Book Image

Cryptography Engineering

By : Niels Ferguson‚ÄØ, Tadayoshi Kohno, Bruce Schneier
Book Image

Cryptography Engineering

By: Niels Ferguson‚ÄØ, Tadayoshi Kohno, Bruce Schneier

Overview of this book

Cryptography is vital to keeping information safe, in an era when the formula to do so becomes more and more challenging. Written by a team of world-renowned cryptography experts, this essential guide is the definitive introduction to all major areas of cryptography: message security, key negotiation, and key management. You'll learn how to think like a cryptographer. You'll discover techniques for building cryptography into products from the start and you'll examine the many technical changes in the field. After a basic overview of cryptography and what it means today, this indispensable resource covers such topics as block ciphers, block modes, hash functions, encryption modes, message authentication codes, implementation issues, negotiation protocols, and more. Helpful examples and hands-on exercises enhance your understanding of the multi-faceted field of cryptography.
Table of Contents (9 chapters)

Chapter 10
Primes

The following two chapters explain public-key cryptographic systems. This requires some mathematics to get started. It is always tempting to dispense with the understanding and only present the formulas and equations, but we feel very strongly that this is a dangerous thing to do. To use a tool, you should understand the properties of that tool. This is easy with something like a hash function. We have an “ideal” model of a hash function, and we desire the actual hash function to behave like the ideal model. This is not so easy to do with public-key systems because there are no “ideal” models to work with. In practice, you have to deal with the mathematical properties of the public-key systems, and to do that safely you must understand these properties. There is no shortcut here; you must understand the mathematics. Fortunately, the only background knowledge required is high school math.

This chapter is about prime numbers. Prime numbers...