This course will consist of an introduction to the mathematical foundations of cryptography. We will study results from number theory and algebra and how they are used for the safe trans- mission of information. We will discuss various security protocols, the mathematical principles needed for them, and the mathematical principles used in possible attacks.
Mathematical Background – Perfect Secrecy- Symmetric Cryptosystems – Asymmetric Cryptosystems – Primality Testing – Factoring Integers – RSA – Discrete Logarithm- Cryptographic Schemes – Diffie-Hellman – ElGamal – Security Questions and Attacks.
- J. A. Buchmann, Introduction to Cryptography, 2nd edition, Springer, 2004.
- D. R. Stinson, Cryptography: Theory and Practice, Third Edition, 2006
- J. Hoffstein, J. Pipher, and J. H. Silverman, An Introduction to Mathematical Cryptography, First Edition, 2008.
Class time and Location:
Sunday and Tuesday 08:00-09:30 AM, Room 305
General mathematical sophistication; and a solid understanding of Linear Algebra, Group Theory, Number Theory, and Probability Theory, at the advanced undergraduate or beginning graduate level, or equivalent.
- Homework – 10%
- Midterm – 40%
- Endterm – 50%
Midterm Examination: Sunday, 94/01/23, 08:00-09:30 AM
Final Examination: Monday, 94/03/25, 08:00-10:00
I’ll be having office hours for this course on Sunday and Tuesday 9:30 AM–10:00 AM. If this isn’t convenient, email me at firstname.lastname@example.org or talk to me after class.