Mathematics 139 - Cryptography: The Mathematics of Sending Secret Messages

Cryptography is the study of secret communication between different groups of people. From 4,000 years ago in ancient Egypt when secret hieroglyphs were used to communicate the messages of royalty to today when credit card numbers are encrypted to be transmitted over the internet, cryptography has been a necessary part of human life. In this class we will discuss classical cryptography and some historical ciphers along with the mathematical concepts of the modern field. We will study public key cryptography, prime numbers, the discrete logarithm problem, the Diffie-Hellman key exchange, and RSA encryption. If time permits we will also discuss elliptic curve encryption. In particular, we will use the Python programming language and Jupyter notebooks to implement the encryption schemes that we study.