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	<title>blog.V1ru8.net &#187; University</title>
	<atom:link href="http://blog.v1ru8.net/category/university/feed/" rel="self" type="application/rss+xml" />
	<link>http://blog.v1ru8.net</link>
	<description></description>
	<lastBuildDate>Mon, 28 Sep 2009 15:55:13 +0000</lastBuildDate>
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		<item>
		<title>Change happens</title>
		<link>http://blog.v1ru8.net/2009/09/28/change-happens/</link>
		<comments>http://blog.v1ru8.net/2009/09/28/change-happens/#comments</comments>
		<pubDate>Mon, 28 Sep 2009 15:55:12 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[Stuff]]></category>
		<category><![CDATA[University]]></category>
		<category><![CDATA[bachelor]]></category>
		<category><![CDATA[Bachelor Thesis]]></category>
		<category><![CDATA[BSc]]></category>
		<category><![CDATA[equinux]]></category>
		<category><![CDATA[fhnw]]></category>
		<category><![CDATA[gran canaria]]></category>

		<guid isPermaLink="false">http://blog.v1ru8.net/?p=309</guid>
		<description><![CDATA[Lets start in spring this year. The semester was my last semester of my undergraduate study. So I started to look for a job. That should be just a temporary job for at most one year. Because I would like to start a Postgraduate study in a year. So I searched for an internship in [...]]]></description>
			<content:encoded><![CDATA[<p>Lets start in spring this year. The semester was my last semester of my undergraduate study. So I started to look for a job. That should be just a temporary job for at most one year. Because I would like to start a Postgraduate study in a year.   So I searched for an internship in the US or the UK (a goal was to improve my english skills). This took a lot of time and it turned out to be a fight against the world economic crisis. Finally after a few months I gave up! The crisis won.</p>
<p><span id="more-309"></span></p>
<p><img style="float:left" src="http://img.skitch.com/20090928-mu3j4t2mhcxp582yihi6t2qc8q.preview.png" alt="ePark24 Logo" />In June/August Roman and I worked together on our <a href="http://web.fhnw.ch/technik/projekte/i/fruehling09/KaufmannPost/index.php">Bachelor Thesis</a>. During this time I started to search for a new job. I got connected to a few people who searched a iPhone/Mac developer in the area of Zurich. But nothing got really concrete. So I took the time and wrote an application to equinux. A well known german Mac software company based in Munich. I went to the job interview and somehow I made a good impression. Which means I finally got the job and I&#8217;m totally glad to start there on October 1st.</p>
<p><img style="float:right" src="http://img.skitch.com/20090928-jhtia3hmjr9a6f8qfcpbbwgdf8.preview.png" alt="Gran Canary Island" />After we finished our Thesis we all went to the canary islands and celebrated the completion of our study. We made up the role that we don&#8217;t share photos from this week so no photos here, sorry. After we returned, we had to present and defend our Thesis. That went very well and we&#8217;ve got a very good mark. As far as we know the best in our branch of study.</p>
<p>In the last few weeks I finally moved to Munich which is definitely harder then to get a job there <img src='http://blog.v1ru8.net/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> . Currently I just have a temporary solution to stay there but a definite solution is close. I&#8217;m already starting to really like this city and germany. And of course I visited the Oktoberfest!</p>
<p>Last weekend I went back to the place where I studied for the last three years for the graduation ceremony. We all enjoyed it and celebrated it condignly with a good party afterwards. Now I&#8217;m &#8220;Bachelor of Science FHNW in Computer Sciences with a Specialization in Distributed Software Systems&#8221;.</p>
