数学密码学导论
An introduction to mathematical cryptography
Jeffrey Hoffstein · 初版 2008 年
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这本自成体系的现代密码学入门著作，重点介绍了公钥密码系统和数字签名方案背后的数学理论。本书聚焦这些核心主题，同时阐发了构建各种密码系统及其安全性分析所需的数学工具。读者只需具备基础线性代数知识；代数、数论和概率论方面的技巧会根据需要在书中逐步引入和展开。本书涵盖了被视为数学密码学核心的诸多课题。核心主题包括：* 经典密码学……
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……工程》（Cryptography Engineering）：https://www.amazon.com/Cryptography-Engineering-Principles-P... ——虽然过时了，某些地方有点小错，但还不至于离谱（不像《应用密码学》Applied Cryptography 那样）。霍夫曼（Hoffman）、皮弗（Pipher）和西尔弗曼（Silverman）合著的《数学密码学导论》（Introduction to Mathematical Cryptography）：https://www.amazon.com/Introduction-Mathematical-Cryptograph... ——迈入理论密码学的一块很好的敲门砖。
…Engineering_: https://www.amazon.com/Cryptography-Engineering-Principles-P... --- dated, a little wrong about some things, but not insane (like _Applied Cryptography_ is). Hoffman, Pipher, and Silverman's _Introduction to Mathematical Cryptography_: https://www.amazon.com/Introduction-Mathematical-Cryptograph... --- a good first step into theoretical cryptography.
……年度最佳博文。LLL 算法在针对非对称密码学的攻击中经常登场。如果你对加密算法或线性代数感兴趣但不知道什么是格（lattice），霍夫斯坦（Hoffstein）的《数学密码学导论》（Introduction to Mathematical Cryptography）是个极佳的切入点：http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.182...（如果你懂什么是向量空间，你就懂什么是格；它其实就是系数只能取整数的向量空间……
…blog post of the year. LLL comes up a lot in attacks on asymmetric cryptography. If you're interested in crypto or linear algebra but don't know what a lattice is, a great starting point is Hoffstein's _Introduction to Mathematical Cryptography_: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.182... (If you know what a vector space is, you know what a lattice is; it's a vector space where only integers are allowed as coefficients…
一些比较“小众/冷门”的推荐：- Staysys Jukna 的《极值组合学》（Extremal Combinatorics）- Boyd 和 Vandenberghe 的《凸优化》（Convex Optimization）- 《延迟不敏感电路》（Delay Insensitive Circuits）[1]- Hoffstein、Pipher 和 Silverman 的《数学密码学导论》（An Introduction to Mathematical Cryptography）- Scott Aaronson 的《从德谟克利特以来的量子计算》（Quantum Computing since Democritus）[1] https://www.delayinsensitive.com 利益声明：我是作者。
some "out there" suggestions: - "Extremal Combinatorics" by Staysys Jukna - "Convex Optimization" by Boyd and Vandenberghe - "Delay Insensitive Circuits" [1] - "An Introduction to Mathematical Cryptography" by Hoffstein, Pipher, and Silverman - "Quantum Computing since Democritus" by Scott AAronson [1] https://www.delayinsensitive.com disclosure: I'm the author.
嗯，确实。Hoffstein 等人合著的《数学密码学导论》（An Introduction to Mathematical Cryptography）是一本极好的教材，评价极高，处理这类问题确实比上面那个链接是更好的选择。另一本篇幅较短的教材是 Koblitz 的《数论与密码学教程》（A Course in Number Theory and Cryptography），但我认为……
Mmm, certainly. Hoffstein et al.'s An Introduction to Mathematical Cryptography is a wonderful text, highly thought of, that really is a better choice than the above link for this sort of thing. Another shorter text is Koblitz's A Course in Number Theory and Cryptography, but I think…
……（http://abstract.pugetsound.edu/sage-aata.html）关于抽象代数的，里面包含 Sage 练习。数论在计算机科学中最重要的应用大概就是密码学了。在那个领域，我强烈推荐 Hoffstein、Pipher 和 Silverman 写的《数学密码学导论》（An Introduction to Mathematical Cryptography）。
…(http://abstract.pugetsound.edu/sage-aata.html) on Abstract Algebra which includes Sage exercises. The most prominent application of number theory in computer science is probably cryptography. I can highly recommend "An Introduction to Mathematical Cryptography" by Hoffstein, Pipher and Silverman in that area.
……目前关于它最好的路径。在书籍方面，JP Aumasson 的《严肃密码学》（Serious Cryptography）前不久出了第二版，第一版就很棒。Katz 和 Lindell 的《现代密码学》（Modern Cryptography）以及 Hoffstein 的《数学密码学导论》（Introduction to Mathematical Cryptography）都是标准教材，我觉得很多课程现在依然拿它们入门。最后，我听说 Esslinger 的《用 CrypTool 和 SageMath 学习与体验密码学》（Learning and Experiencing Cryptography with CrypTool and SageMath）也很不错，出自……
…best present path on it. In terms of books, JP Aumasson's "Serious Cryptography" got a 2nd edition not too long ago and the first edition was good. Katz & Lindell's "Modern Cryptography" and Hoffstein's "Introduction to Mathematical Cryptography" are both standard texts that I think a lot of courses still get started with. Finally I've heard good things about Esslinger's "Learning and Experiencing Cryptography with CrypTool and SageMath" from…