Modern Cryptanalysis: Techniques for Advanced Code Breaking

Chapter 2. Number Theoretical Ciphers

In recent years, many cryptographic algorithms have been based on mathematical structures designed to hide information: Information is very easy to obscure if you know the correct trick. This trick is knowing the scheme and a key of some sort, as is the case for the previously studied simple ciphers.

All ciphers are based on tricks: Those in Chapter 1 were more mechanical in nature. A person or computer can perform the encryption and decryption by using a table or a very simple algorithm, and translating the result. This chapter introduces cryptographic algorithms in which the encryption and decryption algorithms are very mathematical, using recent advances in number theory and algebra to make finding the information difficult.

This is not a mathematics book, but it is necessary to know a little bit about mathematics in order to understand some of these ciphers. Regardless, I do not want to drown you with math notation or obscure notions. This explanation is not exhaustive (or formal), but it should eliminate any reader confusion about the subject.

I am also torn between two desires: the desire to explain everything, but also the desire to not lose the reader in details and in lots of tedious mathematics. I will try to explain everything necessary in as simple terms as possible, but I will understand if you gloss over some of the mathematics and get straight to the juicy stuff. Just know that the math is there if you want or need to read it, although ...