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                  <span class="slideshow-title" style="font-size:14px;">Modular Arithmetic and Trap Door Ciphers</span><br />
                  From: <a href="http://www.slideshare.net/joshuarbholden" class="slideshow-author">joshuarbholden</a>,
                  <span class="ago">3 months ago</span><br /><br />
                  <div class="slideshow-embed"><div style="width:425px;text-align:left" id="__ss_546324"><a style="font:14px Helvetica,Arial,Sans-serif;display:block;margin:12px 0 3px 0;text-decoration:underline;" href="http://www.slideshare.net/joshuarbholden/modular-arithmetic-and-trap-door-ciphers?type=powerpoint" title="Modular Arithmetic and Trap Door Ciphers">Modular Arithmetic and Trap Door Ciphers</a><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=rsatalk-1218160590585322-8&stripped_title=modular-arithmetic-and-trap-door-ciphers" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=rsatalk-1218160590585322-8&stripped_title=modular-arithmetic-and-trap-door-ciphers" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;">View SlideShare <a style="text-decoration:underline;" href="http://www.slideshare.net/joshuarbholden/modular-arithmetic-and-trap-door-ciphers?type=powerpoint" title="View Modular Arithmetic and Trap Door Ciphers on SlideShare">presentation</a> or <a style="text-decoration:underline;" href="http://www.slideshare.net/upload?type=powerpoint">Upload</a> your own. (tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/modular">modular</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/rsa">rsa</a>)</div></div></div><br /><br />
                  <div class="slideshow-description">Like other branches of mathematics, number theory has seen many surprising developments in recent years. One of the most surprising is the fact that number theory, long considered the most "useless" of any field of mathematics, has become vital to the development of modern codes and ciphers. As an example, the RSA cryptosystem,  eveloped in the 1970's by Rivest, Shamir, and Adleman, uses some ideas that are very easy to understand. Yet, these ideas underlie large portions of both modern number theory and modern cryptography. We will explore these ideas, and show how they make RSA the first practical "trap door" cipher. This means that anyone can encode a message but only the recipient can decode it!</div><br /><br />
                  <a href="http://www.slideshare.net/joshuarbholden/modular-arithmetic-and-trap-door-ciphers" class="slideshow-link">SlideShare Link</a>
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Modular Arithmetic and Trap Door Ciphers

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Desc: Like other branches of mathematics, number theory has seen many surprising developments in recent years. One of the most surprising is the fact that number theory, long considered the most "useless" of any field of mathematics, has become vital to the development of modern codes and ciphers. As an example, the RSA cryptosystem, eveloped in the 1970's by Rivest, Shamir, and Adleman, uses some ideas that are very easy to understand. Yet, these ideas underlie large portions of both modern number theory and modern cryptography. We will explore these ideas, and show how they make RSA the first practical "trap door" cipher. This means that anyone can encode a message but only the recipient can decode it!

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Slide 1: Modular arithmetic and trap door ciphers Prof. Joshua Holden, Rose-Hulman Inst. of Tech. http://www.rose-hulman.edu/˜holden Modular arithmetic and trap door ciphers – p.1/31
Slide 2:RSA Setup Ronald Rivest, Adi Shamir, Leonard Adleman, 1977. Pick two primes and . ¡ Compute . ¢ ¡ £ Pick encryption exponent such that and

Modular Arithmetic and Trap Door Ciphers

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