Group Theoretic Cryptography (Chapman & Hall/CRC Cryptography and Network Security Series) Hardcover

Group theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential source of quantum-resilient cryptographic primitives for the future.

Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography.

Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES.

The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups.

The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption―identification protocols, key establishment, and signature schemes are covered.

The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.

群組理論問題在數學、物理、化學和生命科學等多個領域推動了科學成就。許多加密構造利用了群組理論問題的計算難度，並且這個領域被視為未來量子抗干擾加密基元的潛在來源。

《群組理論密碼學》為對群組理論感興趣並希望了解兩個領域之間可能的相互作用的人提供了一個理想的密碼學入門。假設讀者具有大學水平的線性代數和離散數學理解，本書詳細介紹了在密碼學領域中使用非阿貝爾群的具體方法。

此外，本書還證明了群組理論技術如何幫助我們對已知的看似無關的加密構造（如DES）獲得新的洞察。

本書以群組理論、復雜性理論和密碼學的基礎概述開始。第二部分專門介紹公鑰加密，包括可證明的安全性保證、在標準模型中的公鑰加密以及使用無窮群的公鑰加密。

本書的第三部分涵蓋了秘鑰加密。它探討了區塊加密算法（如高級加密標準）以及加密雜湊函數和消息驗證碼。最後一部分深入探討了一些當今與加密同等重要的加密應用，包括身份驗證協議、金鑰建立和簽名方案。

本書提供了對涉及群組理論的密碼構造的正式安全性分析，並突出了潛在的漏洞。每章末尾都包含了進一步閱讀的摘要和參考文獻，以及練習題。本書的附錄提供了部分練習題的解答。