<p>Do to the fact that I signed an employment contract with equinux, I will stop developing my own applications and completely focus on my work at equinux. So I think that&#8217;s pretty much what happens in the last 1/2 year. I enjoyed the time of changes but I&#8217;m also glad to finally start at <a href="http://www.equinux.com">equinux</a> this week.</p>
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		<item>
		<title>Video Filters in OpenCV</title>
		<link>http://blog.v1ru8.net/2009/04/02/video-filters-in-opencv/</link>
		<comments>http://blog.v1ru8.net/2009/04/02/video-filters-in-opencv/#comments</comments>
		<pubDate>Thu, 02 Apr 2009 21:58:14 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[Audio And Video Processing]]></category>
		<category><![CDATA[University]]></category>
		<category><![CDATA[DirectShow]]></category>
		<category><![CDATA[filter]]></category>
		<category><![CDATA[opencv]]></category>
		<category><![CDATA[video]]></category>

		<guid isPermaLink="false">http://blog.v1ru8.net/?p=284</guid>
		<description><![CDATA[For the &#8220;Audio and Video Processing&#8221; lecture tomorrow I had to write some simple video filters. The professor recommended to use the DirectShow SDK. But everyone who knows me knows that when there is a way to do something without Windows I will do it without! So I used the OpenCV library from Intel. Which [...]]]></description>
			<content:encoded><![CDATA[<p>For the &#8220;Audio and Video Processing&#8221; lecture tomorrow I had to write some simple video filters. The professor recommended to use the DirectShow SDK. But everyone who knows me knows that when there is a way to do something without Windows I will do it without! So I used the OpenCV library from Intel. Which I know from my last semester project. I wrote a little program who uses the iSight as video source. (based on the OpenCV XCode example project) You can select 8 diffrent video filters by pressing number 1-8 on your keyboard.</p>
<ul>
<li>0: no filter</li>
<li>1: 3&#215;3 Sobelfilter Horizontal </li>
<li>2: 3&#215;3 Sobelfilter Vertical</li>
<li>3: 3&#215;3 Laplace  </li>
<li>4: 3&#215;3 Box Filter</li>
<li>5: 3&#215;3 Gauss Filter</li>
<li>6: 5&#215;5 Gauss Filter</li>
<li>5: 5&#215;5 Box Filter</li>
<li>6: 7&#215;7 Box Filter (overflow)</li>
</ul>
<p>With the key <b>&#8216;t&#8217;</b> you can add an additional filter who generates four abstract colored pictures.</p>
<table>
<tr>
<td>
<a href="http://img.skitch.com/20090402-djtqbs8338brke47usm31mwqac.png" rel="lightbox[groupname]" title="Filter 1"><img src="http://img.skitch.com/20090402-djtqbs8338brke47usm31mwqac.preview.png" width="186" height="150" alt="Filter 1" /></a>
</td>
<td><a href="http://img.skitch.com/20090402-dn93nnn7x4r5dpcce8hre6mt32.png" rel="lightbox[groupname]" title="Filter 2"><img src="http://img.skitch.com/20090402-dn93nnn7x4r5dpcce8hre6mt32.preview.png" width="186" height="150" alt="Filter 2" /></a>
</td>
<td>
<a href="http://img.skitch.com/20090402-ei1mxct69nsyfq8459xety391.jpg" rel="lightbox[groupname]" title="Filter 2"><img src="http://img.skitch.com/20090402-ei1mxct69nsyfq8459xety391.preview.png" width="186" height="150" alt="Filter 2" /></a>
</td>
</tr>
</table>
<p>Downloads:</p>
<ul>
<li>Sourcecode: <a href="http://files.v1ru8.net/OpenCVFilters/Filters.c">Filters.c</a></li>
<li>XCode Project: <a href="http://files.v1ru8.net/OpenCVFilters/Filters.zip">Filters.zip</a></li>
<li><a href="http://www.ient.rwth-aachen.de/~asbach/OpenCV-Private-Framework-1.1.dmg">OpenCV.framework</a></li>
<li>Compiled Binary: <a href="http://files.v1ru8.net/OpenCVFilters/FaceTracker.app.zip">FaceTracker.app.zip</a></li>
