## 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.**
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.

### 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.

### 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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