Cryptography – Mathematics 1580 (CRN: 14784)
Brown University – Fall, 2012
Professor Joe Silverman

Text An Introduction to Mathematical Cryptography,
J. Hoffstein, J. Pipher, J.H. Silverman
Springer-Verlag, UTM, 2008
NOTE: Be sure to download the Errata Sheet .
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Email jhs@math.brown.edu
Web Site www.math.brown.edu/~jhs/MA0158/MA0158HomePage.html
Office Hours Wednesday 9:30 - 10:30 am and Friday 1:15 - 2:00 pm and by appointment. (Or just drop by. I tend to be in on MWF and not on TTh.)
Last day of regular office hours is Wednesday, December 12.
Final Exam Review Session: I will run a review and Q&A session on Wednesday, December 19, 1:00-2:00pm. It will be held in Barus-Holley 158.
Exam Week Office Hours: During exam period I will have an office hour on Friday, December 21, 11:00am-noon.
Course Time MWF 11:00 - 11:50 AM (D hour)
Course Location CIT 227
Class Meeting Notes There will be no classes on Monday September 17 and Wednesday September 26 due to Rosh Hashanah and Yom Kippur. Class will meet during reading period. The last regular class meeting is Wednesday, December 12. Note that the final exam is on December 21, the last day of exam period. If you won't be here for the final exam, then you cannot take this class.
Problem Sets Note: The problem sets are challenging. Don't leave them until the last minute! We will be moving rapidly. In order to learn the material, it is very important to DO THE HOMEWORK WHEN IT IS ASSIGNED.
Late homework will NOT be accepted. There are NO exceptions to this rule.
Homework on the Web The homework assignments include reading assignments, due the next class, and written assignments, generally due each Monday. There may also be a few assignments available as HTML and/or downloadable PDF files.
Click here to go to the Math 1580 Web Homework Page.
Math 1580 Web Calculator There are various computer packages (e.g. Mathematica, Maple, MatLab) available at Brown that can be used for numerical computatations. There are also free packages available online (e.g. PARI) and sites that allow you to do short computations using free and/or proprietary packages, such as Magma, SAGE, and KASH.

For those who do not want to use these packages, I have written a primitive web-based calculator that performs basic number theoretic calculations such as gcd, extended Euclidean algorithm, and the fast powering algorithm. You are welcome to use this tool for all assignments starting with Chapter 2. It is available on the

Math 1580 Web Calculator Page.

NOTE: Please do not come to me for help installing or using all of the packages listed above. The only one that I really know how to use is PARI. However, if you have installed PARI, then I can answer questions about the specific functions that PARI has available. And I can answer questions about the Math 1580 Web Calculator Page.

Dates to Remember: There will be two in-class hour exams and a final exam.

Hour Exam #1

Fri, Oct 5

In class — Solutions

Hour Exam #2

Fri, Nov 9

In class — Solutions

Final Exam

Fri,Dec 21*
Exam Group 04

Time 2:00-5:00pm
Wilson 302 — Solutions


           *Note that the final exam is on the last day of exam period. If you won't be here for the final exam, then you cannot take this class.

Grading: The course grade will be determined on the following basis:

Problem Sets

20%

Hour Exams (22.5% each)

45%

Final Exam

35%

Brief Syllabus:

Click here for a detailed syllabus and list of homework assignments.

  1. Introduction to Cryptology and Mathematical Preliminaries
  2. Discrete Logarithms and Diffie-Hellman
  3. Integer Factorization and RSA
  4. Digital Signatures
  5. Lattice-Based Cryptography
  6. Elliptic Curves and Cryptography
  7. Probability Theory and Information Theory

Go to Professor Silverman's Home Page.