</ul>
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		<item>
		<title>My Bachelor Thesis</title>
		<link>http://blog.v1ru8.net/2009/02/17/my-bachelor-thesis/</link>
		<comments>http://blog.v1ru8.net/2009/02/17/my-bachelor-thesis/#comments</comments>
		<pubDate>Tue, 17 Feb 2009 20:55:21 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[University]]></category>
		<category><![CDATA[Bachelor Thesis]]></category>
		<category><![CDATA[ePark24]]></category>
		<category><![CDATA[iPhone]]></category>

		<guid isPermaLink="false">http://blog.v1ru8.net/?p=240</guid>
		<description><![CDATA[Today we (Roman and me) started our bachelor thesis. We had a first meeting with our advising professor, scheduled one with our external customer and already had some problems. The thesis comprehends the development of a mobile payment application for the iPhone. With this application a customer should be able to pay parking lots from [...]]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.epark24.ch">
<div style="float:right"><img src="http://img.skitch.com/20090217-nfush1pgd8pup8uxxr617emppn.jpg" alt="ePark24 logo" /></div>
<p></a></p>
<p>Today we (Roman and me) started our bachelor thesis. We had a first meeting with our advising professor, scheduled one with our external customer and already had some problems.</p>
<p>The thesis comprehends the development of a mobile payment application for the iPhone. With this application a customer should be able to pay parking lots from he&#8217;s iPhone as easy as possible. Our external customer called <a href="http://www.epark24.ch">ePark24</a> has already a payment system. That system is a bit circumstantially. So our goal is to take the existing services and put them behind an iPhone application and expand it with some nice, useful and handy features.</p>
<p>Now that service is based on some 0900 numbers. You call them and then you enter your parking location and your license plate &#8211; or lot number. To do that automatically we need to dial so called DTMF codes. But that isn&#8217;t possible. Simple: <a href="http://developer.apple.com/iphone/library/featuredarticles/iPhoneURLScheme_Reference/Articles/PhoneLinks.html">Apple forbids to do that!</a>.</p>
<p>The first version of that iPhone App should be available in the iPhone App Store by mid May 2009. I will try to keep you up to date about my thesis and that app on this blog. ePark24 announced our iPhone App already in their <a href="http://www.epark24.ch/newsletter_januar_2009_d.pdf">january newsletter</a>. Have a look at the bottom of page two.</p>
<p>In this spirit, happy parking!</p>
]]></content:encoded>
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		<item>
		<title>Sometimes Java is just disgusting</title>
		<link>http://blog.v1ru8.net/2008/07/03/sometimes-java-is-just-disgusting/</link>
		<comments>http://blog.v1ru8.net/2008/07/03/sometimes-java-is-just-disgusting/#comments</comments>
		<pubDate>Thu, 03 Jul 2008 17:09:59 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[Java]]></category>
		<category><![CDATA[Regards]]></category>
		<category><![CDATA[Distributed Software Systems]]></category>
		<category><![CDATA[Frameworks]]></category>
		<category><![CDATA[JMS]]></category>
		<category><![CDATA[RMI]]></category>
		<category><![CDATA[Servlets]]></category>
		<category><![CDATA[SOAP]]></category>
		<category><![CDATA[XML-RPC]]></category>

		<guid isPermaLink="false">http://www.v1ru8.net/?p=73</guid>
		<description><![CDATA[This week I was learning for the assessment tomorrow: &#8220;Distributed Software Systems&#8221;. So I had a lot to learn about Servlets, XML-RPC, SOAP, REST, JRI and JMS. All of them are interesting technologies and I learned a lot! But (a big but) most of the time it&#8217;s so hard and complicated to implement them with [...]]]></description>
