# The Mathematics of Cryptography

Assistant Professor
Department of Electrical Engineering
National University of Computer and Emerging Sciences
Foundation for the Advancement of Science and Technology (FAST)
Lahore, Pakistan

This video lesson provides a more advanced approach to cryptography than the more experiential Sturtevant cryptography lesson also in the BLOSSOMS video library. Students will learn about the history of cryptography and they will also learn how powerful even a limited knowledge of mathematics can be as they work through the math used in cryptography. This lesson will require two class sessions (50-60 minutes each) for completion, and the only prerequisite is a 9th grade level of mathematics knowledge. Materials needed include a hexagonal pencil, paper strips, a ruler (12 inches), and the material included in the document, Teachers Material, downloadable below. During the in-class periods between the video breaks, students will be involved in creating cryptography devices with pencils and will be exposed to increasingly more complex cryptography challenges.

Muhammad Aurangzeb has more than twenty years of experience teaching and more than ten years of work in the telecommunications industry. Currently he is at the University of Texas at Arlington, USA, pursuing a PhD in Electrical Engineering.

This tutorial paper gives a fairly gentle introduction to the basic mathematics required to understand encryption systems. Three main areas are covered: modular arithmetic, prime numbers and probability theory.
http://blossoms.mit.edu/sites/default/files/white-paper-Good-Old-Mathematics.pdf

This page is from the website of Thomas Jefferson's home, Monticello, and discusses the history and mechanics of Jefferson's Wheel Cipher.
http://www.monticello.org/reports/interests/wheel_cipher.html

http://www.monticello.org/jefferson/wheelcipher/index2.html

This site provides extensive information on the Enigma Machine, including history, classroom exercises and additional resources on the topic.
http://plus.maths.org/issue34/features/ellis/

Information on cryptography from the Internet Mathematics Library of the Math Forum@Drexel University.
http://mathforum.org/library/topics/cryptography/

A more advanced and comprehensive introduction to cryptography
http://www.ciphersbyritter.com/LEARNING.HTM