Fundamentals of cryptology. A professional reference and interactive tutorial. Incl. 1 CD-ROM (Q2781764)

This book is intended to serve as an introduction to modern cryptographic methods. It is an updated and improved version of \textit{H. C. A. van Tilborg} [An introduction to cryptology, Kluwer International Series in Engineering and Computer Science 52 (Kluwer Academic Publishers, Boston) (1988; Zbl 0699.94005)] with many new sections and two new chapters. Also, the whole text is now available as an interactive Mathematica manuscript on an accompanying CD ROM. NEWLINENEWLINENEWLINEThe book is divided into 15 chapters covering stream and block ciphers, public key cryptosystems and some topics relevant to modern cryptology, like secret sharing and zero knowledge protocols. Four appendices (forming about one third of the book) explain necessary mathematical prerequisites and also give a brief historical introduction of relevant famous mathematicians. Throughout the text, Mathematica is used to describe most of the functions and algorithms explained in the book. Moreover, each chapter ends with a set of problems related to the respective topic. NEWLINENEWLINENEWLINEIntroductory Chapter 1 contains a brief terminology section followed by Shannon's description of a conventional cryptosystem and a section on a statistical description of a plaintext source. The next three chapters are devoted to the conventional cryptosystems. Particularly, Chapter 2 describes a number of classical cryptosystems. Some cryptanalytic methods are outlined here as well, namely the method of a probable word and Kasiski's method. Chapter 3 is devoted to the pseudorandom sequences generated by linear and nonlinear feedback shift registers. Block ciphers are discussed in Chapter 4, where block cipher modes are described followed by brief descriptions of DES, Triple DES and IDEA. NEWLINENEWLINENEWLINEBefore switching to the topics of modern cryptology, some useful general information is presented. Firstly, Chapter 5 explains the notions of entropy, redundancy, unicity distance, mutual information and ends by defining unconditionally secure systems. Subsequently, in Chapter 6 general methods to reduce the redundancy in the plaintext (i.e. data compression techniques) are discussed. NEWLINENEWLINENEWLINEChapter 7 is the first of chapters devoted to the important part of modern cryptology, namely public key cryptography. Here the theoretical model of a public key cryptosystem is briefly described and discussed; the notion of digital signatures is introduced here as well. Next, Chapter 8 presents various systems based on the discrete logarithm problem -- the Diffie-Hellman key exchange system, ElGamal's public key cryptosystem and signature scheme as well as variations of the signature scheme including the Digital Signature Standard. In the rest of the chapter a number of algorithms to calculate discrete logarithms is explained together with their respective computational complexity bounds. Chapter 9 gives a more comprehensive treatment of the RSA based cryptosystems. Besides describing the system and its use for encryption and digital signatures, separate sections are given to discuss factorization algorithms and other attacks. The next section discusses the problem of generating large prime numbers, and the chapter ends with a section devoted to the Rabin variant of the RSA system. NEWLINENEWLINENEWLINEChapter 10 turns its attention to the systems based on elliptic curves. Relevant facets of elliptic curve theory are given here, followed by the description of a cryptosystem based on the discrete logarithm problem over elliptic curves and a brief discussion of its security. Chapter 11 offers an overview of cryptosystems based on algebraic coding theory. After an introduction to Goppa codes, the description of the McEliece cryptosystem and its possible variations are given there. The public key cryptography part of the book ends with Chapter 12, which is devoted to knapsack based systems. Here the knapsack system is described followed by the explanation of the \(L^3\)-attack and the Chor-Rivest variant of the system. NEWLINENEWLINENEWLINEHash codes and authentication techniques form the content of Chapter 13. The bulk of the chapter is in the section on unconditionally secure authentication codes. Chapter 14 is focused on part of the area of cryptograhic protocols, namely zero-knowledge protocols. Here, the Fiat-Shamir protocol and Schnorr's identification protocol are described and discussed. The last chapter of the book (Chapter 15) deals with secret sharing systems. Besides some general treatment of the topic, threshold schemes with and without liars as well as visual secret sharing schemes are described here. NEWLINENEWLINENEWLINEAppendix A contains relevant parts of elementary number theory, while Appendix B gives an introduction to the theory of finite fields. A bit surprisingly, Appendix C gives a list of brief biographies of several famous mathematicians, starting from Euclid and finishing with Wederburn. Finally, Appendix D contains a description of several new Mathematica functions used in the book. NEWLINENEWLINENEWLINEThe book may serve as a useful introduction to modern cryptographic methods. The fact that the whole text is available as an interactive Mathematica notebook can be considered a big plus as it allows for interesting and enjoyable ways of teaching cryptology.