4975 9.495Z" fill="currentColor"/></svg><span class="screen-reader-text">Tags:</span><a href="https://arthurvandermerwe.com/tag/3des/" rel="tag">3DES</a>, <a href="https://arthurvandermerwe.com/tag/atm/" rel="tag">ATM</a>, <a href="https://arthurvandermerwe.com/tag/thales/" rel="tag">Thales</a>, <a href="https://arthurvandermerwe.com/tag/tmk/" rel="tag">TMK</a>, <a href="https://arthurvandermerwe.com/tag/tpk/" rel="tag">TPK</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M10.0458 15.0001L5.99998 17.697L5.99999 6.49478C5.99999 6.22141 6.2216 5.99979 6.49498 5.99978L17.505 5.99951C17.7784 5.9995 18 6.22113 18 6.49451L18 14.5046C18 14.778 17.7784 14.9996 17.505 14.9996L10.0458 15.0001ZM10.5 16.5L17.5051 16.4996C18.6069 16.4995 19.5 15.6063 19.5 14.5046L19.5 6.49451C19.5 5.39268 18.6068 4.49948 17.5049 4.49951L6.49494 4.49978C5.39315 4.49981 4.49999 5.39299 4.49999 6.49478L4.49998 18.3483C4.49998 18.9842 5.01549 19.4997 5.6514 19.4997C5.8787 19.4997 6.10091 19.4324 6.29004 19.3063L10.5 16.5Z" fill="currentColor"/></svg><a href="https://arthurvandermerwe.com/2015/05/20/atm-pin-encryption-using-3des/#respond">Leave a comment<span class="screen-reader-text"> on ATM Pin encryption using&nbsp;3DES</span></a></span> </footer><!-- .entry-footer --> </article><!-- #post-${ID} --> </main><!-- #main --> </section><!-- #primary --> </div><!-- #content --> <footer id="colophon" class="site-footer default-max-width" role="contentinfo" aria-label="Footer"> <div class="widget-area"> <div class="widget-column footer-widget-1"> <section id="recent-posts-4" class="widget widget_recent_entries"> <h2 class="widget-title">Recent Posts</h2><nav aria-label="Recent Posts"> <ul> <li> <a href="https://arthurvandermerwe.com/2020/02/16/a-brief-comparison-of-as2805-and-key-blocks/">A brief comparison of AS2805 and (TR-31) Key&nbsp;Blocks</a> </li> <li> <a href="https://arthurvandermerwe.com/2020/01/19/what-is-the-random-oracle-model-and-why-should-you-care-part-5-a-few-thoughts-on-cryptographic-engineering/">What is the random oracle model and why should you care? (Part 5) — A Few Thoughts on Cryptographic&nbsp;Engineering</a> </li> <li> <a href="https://arthurvandermerwe.com/2019/02/21/attack-of-the-week-searchable-encryption-and-the-ever-expanding-leakage-function-a-few-thoughts-on-cryptographic-engineering/">Attack of the week: searchable encryption and the ever-expanding leakage function — A Few Thoughts on Cryptographic&nbsp;Engineering</a> </li> <li> <a href="https://arthurvandermerwe.com/2017/12/29/from-bi-linear-maps-to-searchable-encryption/">From Bi-Linear Maps to Searchable&nbsp;Encryption</a> </li> <li> <a href="https://arthurvandermerwe.com/2017/02/10/mutual-authentication-using-certificates/">Mutual Authentication using&nbsp;Certificates</a> </li> <li> <a href="https://arthurvandermerwe.com/2016/09/04/importing-zpk-and-zmk-into-thales-payshield-9000-hsm/">Importing ZPK and ZMK into Thales Payshield 9000&nbsp;HSM</a> </li> <li> <a href="https://arthurvandermerwe.com/2016/07/23/signature-and-certificate-based-key-injection-for-atm/">Signature and Certificate based key injection for&nbsp;ATM</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/07/31/the-refund-vulnerability-of-as2805-and-eftpos/">The Refund vulnerability of AS2805 and&nbsp;EFTPOS</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/05/30/dukpt-explained-with-examples/">DUKPT Explained with&nbsp;examples</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/05/28/eftpos-initialisation-using-rsa-cryptography/">EFTPOS