Cryptanalysis of RSA and Its Variants (Chapman & Hall/CRC Cryptography and Network Security Series)

Thirty years after RSA was first publicized, it remains an active research area. Although several good surveys exist, they are either slightly outdated or only focus on one type of attack. Offering an updated look at this field, Cryptanalysis of RSA and Its Variants presents the best known mathematical attacks on RSA and its main variants, including CRT-RSA, multi-prime RSA, and multi-power RSA.

Divided into three parts, the book first introduces RSA and reviews the mathematical background needed for the majority of attacks described in the remainder of the text. It then brings together all of the most popular mathematical attacks on RSA and its variants. For each attack presented, the author includes a mathematical proof if possible or a mathematical justification for attacks that rely on assumptions. For the attacks that cannot be proven, he gives experimental evidence to illustrate their practical effectiveness.

Focusing on mathematical attacks that exploit the structure of RSA and specific parameter choices, this book provides an up-to-date collection of the most well-known attacks, along with details of the attacks. It facilitates an understanding of the cryptanalysis of public-key cryptosystems, applications of lattice basis reduction, and the security of RSA and its variants.

三十年過去了，RSA首次公開後，它仍然是一個活躍的研究領域。儘管有幾篇很好的綜述存在，但它們要麼稍微過時，要麼只關注一種攻擊類型。《RSA及其變體的密碼分析》提供了對這一領域的最新研究，介紹了對RSA及其主要變體（包括CRT-RSA、多質數RSA和多次方RSA）已知的最佳數學攻擊。

本書分為三部分，首先介紹了RSA並回顧了大部分攻擊所需的數學背景。然後匯集了對RSA及其變體的所有最流行的數學攻擊。對於每個攻擊，作者如果可能的話會提供數學證明，或者對依賴於假設的攻擊提供數學理據。對於無法證明的攻擊，他提供實驗證據以說明它們的實際有效性。

本書專注於利用RSA結構和特定參數選擇的數學攻擊，提供了一個最新的、最著名的攻擊集合，以及攻擊的詳細信息。它有助於理解公鑰加密系統的密碼分析、格基底縮減的應用以及RSA及其變體的安全性。