Cryptography – Mathematics 1580 (CRN: 15975)
Brown University – Fall, 2017
Professor Joe Silverman

Text An Introduction to Mathematical Cryptography (2nd edition),
J. Hoffstein, J. Pipher, J.H. Silverman
Springer-Verlag, UTM, 2nd ed., 2016
ISBN-13: 978-1493939381 (approx $60)
NOTE: Be sure to download the Errata Sheet .
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Web Site
Office Hours TBA
Course Time MWF 10:00 - 10:50 AM (C hour)
Course Location TBA
Class Meeting Notes
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

Monday Oct 20

In class

Hour Exam #2

Weds Nov 1

In class

Final Exam

Tues Dec 19
Exam Group 14

Locatation TBA

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

Problem Sets


Hour Exams (22.5% each)


Final Exam


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. Elliptic Curves and Cryptography
  6. Lattice-Based Cryptography
  7. Probability Theory and Information Theory (if time permits)

Course Goals: To learn the fundamentals of mathematical cryptography, intertwined with mastering background material in algebra, number theory, elliptic curves, lattices, and probability theory.

Learning Activities and Time Allocation: Learning activities include class attendance, weekly problem sets, two in-class mid-term exams, and a final exam. The time to complete these activities are (1) attending lectures, approximately 3 hours/week; (2) working on the problem sets and studying for exams, approximately 9 hours/week.

Assessment: Course grades will be determined by the quantity and quality of problem sets submitted (20% of grade) and by grades on the mid-terms (22.5% each) and final exam (35% of grade).

Expectations of Students: It is expected that students will attend all lectures and participate in class discussion in an appropriate manner. Assignments are due on the listed dates. All students are expected to abide by Brown's academic code, which may found here

Go to Professor Silverman's Home Page.