# Math 478

Topics in Number Theory: 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: (If it doesn’t, that’s okay too!)

Alice Eve Bob

makes encryption key E

makes decryption key D

posts encryption key E

“Now Alice can send me a message!”

“I want to send a message to Bob.”

looks up Bob’s encryption key E

“Hi, Bob, this is Alice.”

↓E

JDAOEBCMXFMZNCTKKAKDNZC

JDAOEBCMXFMZNCTKKAKDNZC→

looks up E

“I don’t know D.”

“How do I invert the function?”

JDAOEBCMXFMZNCTKKAKDNZC

↓ D

“Hi, Bob, this is Alice.”

But do you know this one?

Alice Eve Bob

“I want to send a message to Bob, but all I know is his email.”

“Hi, Bob, this is Alice.”

↓bob@bobsemail.com

JDAOEBCMXFMZNCTKKAKDNZC

JDAOEBCMXFMZNCTKKAKDNZC→

looks up bob@bobsemail.com

“How do I invert the function?”

“Oh, look, it’s a message.”

bob@bobsemail.com↓

makes decryption key D

JDAOEBCMXFMZNCTKKAKDNZC

↓ D

“Hi, Bob, this is Alice.”

How can Alice send Bob a secret message before Bob even knows he needs a secret key???

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!

### Requirements

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

### Class Schedule Information from Banner