Initialisation using RSA&nbsp;Cryptography</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/05/20/atm-pin-encryption-using-3des/">ATM Pin encryption using&nbsp;3DES</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/03/03/implementing-as2805-part-3-using-a-thales-9000-and-python/">Implementing AS2805 Part 6 Host to Host Encryption using a Thales 9000 and&nbsp;Python</a> </li> <li> <a href="https://arthurvandermerwe.com/2015/01/04/typical-cryptography-in-as2805-explained/">Typical Cryptography in AS2805&nbsp;Explained</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/12/02/thales-9000-and-as2805-interchange-commands/">Thales 9000 with AS2805 Interchange &amp; RSA EFTPOS&nbsp;Commands.</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/08/06/thales-key-exchange-examples-and-troubleshooting/">Thales Key Exchange Examples and&nbsp;Troubleshooting</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/08/06/testing-dukpt/">Testing DUKPT</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/07/06/parsing-as25058583-messages/">Parsing AS2505/8583 Messages</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/06/25/dynamic-key-exchange-models/">Dynamic Key Exchange&nbsp;Models</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/06/25/doing-pin-translation/">Doing PIN Translation with&nbsp;DUKPT</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/06/25/credit-vs-debit/">Credit vs Debit</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/06/22/as2805-standards-for-eft/">AS2805 Standards for&nbsp;EFT</a> </li> <li> <a href="https://arthurvandermerwe.com/2014/06/22/trace-your-atm-transactions/">Trace your ATM&nbsp;Transactions</a> </li> </ul> </nav></section><section id="archives-6" class="widget widget_archive"><h2 class="widget-title">Archives</h2><nav aria-label="Archives"> <ul> <li><a href='https://arthurvandermerwe.com/2020/02/'>February 2020</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2020/01/'>January 2020</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2019/02/'>February 2019</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2017/12/'>December 2017</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2017/02/'>February 2017</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2016/09/'>September 2016</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2016/07/'>July 2016</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2015/07/'>July 2015</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2015/05/' aria-current="page">May 2015</a>&nbsp;(3)</li> <li><a href='https://arthurvandermerwe.com/2015/03/'>March 2015</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2015/01/'>January 2015</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2014/12/'>December 2014</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2014/08/'>August 2014</a>&nbsp;(2)</li> <li><a href='https://arthurvandermerwe.com/2014/07/'>July 2014</a>&nbsp;(1)</li> <li><a href='https://arthurvandermerwe.com/2014/06/'>June 2014</a>&nbsp;(5)</li> </ul> </nav></section><section id="wpcom_social_media_icons_widget-4" class="widget widget_wpcom_social_media_icons_widget"><h2 class="widget-title">Social</h2><ul><li><a href="https://www.linkedin.com/in/arthur-van-der-merwe-a7a96a27" class="genericon genericon-linkedin" target="_blank"><span class="screen-reader-text">LinkedIn</span></a></li><li><a href="https://github.com/Arthurvdmerwe" class="genericon genericon-github" target="_blank"><span class="screen-reader-text">GitHub</span></a></li></ul></section> </div> </div><!