An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition by Jeffrey Hoffstein (PDF)

Description

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐You will learn so much from this book. To begin, it has an extensive list of references that it consistently points out in the text. This motivates the reader to explore certain topics on their own and it gives them a starting point to do so. You will find that it is also very easy to read. Of course it requires quite a bit mathematical maturity as there is heavy use of Abstract Algebra, but it is easy to follow even with a basic understanding of the material. What I loved the most were the exercises provided at the end of each section. As it goes for any subject, explanations can only go so far. To truly learn the material you need to practice it with problems that go beyond what you read at face value. After doing countless problems, I noticed how they were chosen specifically to further your understandings. They weren’t the type of problem that asked you to regurgitate what you had read. I love this book.

⭐Good introduction to intermediate level coverage of math-based crypto, however, I found the text hard to follow because the cross references were hard to look up. E.g. a back reference to proposition x.y is hard to look up bec propositions are somewhat sparse and each chapter x is very large — so you find yourself thumbing through the chapter trying to find propositions to get your bearing. It really interferes with the reading process. Including a page number would help greatly. (For more purely math books, this isn’t as large of an issue bec there are so many propositions and theorems that it’s easy to isolate the back reference — but for this text, it is quite difficult.)

⭐The text itself is decent and clear. However, I needed the 2nd edition for a class in which I was enrolled, and so rented the kindle version. Unfortunately, the kindle version linked is a reproduction of the first edition and as such is missing some of the exercises I need for the class.Edit (followup):By happy (from my perspective) accident it was the campus bookstore (and therefore the majority of my classmates) who had the wrong edition of the book. This does not alter my rating of the book, since the various formats linked together on a page ought (in my opinion) to be of the same edition of the text.

⭐I used this book to teach a class of math and computer science majors. The book is great. It covers major topics; RSA, El-Gamal. Elliptic Curves, Lattice Based Cryptography. The systems are described and important attacks on the mathematical underpinnings are given in detail. The necessary mathematics is developed. Many homework problems on which the reader can practice are another strength. The students have expressed how much they get from the book. I highly recommend it.

⭐This 500+ pages book is very nice and deals with the Mathematical point of view with many explanations, but one will always neeed an additional support book of Algebra such as Topics in Algebra by I. N. Herstein (LC 74-82577) to fully grasp all the related Math fundamentals.

⭐Solid, introductory text for those familiar with abstract algebra, discrete mathematics and the like — and even those who are not.. and I’m the latter.

⭐I have to deduct 3 stars immediately, as a modern text such as this would be expected to at least mention cryptocurrency, but there’s no mention of any, let alone Bitcoin. The first edition was written in 2008, but even then some cryptocurrencies (i.e. HashCash) existed. This edition was published in 2014, the year of explosive growth of Bitcoin and the authors have nothing to say about it.

⭐This is a very good book, if you have a solid math background. This is not a book for the mathematical novice. If you have a thorough understanding of number theory and of discrete mathematics then this book will help you to learn cryptography.

⭐概略： 多変数を、その内の１変数を仮平均として、他の変数どものそれからの偏移をパラメータ化して、グレブナー基底で処理すれば、レンストラらの ＬＬＬ が適用できます。 詳細： https://www.amazon.co.jp/gp/customer-reviews/R12L66E5ORZGRA?ref=pf_ov_at_pdctrvw_srp（菅野正人『数字パズル ＳｅｅＫ１０問題集』への書評。） 暗号に関する、この洋書に、L L L 法が、基礎から詳しく解説してあります。上記の方法には至っていないものの、L L L 法の一般化の試みも、２例、出ています。

⭐

Keywords

Free Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition in PDF format
An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition PDF Free Download
Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition 2014 PDF Free
An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition 2014 PDF Free Download
Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition PDF
Free Download Ebook An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2nd Edition