Public Key Encryption Algorithms - Revision history

http://wiki.cas.mcmaster.ca/index.php?action=history&feed=atom&title=Public_Key_Encryption_Algorithms Public Key Encryption Algorithms - Revision history 2026-04-06T01:55:49Z Revision history for this page on the wiki MediaWiki 1.15.1 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1915&oldid=prev Zhaoy36: /* How does Public Key Encryption work? */ 2008-04-12T22:34:34Z

<p><span class="autocomment">How does Public Key Encryption work?</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:34, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 8:</td> <td colspan="2" class="diff-lineno">Line 8:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The user has a pair of keys - public key and private key<sup>[http://en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>. A message encrypted with a public key can only be decrypted by the corresponding private key. It is mathematically infeasible to derive private key from public key.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The user has a pair of keys - public key and private key<sup>[http://en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>. A message encrypted with a public key can only be decrypted by the corresponding private key. It is mathematically infeasible to derive private key from public key.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:pk_enc.gif|thumb|300px|center|<del class="diffchange diffchange-inline">Figure 1: Public Key Encryption</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:pk_enc.gif|thumb|300px|center|<ins class="diffchange diffchange-inline">A message encrypted with a public key can only be decrypted by the corresponding private key</ins>]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Advantage over Symmetric Encryption===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Advantage over Symmetric Encryption===</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1914&oldid=prev Zhaoy36: /* Digital signature to ensure authenticity */ 2008-04-12T22:29:06Z

<p><span class="autocomment">Digital signature to ensure authenticity</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:29, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The sender encrypts a message with his own private key <del class="diffchange diffchange-inline">which will be decrypted by </del>the sender’s public key]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The sender encrypts a message with his own private key<ins class="diffchange diffchange-inline">. The receiver decrypts the message using </ins>the sender’s public key]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1913&oldid=prev Zhaoy36: /* Digital signature to ensure authenticity */ 2008-04-12T22:27:53Z

<p><span class="autocomment">Digital signature to ensure authenticity</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:27, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The sender encrypts a message with his own private key<del class="diffchange diffchange-inline">. If the receiver can decrypt the sender’s message using </del>the sender’s public key<del class="diffchange diffchange-inline">, this provides assurance that it is the sender (not a pretender) sent it</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The sender encrypts a message with his own private key <ins class="diffchange diffchange-inline">which will be decrypted by </ins>the sender’s public key]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1912&oldid=prev Zhaoy36: /* Digital signature to ensure authenticity */ 2008-04-12T22:27:02Z

<p><span class="autocomment">Digital signature to ensure authenticity</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:27, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The <del class="diffchange diffchange-inline">security of RSA </del>is <del class="diffchange diffchange-inline">based on </del>the <del class="diffchange diffchange-inline">difficulty of integer factorization</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:digital_signature.jpg|thumb|300px|right|The <ins class="diffchange diffchange-inline">sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it </ins>is the <ins class="diffchange diffchange-inline">sender (not a pretender) sent it</ins>]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1911&oldid=prev Zhaoy36: /* Digital signature to ensure authenticity */ 2008-04-12T22:12:21Z

<p><span class="autocomment">Digital signature to ensure authenticity</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:12, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:digital_signature.<del class="diffchange diffchange-inline">gif</del>|thumb|300px|right|The security of RSA is based on the difficulty of integer factorization]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:digital_signature.<ins class="diffchange diffchange-inline">jpg</ins>|thumb|300px|right|The security of RSA is based on the difficulty of integer factorization]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1910&oldid=prev Zhaoy36: /* Digital signature to ensure authenticity */ 2008-04-12T22:12:08Z

<p><span class="autocomment">Digital signature to ensure authenticity</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:12, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Digital signature to ensure authenticity===</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Image:digital_signature.gif|thumb|300px|right|The security of RSA is based on the difficulty of integer factorization]]</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The sender encrypts a message with his own private key. If the receiver can decrypt the sender’s message using the sender’s public key, this provides assurance that it is the sender (not a pretender) sent it<sup>[http://www.en.wikipedia.org/wiki/Public-key_cryptography R1]</sup>.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Mathematical Theory===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Mathematical Theory===</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1909&oldid=prev Zhaoy36: /* Elliptic curve cryptography */ 2008-04-12T22:08:58Z