-- .widget-area --> <div class="site-info"> <a class="site-name" href="https://arthurvandermerwe.com/" rel="home">Cryptography &amp; Payments</a><span class="comma">,</span> <a href="https://wordpress.com/?ref=footer_blog" rel="nofollow">Blog at WordPress.com.</a> </div><!-- .site-info --> </footer><!-- #colophon --> </div><!-- #page --> <!-- --> <script src="//0.gravatar.com/js/hovercards/hovercards.min.js?ver=2024474048849247f5660a2d05b85c6fc286379897f30a1061ad46e7f037e059ed7fe7" id="grofiles-cards-js"></script> <script id="wpgroho-js-extra"> var WPGroHo = {"my_hash":""}; </script> <script crossorigin='anonymous' type='text/javascript' src='https://s2.wp.com/wp-content/mu-plugins/gravatar-hovercards/wpgroho.js?m=1610363240i'></script> <script> // Initialize and attach hovercards to all gravatars ( function() { function init() { if ( typeof Gravatar === 'undefined' ) { return; } if ( typeof Gravatar.init !== 'function' ) { return; } Gravatar.profile_cb = function ( hash, id ) { WPGroHo.syncProfileData( hash, id ); }; Gravatar.my_hash = WPGroHo.my_hash; Gravatar.init( 'body', '#wp-admin-bar-my-account', { i18n: { 'Edit your profile': 'Edit your profile', 'View profile': 'View profile', 'Sorry, we are unable to load this Gravatar profile.': 'Sorry, we are unable to load this Gravatar profile.', 'Profile not found.': 'Profile not found.', 'Too Many Requests.': 'Too Many Requests.', 'Internal Server Error.': 'Internal Server Error.', }, } ); } if ( document.readyState !== 'loading' ) { init(); } else { document.addEventListener( 'DOMContentLoaded', init ); } } )(); </script> <div style="display:none"> </div> <div id="actionbar" style="display: none;" class="actnbr-pub-seedlet actnbr-has-follow"> <ul> <li class="actnbr-btn actnbr-hidden"> <a class="actnbr-action actnbr-actn-follow " href=""> <svg class="gridicon" height="20" width="20" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 20 20"><path clip-rule="evenodd" d="m4 4.5h12v6.5h1.5v-6.5-1.5h-1.5-12-1.5v1.5 10.5c0 1.1046.89543 2 2 2h7v-1.5h-7c-.27614 0-.5-.2239-.5-.5zm10.5 2h-9v1.5h9zm-5 3h-4v1.5h4zm3.5 1.5h-1v1h1zm-1-1.5h-1.5v1.5 1 1.5h1.5 1 1.5v-1.5-1-1.5h-1.5zm-2.5 2.5h-4v1.5h4zm6.5 1.25h1.5v2.25h2.25v1.5h-2.25v2.25h-1.5v-2.25h-2.25v-1.5h2.25z" fill-rule="evenodd"></path></svg> <span>Subscribe</span> </a> <a class="actnbr-action actnbr-actn-following no-display" href=""> <svg class="gridicon" height="20" width="20" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 20 20"><path fill-rule="evenodd" clip-rule="evenodd" d="M16 4.5H4V15C4 15.2761 4.22386 15.5 4.5 15.5H11.5V17H4.5C3.39543 17 2.5 16.1046 2.5 15V4.5V3H4H16H17.5V4.5V12.5H16V4.5ZM5.5 6.5H14.5V8H5.5V6.5ZM5.5 9.5H9.5V11H5.5V9.5ZM12 11H13V12H12V11ZM10.5 9.5H12H13H14.5V11V12V13.5H13H12H10.5V12V11V9.5ZM5.5 12H9.5V13.5H5.5V12Z" fill="#008A20"></path><path class="following-icon-tick" d="M13.5 16L15.5 18L19 14.5" stroke="#008A20" stroke-width="1.5"></path></svg> <span>Subscribed</span> </a> <div class="actnbr-popover tip tip-top-left actnbr-notice" id="follow-bubble"> <div class="tip-arrow"></div> <div class="tip-inner actnbr-follow-bubble"> <ul> <li class="actnbr-sitename"> <a href="https://arthurvandermerwe.com"> <img loading='lazy' alt='' src='https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=50' srcset='https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=50 1x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=75 1.5x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=100 