### Course Introduction

Cryptography is essentially the science of writing in secret code. In data and telecommunications, cryptography has specific security requirements, such as authentication, privacy or confidentiality, integrity, and non-repudiation. To meet these security requirements, we employ secret key (or symmetric) cryptography, public-key (or asymmetric) cryptography, and hash functions.

In the first part of the course, we will review a number of different ciphers that were used before World War II. These ciphers would be easily broken nowadays, since cryptography has advanced quickly over the past couple of decades with the advent of modern computers. We will cover block cipher algorithms and describe the advanced encryption standard for a symmetric-key encryption adopted by the U.S. government. We will also learn about the important MD5 and SHA-1 hash functions as well as the message authentication code.

This course will focus on public key cryptography, which is best exemplified by the RSA algorithm (named after the algorithm inventors Rivest, Shamir, and Adleman). The RSA algorithm is considered particularly strong due to the fact that it relies on prime factorization, a computationally difficult process. We will take a careful look at this algorithm in this course. We will also learn about elliptic curves, another important mathematical function in cryptography, as well as the Diffie-Hellman key exchange and the elliptic curve discrete logarithm problem.

In the final part of the course, we will cover key exchange methods, study signature schemes, and provide an overview and discussion of public key infrastructure.