Readings, W4261 Introduction to Cryptography

Textbooks and Suggested Readings

The required textbook for the class is "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell, Chapman and Hall/CRC Press, 2nd edition. This book will be on reserve in the engineering library, and available from the Columbia bookstore. Additional pointers, handouts, or papers may occasionally be distributed in class. Following are some useful materials for those who wish to explore further. All these texts are available either on-line or in the Engineering library (or both).

Other Cryptography Texts

The following are textbooks that take a (more or less) similar approach to the one we take in this class, although they do differ from our class (and from each other) in some content and notation. They are all free for download.

Rafael Pass and abhi shelat. A Course in Cryptography.
Mike Rosulek. The Joy of Cryptography.
Nigel Smart. Cryptography, An Introduction.
Dan Boneh and Victor Shoup. A Graduate Course in Applied Cryptography.
Other cryptography lecture note collections: Luca Trevisan (Berkeley), Shafi Goldwasser and Mihir Bellare (MIT summer class), Mihir Bellare and Phil Rogaway (UCSD).
Ronald Cramer, Ivan Damgård, Jesper Buus Nielsen. Secure Multiparty Computation and Secret Sharing (This mostly covers material that we will not get to in our class).

The following book presents a comprehensive treatment of the theoretical foundations of cryptography, taking a very abstract, theoretical approach. This book is much more advanced than our class, and covers the material in far greater depth. This book is recommended for advanced students who are interested in conducting research in cryptography.

Oded Goldreich. Foundations of Cryptography. This is a three-volume book. Volumes I and II have appeared in print (preliminary versions available on author's website).

The following two books (note that the first one is available on-line) are comprehensive reference books for all areas in cryptography. However, these texts take a less careful approach to definitions and proofs of security than we do, often giving only intuitive treatment and omitting the precise details.

A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone: Handbook of Applied Cryptography
D. R. Stinson: Cryptography: Theory and Practice (2nd edition).

Computational Number Theory and Algebra

Some excellent references for computational number theory and applied algebra include:

V. Shoup: A Computational Introduction to Number Theory and Algebra. This is a very comprehensive introduction to algorithmic number theory, with all the necessary mathematical background self-contained.
D. Angluin: Lecture Notes on the Complexity of Some Problems in Number Theory. Available for download here. Much shorter (and much much older) than the above, and sufficient for the purposes of our class.

Background Reading

The appendix of the textbook (by Lindell and Katz) reviews some mathematical background such as basic probability and number theory. Additional background reading on discrete math, probability, algorithms and complexity theory can be found in several of the above references (in particular the one by Shoup, and the one by Menezes, van Oorschot, and Vanstone), as well as in the following books.

M. Sipser: Introduction to the Theory of Computation. See chapter 0 for basic discrete math, and chapter 7 for basic complexity notions.
T. H. Cormen, C. E. Leiserson, R. L, Rivest, C. Stein: Introduction to Algorithms. See first part for introduction to algorithms and randomized algorithms, and appendix for discrete math and probability overview.
L. Trevisan: Notes on Discrete Probability. Overview of discrete probability, independence, expectation and variance.

Non-Technical Reading

Some interesting non-technical books about the history of cryptology (which will not be addressed in this class), include the following two, originally written in 1967 and 1999, respectively.

D. Kahn: The Codebreakers -- The Comprehensive History of Secret Communication from Ancient Times to the Internet.
S. Singh: The Code Book -- The Secret History of Codes and Code Breaking.

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