2x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=150 3x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=200 4x' class='avatar avatar-50' height='50' width='50' /> Cryptography &amp; Payments </a> </li> <div class="actnbr-message no-display"></div> <form method="post" action="https://subscribe.wordpress.com" accept-charset="utf-8" style="display: none;"> <div class="actnbr-follow-count">Join 30 other subscribers</div> <div> <input type="email" name="email" placeholder="Enter your email address" class="actnbr-email-field" aria-label="Enter your email address" /> </div> <input type="hidden" name="action" value="subscribe" /> <input type="hidden" name="blog_id" value="70204527" /> <input type="hidden" name="source" value="https://arthurvandermerwe.com/2015/05/" /> <input type="hidden" name="sub-type" value="actionbar-follow" /> <input type="hidden" id="_wpnonce" name="_wpnonce" value="e65172ef6c" /> <div class="actnbr-button-wrap"> <button type="submit" value="Sign me up"> Sign me up </button> </div> </form> <li class="actnbr-login-nudge"> <div> Already have a WordPress.com account? <a href="https://wordpress.com/log-in?redirect_to=https%3A%2F%2Fr-login.wordpress.com%2Fremote-login.php%3Faction%3Dlink%26back%3Dhttps%253A%252F%252Farthurvandermerwe.com%252F2015%252F05%252F30%252Fdukpt-explained-with-examples%252F">Log in now.</a> </div> </li> </ul> </div> </div> </li> <li class="actnbr-ellipsis actnbr-hidden"> <svg class="gridicon gridicons-ellipsis" height="24" width="24" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><g><path d="M7 12c0 1.104-.896 2-2 2s-2-.896-2-2 .896-2 2-2 2 .896 2 2zm12-2c-1.104 0-2 .896-2 2s.896 2 2 2 2-.896 2-2-.896-2-2-2zm-7 0c-1.104 0-2 .896-2 2s.896 2 2 2 2-.896 2-2-.896-2-2-2z"/></g></svg> <div class="actnbr-popover tip tip-top-left actnbr-more"> <div class="tip-arrow"></div> <div class="tip-inner"> <ul> <li class="actnbr-sitename"> <a href="https://arthurvandermerwe.com"> <img loading='lazy' alt='' src='https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=50' srcset='https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=50 1x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=75 1.5x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=100 2x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=150 3x, https://arthurvandermerwe.com/wp-content/uploads/2018/09/cropped-arthur4.png?w=200 4x' class='avatar avatar-50' height='50' width='50' /> Cryptography &amp; Payments </a> </li> <li class="actnbr-folded-customize"> <a href="https://arthurvandermerwe.wordpress.com/wp-admin/customize.php?url=https%3A%2F%2Farthurvandermerwe.wordpress.com%2F2015%2F05%2F"> <svg class="gridicon gridicons-customize" height="20" width="20" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><g><path d="M2 6c0-1.505.78-3.08 2-4 0 .845.69 2 2 2 1.657 0 3 1.343 3 3 0 .386-.08.752-.212 1.09.74.594 1.476 1.19 2.19 1.81L8.9 11.98c-.62-.716-1.214-1.454-1.807-2.192C6.753 9.92 6.387 10 6 10c-2.21 0-4-1.79-4-4zm12.152 6.848l1.34-1.34c.607.304 1.283.492 2.008.492 2.485 0 4.5-2.015 4.5-4.5 0-.725-.188-1.4-.493-2.007L18 9l-2-2 3.507-3.507C18.9 3.188 18.225 3 17.5 3 15.015 3 13 5.015 13 7.5c0 .725.188 1.4.493 2.007L3 20l2 2 6.848-6.848c1.885 1.928 3.874 3.753 5.977 5.45l1.425 1.148 1.5-1.5-1.15-1.425c-1.695-2.103-3.52-4.092-5.448-5.977z"/></g></svg> <span>Customize</span> </a> </li> <li class="actnbr-folded-follow"> <a class="actnbr-action actnbr-actn-follow " href=""> <svg class="gridicon" height="20" width="20" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 