Discrete Mathematical Structures, Lecture 5.1: Symmetric cryptographic ciphers

Discrete Mathematical Structures, Lecture 5.1: Symmetric cryptographic ciphers.

The practice of sending encrypted messages has been around since at least Julius Caesar, in the 1st century B.C. In this lecture, we look at some basic "symmetric" cryptographic ciphers, which means that the decoding function d(x) is simply the inverse e(x) of the encoding function. We begin with the Caesar cipher, which encodes messages by shifting each letter by a fixed amount. Formally, this is an encryption function e(x)=x+k (mod 26). We can makes things harder by using a general affine cipher, which uses an encryption function e(x)=ax+b (mod 26), where gcd(26,a)=1. Unfortunately, all of these can be cracked quite easily by analyzing letter frequency. So we can make things harder with a block cipher, which shifts letters by varying amounts, depending on the key, which is a short string of text. We do an example using the Vigenère cipher.

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