			<content:encoded><![CDATA[<p><a href='http://blog.v1ru8.net/wp-content/uploads/2008/07/java-evil-edition-orfjackal_net-lores.png' rel="lightbox[java]" style="float:left;"><img style="padding:10px" src="http://blog.v1ru8.net/wp-content/uploads/2008/07/java-evil-edition-orfjackal_net-lores.png" alt="" title="Evil Java" width="144" height="232" class="alignnone size-thumbnail wp-image-74" /></a>
<p>This week I was learning for the assessment tomorrow: &#8220;Distributed Software Systems&#8221;. So I had a lot to learn about Servlets, XML-RPC, SOAP, REST, JRI and JMS. All of them are interesting technologies and I learned a lot! </p>
<p>But (a big but) most of the time it&#8217;s so hard and complicated to implement them with Java. For all of them (except RMI) you need an external framework who isn&#8217;t included in the Java SE. Even JMS although it&#8217;s a technology that is specified by sun! That means for every technology you have to deal with different types of documentations, different webpages and peculiarities of every API. There is no &#8220;standard&#8221; how such things are done in the Java world. I needed a lot of time to learn all the stuff and there is almost no framework where I can say now: &#8220;wow that&#8217;s cool&#8221;. RMI is here an except too. RMI is quite nice.</p>
<p>For me, more and more the only reason why Java has its right to exist is its platform independence. Due to the fact that the Java framework itself is not how I expect it from a framewrok that has such a big market share (and the reasons above are far not the only ones!)</p>
]]></content:encoded>
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		<item>
		<title>Status Update</title>
		<link>http://blog.v1ru8.net/2008/06/16/status-update/</link>
		<comments>http://blog.v1ru8.net/2008/06/16/status-update/#comments</comments>
		<pubDate>Mon, 16 Jun 2008 11:29:26 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[iPhone]]></category>
		<category><![CDATA[Management]]></category>
		<category><![CDATA[Stuff]]></category>
		<category><![CDATA[app store]]></category>
		<category><![CDATA[apprenticeship]]></category>
		<category><![CDATA[iPhoneNotes]]></category>
		<category><![CDATA[job]]></category>
		<category><![CDATA[marks]]></category>
		<category><![CDATA[University]]></category>
		<category><![CDATA[vacation]]></category>

		<guid isPermaLink="false">http://www.v1ru8.net/?p=65</guid>
		<description><![CDATA[After some time of silence (i had a lot to do for the University) I&#8217;d like to post what is going on with V1ru8.net. How you&#8217;ve seen, two weeks ago i released a new version of iPhoneNotes 0.7. I think thats a quite final version but maybe it&#8217;s the last version of iPhoneNotes because of [...]]]></description>
			<content:encoded><![CDATA[<p>After some time of silence (i had a lot to do for the University) I&#8217;d like to post what is going on with V1ru8.net. How you&#8217;ve seen, two weeks ago i released a new version of iPhoneNotes 0.7. I think thats a quite final version but maybe it&#8217;s the last version of iPhoneNotes because of the iPhone 2.0 firmware. If it has a proper implementation of Notes synchronization I will stop developing it and it is possible that I release it under GPL. So that&#8217;s all about iPhoenNotes.</p>
<p>Now I&#8217;m working on a new Project called Marks. It&#8217;s a small iPhone app for students to manage their modules, credits and marks.<br />
<center><br />
<table>
<tr>
<td>
<a href="http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-3.png" rel="lightbox[marks]" title="Modules"><img src="http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-3-161x300.png" width="161" height="300" alt="" /></a></td>