20 20"><path clip-rule="evenodd" d="m4 4.5h12v6.5h1.5v-6.5-1.5h-1.5-12-1.5v1.5 10.5c0 1.1046.89543 2 2 2h7v-1.5h-7c-.27614 0-.5-.2239-.5-.5zm10.5 2h-9v1.5h9zm-5 3h-4v1.5h4zm3.5 1.5h-1v1h1zm-1-1.5h-1.5v1.5 1 1.5h1.5 1 1.5v-1.5-1-1.5h-1.5zm-2.5 2.5h-4v1.5h4zm6.5 1.25h1.5v2.25h2.25v1.5h-2.25v2.25h-1.5v-2.25h-2.25v-1.5h2.25z" fill-rule="evenodd"></path></svg> <span>Subscribe</span> </a> <a class="actnbr-action actnbr-actn-following no-display" href=""> <svg class="gridicon" height="20" width="20" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 20 20"><path fill-rule="evenodd" clip-rule="evenodd" d="M16 4.5H4V15C4 15.2761 4.22386 15.5 4.5 15.5H11.5V17H4.5C3.39543 17 2.5 16.1046 2.5 15V4.5V3H4H16H17.5V4.5V12.5H16V4.5ZM5.5 6.5H14.5V8H5.5V6.5ZM5.5 9.5H9.5V11H5.5V9.5ZM12 11H13V12H12V11ZM10.5 9.5H12H13H14.5V11V12V13.5H13H12H10.5V12V11V9.5ZM5.5 12H9.5V13.5H5.5V12Z" fill="#008A20"></path><path class="following-icon-tick" d="M13.5 16L15.5 18L19 14.5" stroke="#008A20" stroke-width="1.5"></path></svg> <span>Subscribed</span> </a> </li> <li class="actnbr-signup"><a href="https://wordpress.com/start/">Sign up</a></li> <li class="actnbr-login"><a href="https://wordpress.com/log-in?redirect_to=https%3A%2F%2Fr-login.wordpress.com%2Fremote-login.php%3Faction%3Dlink%26back%3Dhttps%253A%252F%252Farthurvandermerwe.com%252F2015%252F05%252F30%252Fdukpt-explained-with-examples%252F">Log in</a></li> <li class="flb-report"> <a href="https://wordpress.com/abuse/?report_url=https://arthurvandermerwe.com" target="_blank" rel="noopener noreferrer"> Report this content </a> </li> <li class="actnbr-reader"> <a href="https://wordpress.com/read/feeds/22152776"> View site in Reader </a> </li> <li class="actnbr-subs"> <a href="https://subscribe.wordpress.com/">Manage subscriptions</a> </li> <li class="actnbr-fold"><a href="">Collapse this bar</a></li> </ul> </div> </div> </li> </ul> </div> <script> window.addEventListener( "load", function( event ) { var link = document.createElement( "link" ); link.href = "https://s0.wp.com/wp-content/mu-plugins/actionbar/actionbar.css?v=20241015"; link.type = "text/css"; link.rel = "stylesheet"; document.head.appendChild( link ); var script = document.createElement( "script" ); script.src = "https://s0.wp.com/wp-content/mu-plugins/actionbar/actionbar.js?v=20231122"; script.defer = true; document.body.appendChild( script ); } ); </script> <link crossorigin='anonymous' rel='stylesheet' id='all-css-0-2' href='https://s2.wp.com/_static/??-eJyNzDEOgzAMheELNTUZQF2qHgVFjhWZJk5UO0K9fYtgZGB7//A+WJvDKkZiULpruScWhYWsBXwfDdoFZhaEREIf/h/0fN5R9QaXzVJjz6SwckxkClqRQ3aFIge322rfTBv7Kk8/PUbvx2Ealh973US5&cssminify=yes' type='text/css' media='all' /> <script crossorigin='anonymous' type='text/javascript' src='https://s0.wp.com/_static/??/wp-content/js/mobile-useragent-info.js,/wp-content/blog-plugins/wordads-classes/js/watl.js,/wp-content/themes/pub/seedlet/assets/js/primary-navigation.js?m=1731430359j'></script> <script> /(trident|msie)/i.test(navigator.userAgent)&&document.getElementById&&window.addEventListener&&window.addEventListener("hashchange",function(){var t,e=location.hash.substring(1);/^[A-z0-9_-]+$/.test(e)&&(t=document.getElementById(e))&&(/^(?:a|select|input|button|textarea)$/i.test(t.tagName)||(t.tabIndex=-1),t.focus())},!1); </script> <script type="text/javascript"> (function () { var wpcom_reblog = { source: 'toolbar', toggle_reblog_box_flair: function (obj_id, post_id) { // Go to site selector. This will redirect to their