Cryptological mathematics (Q2716341)

This tutorial book gives an easily readable introduction into cryptology and uses the subject to motivate the study of different mathematical branches such as matrix algebra, elementary probability theory, modular arithmetic and number theory (Eulerian \(\phi\)-function, Fermat's and Euler's theorems). All of the mathematical concepts presented in this book have applications to enciphering and deciphering messages; the book explains how and why these enciphering/deciphering methods work. It descibes monoalphabetic, polyalphabetic and polygraphic symmetric ciphers (among others additive ciphers, Vigenère's system with Kasiski and (simplified) Friedman tests, Hill's system and Playfair) and public key cryptography (RSA, Diffie and Hellman key exchange and the Massey-Omura system). \medbreak Each section includes many well elaborated examples and a collection of exercises (with answers to most of the even-numbered problems in the appendix), some of which use a programming language or a symbolic algebra system such as Maple or Mathematica. Another feature of this book is the occasional biographical sketch about cryptographic pioneers (Herbert Yardley, William Friedman, Agnes Meyer Driscoll and Frank Rowlett).NEWLINENEWLINEThe author wants to be read by bright young people of every age and has selected the material accordingly; thus the expert may miss the Vernam or one-time-pad system, the ElGamal chiffre using discrete logarithm and elliptic curve cryptography. The Caesar system is called only ``additive cipher with \(k=3\)''. It is unusual that the ``well ordering axiom'' is defined only for the set \({\mathbb N}\). \medbreak Apart from these facts, the book is very well written, easy to understand (due to the numerous and detailed examples) and interesting to read. Errata and clarifications can be found on the author's webpage, which also contains computer programs to download the modules needed to answer the computer problems in the book. \medbreak I very much recommend this book as a tutorial introduction.