{"id":482,"date":"2017-10-16T00:25:31","date_gmt":"2017-10-16T00:25:31","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/holden\/?page_id=482"},"modified":"2017-10-24T16:51:40","modified_gmt":"2017-10-24T16:51:40","slug":"math-478-the-mathematics-of-public-key-cryptography","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/holden\/math-478-the-mathematics-of-public-key-cryptography\/","title":{"rendered":"Math 478: The Mathematics of Public Key Cryptography"},"content":{"rendered":"

Math 478<\/h1>\n

Topics in Number Theory:\u00a0 The Mathematics of Public Key Cryptography<\/p>\n

Winter 2017-2018<\/p>\n

Instructor:<\/b> Joshua Holden
\nOffice:<\/b> G207
\nOffice Phone:<\/b> 877-8320
\nE-mail:<\/b> holden@rose-hulman.edu<\/code><\/a>
\nWeb Page:<\/b> http:\/\/www.rose-hulman.edu\/~holden<\/code><\/a><\/p>\n

\n

Description<\/h3>\n

Maybe this looks familiar:\u00a0 (If it doesn’t, that’s okay too!)<\/p>\n

\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \"\" \u00a0 \u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \"\"<\/p>\n

Alice\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Eve\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Bob<\/p>\n

makes encryption key E
\nmakes decryption key D
\nposts encryption key E
\n“Now Alice can send me a message!”<\/p>\n

“I want to send a message to Bob.”
\nlooks up Bob’s encryption key E<\/p>\n

“Hi, Bob, this is Alice.”
\n\u2193E
\nJDAOEBCMXFMZNCTKKAKDNZC<\/p>\n

JDAOEBCMXFMZNCTKKAKDNZC\u2192
\nlooks up E
\n“I don’t know D.”
\n“How do I invert the function?”<\/p>\n

JDAOEBCMXFMZNCTKKAKDNZC
\n\u2193 D
\n“Hi, Bob, this is Alice.”<\/p>\n

 <\/p>\n

But do you know this one?<\/p>\n

\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \"\" \u00a0 \u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \"\"<\/p>\n

Alice\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Eve\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Bob<\/p>\n

“I want to send a message to Bob, but all I know is his email.”<\/p>\n

“Hi, Bob, this is Alice.”
\n\u2193bob@bobsemail.com
\nJDAOEBCMXFMZNCTKKAKDNZC<\/p>\n

JDAOEBCMXFMZNCTKKAKDNZC\u2192
\nlooks up bob@bobsemail.com
\n“How do I invert the function?”<\/p>\n

“Oh, look, it’s a message.”
\nbob@bobsemail.com\u2193
\nmakes decryption key D<\/p>\n

JDAOEBCMXFMZNCTKKAKDNZC
\n\u2193 D
\n“Hi, Bob, this is Alice.”<\/p>\n

How can Alice send Bob a secret message before Bob even knows he needs a secret key???<\/p>\n

We are going to be using facts about integers to do some cool things in cryptography, like Identity-Based Encryption. You don’t have to know anything about cryptography to start, but if you do I think you will still learn something new!<\/p>\n

Requirements<\/h3>\n

The prerequisite for this class is DISCO I (Math 275) or Number Theory (Math 378).\u00a0\u00a0 (Banner says Math 375 but I will waive that if you have had Math 275.)\u00a0 If you have had some other experience with number theory or cryptography, come see me and we’ll talk.<\/p>\n

Class Schedule Information<\/a> from Banner<\/h3>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Math 478 Topics in Number Theory:\u00a0 The Mathematics of Public Key Cryptography Winter 2017-2018 Instructor: Joshua Holden Office: G207 Office Phone: 877-8320 E-mail: holden@rose-hulman.edu Web Page: http:\/\/www.rose-hulman.edu\/~holden Description Maybe this looks familiar:\u00a0 (If it doesn’t, that’s okay too!) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Alice\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Eve\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Bob makes encryption key E makes decryption key D posts encryption … Continue reading Math 478: The Mathematics of Public Key Cryptography<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":938,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-482","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8uE0W-7M","_links":{"self":[{"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/pages\/482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/users\/938"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/comments?post=482"}],"version-history":[{"count":7,"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/pages\/482\/revisions"}],"predecessor-version":[{"id":520,"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/pages\/482\/revisions\/520"}],"wp:attachment":[{"href":"https:\/\/wordpress.rose-hulman.edu\/holden\/wp-json\/wp\/v2\/media?parent=482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}