Join our book community on Discord

https://packt.link/SecNet

This chapter provides an introduction to cryptography, what it is needed for, and why it is so important in IT. This chapter also gives a panoramic view of the principal algorithms from the history of cryptography, from the Caesar algorithm to the Vernam cipher and other lesser-known algorithms, such as the Beale cipher. Then, Rivest-Shamir-Adleman (RSA), Diffie–Hellman, and other famous algorithms will be described in detail in the proceeding part of this book. Finally, this chapter will give you the instruments to learn cryptography and the pillars of security conservation.In this chapter, we will cover the following topics:

• A brief introduction to cryptography
• Basic definitions and principal mathematical notations used in the book
• Binary conversion and ASCII code
• Fermat Last's Theorem, prime numbers, and modular mathematics
• The history of the principal cryptographic algorithms and an explanation of some of them...

An introduction to cryptography

One of the most important things in cryptography is to understand definitions and notations. I have never been a fan of definitions and notations, first of all, because I am the only one to use notations that I've invented. But I realize that it is very important, especially when we are talking about something related to mathematics, to agree among ourselves. Thus, in this section, I will introduce basic information and citations relating to cryptography.We start with a definition of an algorithm.In mathematics and computer science, an algorithm is a finite sequence of well-defined computer-implementable instructions.An important question is: what is a cipher?A cipher is a system of any type able to transform plaintext (a message) into not-intelligible text (a ciphertext or cryptogram):

To get some utility from a cipher, we have to set up two operations: encryption and decryption. In simpler terms, we have to...

A brief history and a panoramic overview of cryptographic algorithms

Nobody probably knows which cryptogram was the first to be invented. Cryptography has been used for a long time, approximately 4,000 years, and it has changed its paradigms a lot. First, it was a kind of hidden language, then cryptography was based on a transposition of letters in a mechanical fashion, then finally, mathematics and logic were used to solve complicated problems. What will the future hold? Probably, new methods will be invented to hide our secrets: quantum cryptography, for example, is already being experimented with and will come soon. I will explain new algorithms and methods throughout this book, but let me use this section to show you some interesting ciphers related to the classical period. Despite the computation power we have now, some of these algorithms have not yet been broken.

Notes on security and computation

All the algorithms we have seen in this chapter are symmetric. The basic problem that remains unsolved is the transmission of the key. As I've already said, this problem will be overcome by the asymmetric cryptography that we will explore in the next chapter. In this section, we will analyze the computational problem related to the security of cryptographic algorithms generally speaking. Later in the book, we will focus on the security of any algorithm we will analyze.To make a similitude, we can say that in cryptography the weak link of the chain destroys the entire chain. That is the same problem as using a very strong cryptographic algorithm to protect the data but leaving its password on the computer screen. In other words, a cryptographic algorithm has to be made of a similar grade of security with respect to mathematical problems. To clarify this concept with an example: factorization and discrete logarithm problems hold similar computational...