Cryptography is the study of secure communication over insecure channels. We will study the basic methods and concepts in theoretical cryptography along with their applications. The course will look at concepts such as one-way functions and trapdoor permutations (functions that are easy to compute but computationally hard to invert), pseudorandom generators (devices that produces sequences that are computationally random), public-key cryptosystems (secure systems that require no secret agreement), one-way hash functions (tools to authenticate messages and to verify data integrity), digital signatures (mechanisms for signing documents), and zero-knowledge proofs (convincing a party of an undeniable fact without revealing its proof).

Most of these topics require background in number theory and probability theory. The first part of the course will be spent on developing the necessary background in these areas, mainly number theory. The second part of the course is spent on the applications of these to building cryptographic tools.

*An alternative underlying theme of the course is the rise and "fall" of
the RSA cryptographic system. Theoretical properties and improvements of the RSA
system will be discussed in detail. Then a discussion of Shor's quantum
algorithm for Factoring will be described. Finally, a brief look at simple
quantum cryptography will be given.*

**TEXT**

Douglas R. Stinson, "Cryptography: Theory and Practice," 3rd
edition, Chapman & Hall/CRC, 2006.

*Recommended*:

- Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford
Stein, "Introduction to Algorithms," 2nd edition, The MIT Press, 2001
*(on reserve)*; - Bruce Schneier, "Applied Cryptography," 2nd edition, John Wiley &
Sons, 1986
*(on reserve)*

The objective of this course is to learn fundamental issues and important algorithms involved in the field of cryptography.

The specific outcomes are as follows:

- Knowledge of some secret-key cryptographic systems.
- Knowledge of important ideas in public-key cryptographic systems.
- Knowledge of basic ideas in number theory that are relevant to cryptography.
- Knowledge of various cryptographic protocols for implementing different types of communication that requires secrecy and protection.
- Knowledge of modern programming languages with support for cryptographic applications.

Although attendance is not mandatory, students are responsible for all course materials covered in lectures and any exams given during class periods. Students that need to make up missing course work must provide the required Clarkson official exempt form. All students must submit their own work; the exchange of ideas are encouraged but ultimately the submitted work must be the student's own. Please refer to the Clarkson University Regulations for more guidelines on academic integrity and related matters.

**ASSIGNMENTS**

**LINKS**:

- Java at Sun Microsystems.
- NTL package.
- Crypto ePrint archive.