An introduction to cryptography, Second Edition

As the title states the book by Johannes Buchmann provides an introduction to cryptography. Buchmann’s text in only 324 pages (excluding the appendices) presents a stand alone introduction to some modern cryptographic methods. The book begins with the mathematical background that will be used as foundation for the cryptographic methods discussed in this book. Chapter one explains the important properties of integers and the extended Euclidean algorithm. Chapter two includes some important algebraic definitions (groups, residue class, ring, fields,...). Also, it contains algorithms for fast evaluation of power products and the Chinese remainder theorem. Probability theory and Shannon’s view of perfect secrecy are presented in chapter 4. There are three chapters discussing symmetric cryptography and to be more specific they are devoted to block ciphers. Chapter 3 explains the meaning of cryptosystems and gives some different encryption schemes. For the symmetric cryptography the author just defines the structure of stream ciphers and provides two examples, whereas he explains the block cipher in more details. Moreover chapter 5 and chapter 6 represent a complete study to the most famous block ciphers DES and AES, respectively. In the next four chapters, the author discusses asymmetric cryptography (public key cryptography). Since many public key cryptosystems use large prime numbers, the author gives more additional mathematical preliminaries for the prime number generation and some algorithms used for testing the primality of large numbers in chapter 7. The idea of public key cryptosystems and a description to the most important schemes are given in chapter 8, for examples RSA and ElGamal. The security of RSA is based on the difficulty of the factorization problem and is studied in chapter 9. It is focusing on the quadratic sieve algorithm and providing an estimation to the efficiency of it and some other factoring algorithms. Similarly, in chapter 10 the security analysis of ElGamal cryptosystem is discussed by analyzing the algorithms that solve the discrete logarithm problem.