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 12

The RSA system is probably the most widely used public-key cryptosystem in the world. It is certainly the best known. It provides both digital signatures and public-key encryption, which makes it a very versatile tool, and it is based on the difficulty of factoring large numbers, a problem that has fascinated many people over the last few millennia and has been studied extensively.

12.1 Introduction

RSA is similar to, yet very different from, Diffie-Hellman (see Chapter 11). Diffie-Hellman (DH for short) is based on a one-way function: assuming p and g are publicly known, you can compute (gx mod p) from x, but you cannot compute x given gx mod p. RSA is based on a trapdoor one-way function. Given the publicly known information n and e, it is easy to compute me mod n from m, but not the other way around. However, if you know the factorization of n, then it is easy to do the inverse computation. The factorization of n is the trapdoor information. If you know it, you can...