Cryptography – Mathematics 1580 (CRN:13188)
Brown University – Fall, 2007
Professor Joe Silverman

Final Exam Study Material:
Click here for a Course Summary that you can use to help you study for the final exam.

Text An Introduction to Mathematical Cryptography,
J. Hoffstein, J. Pipher, J.H. Silverman
The book will be distributed electronically at no cost to students.
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 9:00 - 9:45 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.)
Regular office hours end on Monday, December 10.
Exam Week Office Hours: During exam period I will have office hours on Friday, December 14, 11:00-11:45am and 3:00-4:00pm.
Final Exam Review Session: I will run a review session for the final exam on Wednesday, December 19, 12:30-2:00pm. It will be held in the Math Dept (Kassar House), Room 105.
Course Time MWF 10:00 - 10:50 AM (C hour)
Course Location Barus-Holley 160
Problem Session Sunday 7:00 - 9:00 PM, lobby of the CIT, run by teaching assistant/grader Sarah Meiklejohn
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 am 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

Weds, October 3

In class — Solutions

Hour Exam #2

Weds, November 7

In class — Solutions

Final Exam

Thursday, December 20
Exam Group 03

2:00pm-5:00pm
Kassar House – Foxboro Auditorium

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

Problem Sets

20%

Hour Exams (22.5% each)

45%

Final Exam

35%

Syllabus: Click here for a detailed syllabus.

  1. Mathematical Preliminaries and an Introduction to Cryptography
  2. Discrete Logarithms and Diffie-Hellman
  3. Integer Factorization and RSA
  4. Probability Theory
  5. Elliptic Curves and Cryptography
  6. Digital Signatures
  7. Lattices and Cryptography [as time permits]

Go to Professor Silverman's Home Page.