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 . |
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Office | Mathematics Department, Kassar House, Room 202 |
Phone | 863-1124 |
jhs@math.brown.edu | |
Web Site | www.math.brown.edu/~jhs/MA0158/MA0158HomePage.html |
Office Hours |
Mondays 9:00-9:45am, Fridays 2:45-3:30pm, and by appointment.
Note: The last day of regular office hours is Mon Dec 11. Exam Week Office Hours: During exam period I will have office hours on Monday, December 18, 10:00am-11:00am and 2:00-3:00pm. |
Course Time | MWF 10:00 - 10:50 AM (C hour) |
Course Location | Lincoln Field Building, Room 209 |
Class Meeting Notes | There will be no class on Friday October 27 because I have to be out of town. We will make up this class during reading period. |
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
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 2 |
In class — Solutions |
Hour Exam #2 |
Weds Nov 1 |
In class — Solutions |
Final Exam |
Tues Dec 19^{} |
9:00am-12:00am |
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.
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 10 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