Introduction to Cryptography with Open-Source Software (Hardcover)

Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experience by progressing at a gentle pace, keeping mathematics at a manageable level, and including numerous end-of-chapter exercises.

Focusing on the cryptosystems themselves rather than the means of breaking them, the book first explores when and how the methods of modern cryptography can be used and misused. It then presents number theory and the algorithms and methods that make up the basis of cryptography today. After a brief review of "classical" cryptography, the book introduces information theory and examines the public-key cryptosystems of RSA and Rabin’s cryptosystem. Other public-key systems studied include the El Gamal cryptosystem, systems based on knapsack problems, and algorithms for creating digital signature schemes.

The second half of the text moves on to consider bit-oriented secret-key, or symmetric, systems suitable for encrypting large amounts of data. The author describes block ciphers (including the Data Encryption Standard), cryptographic hash functions, finite fields, the Advanced Encryption Standard, cryptosystems based on elliptical curves, random number generation, and stream ciphers. The book concludes with a look at examples and applications of modern cryptographic systems, such as multi-party computation, zero-knowledge proofs, oblivious transfer, and voting protocols.

曾經只有少數人知曉的特權，現在密碼學已經在世界各地的大學中教授。《使用開源軟體介紹密碼學》以例子和開源計算代數系統Sage來說明演算法和密碼系統。作者是該領域的知名教育者，通過以緩慢的節奏進行、保持數學在可控範圍內、並包含大量章末練習，提供了一個非常實用的學習體驗。

本書專注於密碼系統本身，而不是破解方法，首先探討了現代密碼學的使用和濫用時機和方式。然後介紹了數論以及構成當今密碼學基礎的演算法和方法。在對“古典”密碼學進行簡要回顧後，本書介紹了信息理論，並檢視了RSA和Rabin的公鑰密碼系統。其他研究的公鑰系統包括El Gamal密碼系統、基於背包問題的系統以及用於創建數字簽名方案的演算法。

本書的後半部分則考慮了適用於加密大量數據的位導向密鑰或對稱系統。作者描述了區塊密碼（包括數據加密標準）、密碼雜湊函數、有限域、高級加密標準、基於橢圓曲線的密碼系統、隨機數生成和流密碼。本書最後探討了現代密碼系統的例子和應用，如多方計算、零知識證明、遺忘傳輸和投票協議。