<td>
<a href='http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-5.png' rel="lightbox[marks]"><img src="http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-5-161x300.png" alt="" title="picture-5" width="161" height="300" class="alignnone size-medium wp-image-68" /></a></td>
<td>
<a href='http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-21.png' rel="lightbox[marks]"><img src="http://blog.v1ru8.net/wp-content/uploads/2008/06/picture-21-161x300.png" alt="" title="picture-21" width="161" height="300" class="alignnone size-medium wp-image-69" /></a>
</td>
</tr>
</table>
<p></center></p>
<p>I hope this application will be available at the App Store in mid june. If you have any ideas or wishes what should be included in this app &#8211; then let me know!</p>
<p>Now let&#8217;s start to search a vacation job. I&#8217;d like to get one where I can work on a software project. But there are just two weeks time so I think I try to get a vacation job at the company where I made my apprenticeship and administrate Windows NT domains <img src='http://blog.v1ru8.net/wp-includes/images/smilies/icon_sad.gif' alt=':-(' class='wp-smiley' /> </p>
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		<item>
		<title>Probability and Statistics with Mathematica and Excel</title>
		<link>http://blog.v1ru8.net/2008/01/31/probability-and-statistics-with-mathematica-and-excel/</link>
		<comments>http://blog.v1ru8.net/2008/01/31/probability-and-statistics-with-mathematica-and-excel/#comments</comments>
		<pubDate>Thu, 31 Jan 2008 19:18:09 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[excel]]></category>
		<category><![CDATA[mathematica]]></category>
		<category><![CDATA[probability]]></category>
		<category><![CDATA[statistics]]></category>

		<guid isPermaLink="false">http://www.v1ru8.net/2008/01/31/probability-and-statistics-with-mathematica-and-excel/</guid>
		<description><![CDATA[Mathematica: Binomial: Binomial Average: Mean Median: Median Modus: Commonest Excel: Binomial Distribution: Poisson: Hypergeometric Distribution: Normal Distribution: Standard Deviation: Experimental Standard Deviation:]]></description>
			<content:encoded><![CDATA[<p><strong>Mathematica:</strong><br />
Binomial: <img src='/wp-content/latexrender/pictures/884fead63bb1fb0a92ce0aa667b019a1.gif' title='\binom{a}{b} \Rightarrow $Binomial$[n,m]' alt='\binom{a}{b} \Rightarrow $Binomial$[n,m]' align=absmiddle> <a target="_blank" href="http://reference.wolfram.com/mathematica/ref/Binomial.html">Binomial</a><br/><br />
Average: <img src='/wp-content/latexrender/pictures/6fee6c25525e7744c02896055768bc96.gif' title='\frac{1}{n} \cdot \sum_{i=1}^{n}x_i \Rightarrow $Mean$[\{x_1,x_2,\hdots,x_n\}]' alt='\frac{1}{n} \cdot \sum_{i=1}^{n}x_i \Rightarrow $Mean$[\{x_1,x_2,\hdots,x_n\}]' align=absmiddle> <a target="_blank" href="http://reference.wolfram.com/mathematica/ref/Mean.html">Mean</a><br/><br />
Median:<img src='/wp-content/latexrender/pictures/e59e48faef08d887dc66f8e346a9d587.gif' title='\text{Median}[\{x_1,x_2,\hdots,x_n\}]' alt='\text{Median}[\{x_1,x_2,\hdots,x_n\}]' align=absmiddle> <a target="_blank" href="http://reference.wolfram.com/mathematica/ref/Median.html">Median</a><br/><br />
Modus: <img src='/wp-content/latexrender/pictures/bd7479c4325ba0817be1c208d84ad0a1.gif' title='\text{Commonest}[\{x_1,x_2,\hdots,x_n\}]' alt='\text{Commonest}[\{x_1,x_2,\hdots,x_n\}]' align=absmiddle> <a target="_blank" href="http://reference.wolfram.com/mathematica/ref/Commonest.html">Commonest</a><br/><br />
<strong>Excel:</strong><br />
