Discrete Dynamical Systems and Chaotic Machines: Theory and Applications (Hardcover)

For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.

Covering both theoretical and practical aspects, the book presents:

• Key mathematical and physical ideas in chaos theory
• Computer science fundamentals, clearly establishing that chaos properties can be satisfied by finite state machines
• Concrete applications of chaotic machines in computer security, including pseudorandom number generators, hash functions, digital watermarking, and steganography
• Concrete applications of chaotic machines in wireless sensor networks, including secure data aggregation and video surveillance

Until the authors’ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book illustrates how chaos theory enables the study of computer security problems, such as steganalysis, that otherwise could not be tackled. It also explains how the theory reinforces existing cryptographically secure tools and schemes.

對於計算機科學家，特別是安全領域的科學家來說，混沌的應用一直被限制在計算一小部分著名但不適用的映射上，這些映射無法解釋為什麼混沌在相關情境中是相關的。《離散動力系統和混沌機器：理論與應用》展示了如何在嚴謹的數學框架中使有限機器（如計算機、神經網絡和無線感測網絡）以混沌方式工作。考慮到這些機器必須在現實世界中進行交互，作者們分享了他們在離散動力系統行為及其在計算機科學中的應用方面的研究結果。

本書涵蓋了理論和實踐兩個方面，提供了以下內容：
- 混沌理論中的關鍵數學和物理思想
- 計算機科學基礎，明確確立了有限狀態機可以滿足混沌特性
- 混沌機器在計算機安全中的具體應用，包括偽隨機數生成器、哈希函數、數字水印和隱寫術
- 混沌機器在無線感測網絡中的具體應用，包括安全數據聚合和視頻監控

在作者最近的研究之前，將混沌數學理論應用於有限機器的實際實現引發了幾個問題。這本自成一體的書說明了混沌理論如何使得研究計算機安全問題（如隱寫分析）成為可能。它還解釋了這一理論如何加強現有的具有密碼學安全性的工具和方案。