An Introduction to Mathematical Cryptography

by Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman

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

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.

Genres: Mathematics, Textbooks, Nonfiction, Computers, Computer Science, Programming, Reference

555 pages, Paperback

First published January 1, 2008

Reviews

[Emilia Dunfelt · Rating 5 out of 5]

Excellent introductory book! Very clear and engaging, gives the reader a nice blend of pure mathematics and insights into cryptographic research. Includes a couple of sections on basic group and ring theory, as well as sections on probability theory, which makes the book very accessible for students at different levels.

[Murray · Rating 5 out of 5]

I got half way through the first edition, then the second edition came out. I don't think one is ever really 'finished' a book like this, as every time I pick it up, with a view toward figuring something out, I invariably gain new insight. An excellent illustration of 'the more I learn, the less I know'.

[Brian Powell · Rating 5 out of 5]

Excellent resource on public key cryptography.

[Ryan Lavin · Rating 5 out of 5]

By the authors of the NTRU cryptosystem, if you're interested in lattice-based cryptography then chapter 7 is an amazing visually-engaging buildup into their properties. Unfortunately LWE and SIS aren't covered (and there's not must cryptanalysis in here), but the authors do really well at minimizing the pre-requisites (no topology or measure theory needed, but group/ring theory definitely are, and calculus/analytic-tools help a lot) needed to understand cryptographic lattices.

While chapter 7 was my favorite the first three chapters are a rigorous and axiomatic intro to mathematical cryptography from the theorist perspective (although from a pure protocol-based perspective ie there are no attack games in here). I thought chapter 5 on probability and information theory was a bit rushed – they introduce ideas in full generality (very few examples) and leave a bit to be desired. Skipped chapter 6 because elliptic curves will likely be mostly obsolete in 10 years anyway

[Lumos Ktbspa · Rating 5 out of 5]

Interesting.

[Thomas · Rating 5 out of 5]

A great book with the right amount of mathematics (for undergrads).

[Saman Givian · Rating 5 out of 5]

Very good intro book for college students.

[John Davies · Rating 5 out of 5]

Truly phenomenal work. Ideas are laid out in a clear and coherent fashion. Elegant and engaging. While one can theoretically use this to attain a fairly robust understanding of modern cryptography from virtually nothing, I would encourage the prospective reader to first gain a reasonable working knowledge of number theory and abstract algebra before approaching this book.

Some chapters are interspersed with historical and philosophical context which is both refreshing and thought provoking. I found the first two chapters to be useful because of how foundational they are, and chapter five on elliptic curves (especially those over F2k) to be particularly compelling.

This work is particularly interesting when considered in the context of recent developments in cryptography and the changing nature of the economic and social environment we live in today.

I have spent hours in recent years pouring over this fascinating book and will no doubt spend many more in time to come.

All in all, a great read for the amateur, student and engineer alike.

[Nedya Prakasa · Rating 5 out of 5]

Nothing fo now