Binomial Distribution: <img src='/wp-content/latexrender/pictures/2bee06d022850895b0bcc2261948e34e.gif' title='P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{n-k} \Rightarrow $binomdist$(k$,$n$,$p$,true/false$) ' alt='P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{n-k} \Rightarrow $binomdist$(k$,$n$,$p$,true/false$) ' align=absmiddle> <br/><br />
Poisson: <img src='/wp-content/latexrender/pictures/1c7dd7790b414f68661307439982f703.gif' title='P(X = k) = \frac{\mu^k}{k!}\cdot e^{-\mu} \Rightarrow $poisson$(\mu$,$k)' alt='P(X = k) = \frac{\mu^k}{k!}\cdot e^{-\mu} \Rightarrow $poisson$(\mu$,$k)' align=absmiddle><br/><br />
Hypergeometric Distribution: <img src='/wp-content/latexrender/pictures/01fe0a0ae881dfbd67617ccac48e212a.gif' title='P(X=k) = \frac{\binom{M}{k} \cdot \binom{N-M}{n-k}}{\binom{N}{n}} \Rightarrow $hypergeomdist$(k$,$M$,$N$,$n)' alt='P(X=k) = \frac{\binom{M}{k} \cdot \binom{N-M}{n-k}}{\binom{N}{n}} \Rightarrow $hypergeomdist$(k$,$M$,$N$,$n)' align=absmiddle><br/><br />
Normal Distribution: <img src='/wp-content/latexrender/pictures/d23d2adc07612190b9a6e914a1b7720e.gif' title='\Phi_{\mu,\sigma}(x) = \Phi \left( \frac{x-\mu}{\sigma} \right) \Rightarrow $normdist$(x,\mu,\sigma,$true/false$)' alt='\Phi_{\mu,\sigma}(x) = \Phi \left( \frac{x-\mu}{\sigma} \right) \Rightarrow $normdist$(x,\mu,\sigma,$true/false$)' align=absmiddle><br/><br />
 <img src='/wp-content/latexrender/pictures/a6e81dd9e6f9566b5452467ba70c765e.gif' title='\Rightarrow $norminv$(P(X),0,1)' alt='\Rightarrow $norminv$(P(X),0,1)' align=absmiddle><br/><br />
Standard Deviation: <img src='/wp-content/latexrender/pictures/7bce1f42392ef3d84b9dde15b1379af9.gif' title='\sigma := \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_i &amp;#8211; \bar{x})^2} \Rightarrow $stdev$(x_1,x_2,\hdots,x_n)' alt='\sigma := \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_i &amp;#8211; \bar{x})^2} \Rightarrow $stdev$(x_1,x_2,\hdots,x_n)' align=absmiddle><br/><br />
Experimental Standard Deviation: <img src='/wp-content/latexrender/pictures/830e69940fb379ed133745e13247d280.gif' title='\sigma := \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i &amp;#8211; \bar{x})^2} \Rightarrow $stdevp$(x_1,x_2,\hdots,x_n)' alt='\sigma := \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i &amp;#8211; \bar{x})^2} \Rightarrow $stdevp$(x_1,x_2,\hdots,x_n)' align=absmiddle><br/></p>
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		<item>
		<title>Helpfully functions in mathematica for cryptographic</title>
		<link>http://blog.v1ru8.net/2008/01/04/helpfully-functions-in-mathematica-for-cryptographic/</link>
		<comments>http://blog.v1ru8.net/2008/01/04/helpfully-functions-in-mathematica-for-cryptographic/#comments</comments>
		<pubDate>Fri, 04 Jan 2008 19:00:22 +0000</pubDate>
		<dc:creator>Thomas Post</dc:creator>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[crypto]]></category>
		<category><![CDATA[LaTeX]]></category>
		<category><![CDATA[mathematica]]></category>

		<guid isPermaLink="false">http://www.v1ru8.net/2008/01/04/helpfully-functions-in-mathematica-for-cryptographic/</guid>
		<description><![CDATA[Square and multiply algorithm:  PowerMod Inverse function  PowerMod Chinese Remainder  Chinese Remainder Square root PowerModList Discrete Logarithm  Prime Numbers  returns you a prime RandomPrime Prime Factors  FactorInteger Euler Phi  EulerPhi]]></description>
			<content:encoded><![CDATA[<ul>
<li><span style="font-weight: bold" class="Apple-style-span">Square and multiply algorithm:</span> <span><img src='/wp-content/latexrender/pictures/d022feda8350d8d0e9fbdd039e16fdcb.gif' title='x^y \mod n \Rightarrow $PowerMod$[x,y,n] ' alt='x^y \mod n \Rightarrow $PowerMod$[x,y,n] ' align=absmiddle> <a href="http://reference.wolfram.com/mathematica/ref/PowerMod.html" target="_blank" title="Mathematica Manual">PowerMod</a></span></li>