blog if they only have one. const postEndpoint = `https://wordpress.com/post`; // Ideally we would use the permalink here, but fortunately this will be replaced with the // post permalink in the editor. const originalURL = `${ document.location.href }?page_id=${ post_id }`; const url = postEndpoint + '?url=' + encodeURIComponent( originalURL ) + '&is_post_share=true' + '&v=5'; const redirect = function () { if ( ! window.open( url, '_blank' ) ) { location.href = url; } }; if ( /Firefox/.test( navigator.userAgent ) ) { setTimeout( redirect, 0 ); } else { redirect(); } }, }; window.wpcom_reblog = wpcom_reblog; })(); </script> <script type="text/javascript"> // <![CDATA[ (function() { try{ if ( window.external &&'msIsSiteMode' in window.external) { if (window.external.msIsSiteMode()) { var jl = document.createElement('script'); jl.type='text/javascript'; jl.async=true; jl.src='/wp-content/plugins/ie-sitemode/custom-jumplist.php'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(jl, s); } } }catch(e){} })(); // ]]> </script><script src="//stats.wp.com/w.js?67" defer></script> <script type="text/javascript"> _tkq = window._tkq || []; _stq = window._stq || []; _tkq.push(['storeContext', {'blog_id':'70204527','blog_tz':'11','user_lang':'en','blog_lang':'en','user_id':'0'}]); _stq.push(['view', {'blog':'70204527','v':'wpcom','tz':'11','user_id':'0','subd':'arthurvandermerwe'}]); _stq.push(['extra', {'crypt':'UE5VTUIlVktzQVNtcFdrRlVoJUNZcTJRQnxOUXcyQXBGVjdTZVlnSlY3P0dzcjlxYzIrNExdSDFwWT1HLEN1ZUpvZWZWfnIxLnNwSG1MMjB6UkUwTHhNMEpKdkw3QzV8fGZhPUUxeHRPdjktdGExbXAvZnV4SCtFSC0lSW93WHoxQlRYXW5wckolP2dPSjFSQltBfDNwYjNGQkdHbV9uSldPckVVYUxLPTd3aF83QTc1RkxBWVA1VkgmYkJkejcxZmNrUU9DVUpGfDgmSDd3W2JoZTdkQ19YPyZhLTRndz9vXWhNNzE='}]); _stq.push([ 'clickTrackerInit', '70204527', '0' ]); </script> <noscript><img src="https://pixel.wp.com/b.gif?v=noscript" style="height:1px;width:1px;overflow:hidden;position:absolute;bottom:1px;" alt="" /></noscript> <script defer id="bilmur" data-customproperties="{&quot;logged_in&quot;:&quot;0&quot;,&quot;wptheme&quot;:&quot;pub\/seedlet&quot;,&quot;wptheme_is_block&quot;:&quot;0&quot;}" data-provider="wordpress.com" data-service="simple" src="/wp-content/js/bilmur.min.js?i=12&m=202447"></script><script defer id="bilmur" data-customproperties="{&quot;logged_in&quot;:&quot;0&quot;,&quot;wptheme&quot;:&quot;pub\/seedlet&quot;,&quot;wptheme_is_block&quot;:&quot;0&quot;}" data-provider="wordpress.com" data-service="simple" src="/wp-content/js/bilmur-4.min.js?i=12&m=202447"></script><script> ( function() { function getMobileUserAgentInfo() { if ( typeof wpcom_mobile_user_agent_info === 'object' ) { wpcom_mobile_user_agent_info.init(); var mobileStatsQueryString = ''; if ( wpcom_mobile_user_agent_info.matchedPlatformName !== false ) { mobileStatsQueryString += '&x_' + 'mobile_platforms' + '=' + wpcom_mobile_user_agent_info.matchedPlatformName; } if ( wpcom_mobile_user_agent_info.matchedUserAgentName !== false ) { mobileStatsQueryString += '&x_' + 'mobile_devices' + '=' + wpcom_mobile_user_agent_info.matchedUserAgentName; } if ( wpcom_mobile_user_agent_info.isIPad() ) { mobileStatsQueryString += '&x_' + 'ipad_views' + '=' + 'views'; } if ( mobileStatsQueryString != '' ) { new Image().src = document.location.protocol + '//pixel.wp.com/g.gif?v=wpcom-no-pv' + mobileStatsQueryString + '&baba=' + Math.random(); } } } document.addEventListener( 'DOMContentLoaded', getMobileUserAgentInfo ); } )(); </script> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10