This book covers encryption-decryption with dynamic systems and fractals using state observers and the synchronization property. The book contains 9 chapters. Chapter 1 gives a brief overview of encryption and decryption technology. Chapter 2 presents basic facts about dynamic systems: the Lyapunov exponents, stability, synchronization, and state observers; here are introduced also fractals. Chapter 3 explains stream and block ciphers and encoding of text and images (list of binary representations of integers 1..15 and tables for the XOR and negotion functions). Chapter 4 considers the application of Liouville systems in cryptography. Chapter 5 presents the exponential polynomial observer used as a decoder. Chapter 6 introduces fractional calculus. Chapter 7 covers the use of systems with fractional order for encryption and decryption. Chapter 8 explains the use of robust fractional order state observers for encryption and decryption and presents a security analysis of situations leading to decryption failures. Chapter 9 presents encryption and decryption algorithms using state observers that are represented by means of fractional-order chaotic systems with the Atangana-Baleunu fractional derivative.
The book contains many images, examples, exercises, and a list of references in every chapter, but the value of the book is greatly reduced by its language. Bizarre or semantically erroneous expressions appear nearly on every page, from exaggeratedly long sentences (sentence with 127 words on p. vii), sentences without verbs: “With the nonlinear vector function \(f (x, t)\)”, circular definitions “The Lyapunov numbers and exponents of a trajectory are defined as the Lyapunov numbers and exponents of the associated time map” (p. 10, the “associated time map” is nowhere explained), variables with assigned value are shown in the solution, but some solutions are not (p. 14), integrals \(\int {(y - d)} \) without integration variable (p. 99) and so on; problems appear on nearly every page.
The book may be of interest to specialists in dynamic systems who can manage the language and want to learn about the use of dynamic systems and fractals in cryptography.