<li><span style="font-weight: bold" class="Apple-style-span">Inverse function </span> <img src='/wp-content/latexrender/pictures/5f9adc4f56c1db8155451e780df7a7af.gif' title='x \cdot x^{-1} \equiv 1 \mod n \Rightarrow n = $PowerMod$[x,-1,n]' alt='x \cdot x^{-1} \equiv 1 \mod n \Rightarrow n = $PowerMod$[x,-1,n]' align=absmiddle><a href="http://reference.wolfram.com/mathematica/ref/PowerMod.html" target="_blank" title="Mathematica Manual">PowerMod</a></li>
<li><span class="Apple-style-span" style="font-weight: bold">Chinese Remainder </span>
<ul>
<li><img src='/wp-content/latexrender/pictures/20e3bbb28cfdd985e6bdd33b7da5d816.gif' title='x \equiv 2 \mod 3' alt='x \equiv 2 \mod 3' align=absmiddle></li>
</ul>
<ul>
<li><img src='/wp-content/latexrender/pictures/fdfb3a310582aef976a5be38870b59eb.gif' title='x \equiv 3 \mod 4' alt='x \equiv 3 \mod 4' align=absmiddle></li>
<li><img src='/wp-content/latexrender/pictures/48b6f35bb5208dcf91b6901166a3a39e.gif' title='x \equiv 2 \mod 5' alt='x \equiv 2 \mod 5' align=absmiddle></li>
</ul>
<ul>
<li><img src='/wp-content/latexrender/pictures/0ca5fe2563a31839b2974c5aa96165a4.gif' title=' \Rightarrow x = $ChineseRemainder$[\{2,3,2\},\{3,4,5\}]' alt=' \Rightarrow x = $ChineseRemainder$[\{2,3,2\},\{3,4,5\}]' align=absmiddle></li>
<li><span style="color: #551a8b; text-decoration: underline" class="Apple-style-span"><a href="http://reference.wolfram.com/mathematica/ref/ChineseRemainder.html" target="_blank" title="Chinese Remainder">Chinese Remainder</a></span></li>
</ul>
</li>
<li><span class="Apple-style-span" style="font-weight: bold">Square root</span> <img src='/wp-content/latexrender/pictures/5190035efb4b60366280eaa23e1eb581.gif' title='\sqrt{y} \equiv x \mod n \Rightarrow x = $PowerModList$[y,\frac{1}{2},n]' alt='\sqrt{y} \equiv x \mod n \Rightarrow x = $PowerModList$[y,\frac{1}{2},n]' align=absmiddle><a href="http://reference.wolfram.com/mathematica/ref/PowerModList.html" title="Mathematica Manual" target="_blank">PowerModList</a></li>
<li><span class="Apple-style-span" style="font-weight: bold">D</span><span style="font-weight: bold" class="Apple-style-span">iscrete Logarithm</span> <img src='/wp-content/latexrender/pictures/362a0ae3cc8397dd0923ad5fee3c38a9.gif' title='y^x \equiv z \mod n \Rightarrow x = \text{MultiplicativeOrder}[y,n,\{r\}]' alt='y^x \equiv z \mod n \Rightarrow x = \text{MultiplicativeOrder}[y,n,\{r\}]' align=absmiddle></li>
<li><span class="Apple-style-span" style="font-weight: bold">Prime Numbers</span> <img src='/wp-content/latexrender/pictures/bd7bb430d0a85b5f73e9856752370188.gif' title='\text{RandomPrime}[\{x,y\}]' alt='\text{RandomPrime}[\{x,y\}]' align=absmiddle> returns you a prime <img src='/wp-content/latexrender/pictures/3622d8b560f9c872fc749310e2450bc9.gif' title='x &amp;lt; p &amp;lt; y' alt='x &amp;lt; p &amp;lt; y' align=absmiddle><a href="http://reference.wolfram.com/mathematica/ref/RandomPrime.html" title="Mathematica Manual" target="_blank">RandomPrime</a></li>
<li><span class="Apple-style-span" style="font-weight: bold">Prime Factors</span> <img src='/wp-content/latexrender/pictures/834aa730b0bc48bf1c6167882462fe64.gif' title='\text{FactorInteger}[n]' alt='\text{FactorInteger}[n]' align=absmiddle> <a href="http://reference.wolfram.com/mathematica/ref/FactorInteger.html" title="Mathematica Manual" target="_blank">FactorInteger</a></li>
<li><span style="font-weight: bold" class="Apple-style-span">Euler Phi</span> <img src='/wp-content/latexrender/pictures/ef3e9a54b095b1507fccb1c3a600c436.gif' title='\varphi(n) \Rightarrow \text{EulerPhi}[n]' alt='\varphi(n) \Rightarrow \text{EulerPhi}[n]' align=absmiddle> <a href="http://reference.wolfram.com/mathematica/ref/EulerPhi.html" title="Mathematica Manual" target="_blank">EulerPhi</a></li>
</ul>
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