<p><span class="autocomment">Elliptic curve cryptography</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:08, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 74:</td> <td colspan="2" class="diff-lineno">Line 74:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Decrypted message M’ = C^D mod N = 13^7 mod 33 = 7</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Decrypted message M’ = C^D mod N = 13^7 mod 33 = 7</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Elliptic curve cryptography ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Elliptic curve cryptography ==</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 99:</td> <td colspan="2" class="diff-lineno">Line 100:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Comparing with other public key algorithms<sup>[http://en.wikipedia.org/wiki/Elliptic_curve_cryptography R7]</sup>, if the user wants 128-bit security, he needs a curve to create 256-bit key.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Comparing with other public key algorithms<sup>[http://en.wikipedia.org/wiki/Elliptic_curve_cryptography R7]</sup>, if the user wants 128-bit security, he needs a curve to create 256-bit key.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>However, if the user chooses DSA, it would require 3072-bit public keys and 256-bit private keys. For RSA, it would require 3072-bit public and private keys.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>However, if the user chooses DSA, it would require 3072-bit public keys and 256-bit private keys. For RSA, it would require 3072-bit public and private keys.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Rabin cryptosystem ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Rabin cryptosystem ==</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1908&oldid=prev Zhaoy36: /* A Working Example */ 2008-04-12T22:08:24Z

<p><span class="autocomment">A Working Example</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:08, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===A Working Example===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===A Working Example===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:math_theory.gif|thumb|300px|right|<del class="diffchange diffchange-inline">Figure 1: Public Key Encryption</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:math_theory.gif|thumb|300px|right|<ins class="diffchange diffchange-inline">The security of RSA is based on the difficulty of integer factorization</ins>]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>1. choose 2 prime numbers<sup>[http://www.di-mgt.com.au/rsa_alg.html R6]</sup> :</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>1. choose 2 prime numbers<sup>[http://www.di-mgt.com.au/rsa_alg.html R6]</sup> :</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1907&oldid=prev Zhaoy36: /* A Working Example */ 2008-04-12T22:07:43Z

<p><span class="autocomment">A Working Example</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:07, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===A Working Example===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===A Working Example===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">[[Image:math_theory.gif|thumb|300px|right|Figure 1: Public Key Encryption]]</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>1. choose 2 prime numbers<sup>[http://www.di-mgt.com.au/rsa_alg.html R6]</sup> :</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>1. choose 2 prime numbers<sup>[http://www.di-mgt.com.au/rsa_alg.html R6]</sup> :</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2" class="diff-lineno">Line 74:</td> <td colspan="2" class="diff-lineno">Line 74:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Decrypted message M’ = C^D mod N = 13^7 mod 33 = 7</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Decrypted message M’ = C^D mod N = 13^7 mod 33 = 7</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Elliptic curve cryptography ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Elliptic curve cryptography ==</div></td></tr>  </table>

Zhaoy36 http://wiki.cas.mcmaster.ca/index.php?title=Public_Key_Encryption_Algorithms&diff=1906&oldid=prev Zhaoy36: /* Mathematical Theory */ 2008-04-12T22:07:30Z

<p><span class="autocomment">Mathematical Theory</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 22:07, 12 April 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 23:</td> <td colspan="2" class="diff-lineno">Line 23:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Mathematical Theory===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Mathematical Theory===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Image:math_theory.gif|thumb|300px|right|Figure 1: Public Key Encryption]]</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Many public key encryption algorithms are based on “Trap Door function”<sup>[http://www.krellinst.org/UCES/archive/modules/charlie/pke/node4.html R4]</sup>. Such type of function is easy to compute in one direction and difficult to calculate from the inverse direction. For example, f(x)=y is easy to compute y when x is given, but it is difficult to compute x when y is given.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Many public key encryption algorithms are based on “Trap Door function”<sup>[http://www.krellinst.org/UCES/archive/modules/charlie/pke/node4.html R4]</sup>. Such type of function is easy to compute in one direction and difficult to calculate from the inverse direction. For example, f(x)=y is easy to compute y when x is given, but it is difficult to compute x when y is given.</div></td></tr>  </table>

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