Basic Information:
- Instructor: Karl Dilcher
- Office: Chase Building Room 325; ph.: 494-3784
- Office hours: M-W: 1:30 - 2:30 pm, F: 11:30 - 12:30, or by appointment
Class time: M-W-F, 3:35 - 4:25 pm
Classroom: Dunn 135
This course will have a presence on OWL (BbLearn).
Course materials:
Course Notes:"Cryptography".
Required -- Available in the Dal Bookstore.
Suggested reading: J. A. Buchmann, "Introduction to Cryptography", 2nd Ed.,
Springer-Verlag, New York, 2004.
For a list of other interesting books see the
book list below.
Prerequisites:
MATH 1000, 1010, 2030
and at least two other half courses in mathematics beyond the first year,
or instructor's permission.
Calendar entry:
This course is an introduction to modern cryptographic techniques
and its mathematical foundations. The material covered includes:
Elementary number theory and algebra; classical cryptosystems;
probability; the Data Encryption Standard; prime number generation
and primality tests; public key cryptosystems; further applications,
such as digital signatures and identification. The course ends with
a brief overview of other cryptosystems, such as elliptic curve cryptography.
More about the topic:
Cryptography is the art and science of keeping messages secure.
Formerly almost exclusively used by state and military authorities,
it has in recent decades become of great public importance for a
variety of different uses in the transmission of electronic data.
Modern cryptography can be called the science and technology of
electronic key systems. It is used to keep data secret, digitally
sign documents, control access, etc. Users should not only know how
its techniques work, but they must also be able to estimate their
efficiency and security.
... and about the course:
This course is an introduction to modern cryptographic techniques
and their mathematical foundations. Although some particular cryptosystems
and their implementations will be discussed as examples, the main
emphasis of the course will be on the theoretical background.
The course does not assume any particular mathematical background,
but a certain amount of mathematical maturity is required. It is
therefore expected that students have taken MATH-1000,
MATH-1010, MATH-2030, and at least two other half-courses beyond the first
year.
Course content
The particular topics covered in the course are:
- Mathematical Background: Some elementary number theory; groups; linear algebra.
- Encryptions: Block ciphers (in different modes), One-Time-Pad systems, etc.
- Probability theory and pseudo-random numbers.
- The Advanced Encryption Standard (AES).
- Computational number theory: Prime number generation and primality tests.
- Public key cryptosystems: RSA, Rabin, ElGamal, etc.
- More number theory: Factoring, discrete logarithms.
- Further topics: Hash functions, digital signatures, identification, etc.
Intended audience:
Upper-year undergraduate students in
- computer science or statistics, with an interest in mathematics;
- mathematics who want to learn about a modern application of pure mathematics.
Use of technology:
Occasionally the use of the computer algebra system Maple will be required,
mainly for some homework assignments.
You can download Maple for free, using your netID and password, at
https://software.library.dal.ca/.
Evaluation (subject to change until beginning of term):
- Weekly assignments: 30%
These will be mainly routine questions and
exercises, designed to ensure continuous work on the course material and
to test understanding. Each assignment will also contain a few
problems that are more challenging and problems requiring computations.
- Midterm test: 30% -- Date TBA.
- Final exam: 40% -- Date TBA.
This 3-hour exam will consist of two equal parts:
(i) More mathematical questions, similar to the ones in the assignments and
the midterm test; (ii) ``essay-type" questions, to test the understanding of
concepts and issues concerning the course material.
- No supplemental exams will be available.
Conversion to letter grades (Faculty of Science default scheme):
| 90-100 | A+ | |
75-79.9 | B+ | |
62-64.9 | C+ | |
50-54.9 | D |
| 85-89.9 | A | |
70-74.9 | B | |
58-61.9 | C | |
< 50 | F |
| 80-84.9 | A- | |
65-69.9 | B- | |
55-57.9 | C- |
Smartphone policy:
I request that you refrain from the use of your smartphone during class.
The main reasons are:
- It is distracting to those sitting near you.
- "Multitasking" doesn't work, as studies have shown; you'll do poorly at
both tasks.
- Concentration is absulutely essential in mathematics. Without the ability
to concentrate you will not be able to go beyond a certain (relatively low)
level.
- Please consider your classes (not just this one) as opportunities to
practice concentrating on just one task.
Thank you for your consideration.
Students With Disabilities
... are encouraged to register as quickly as possible at the Student Accessibility
Services if they wish to receive academic accommodations. To do so please
phone 494-2836, e-mail access@dal.ca, drop
in at the Mark A. Hill Accessibility Centre, Killam G28, or visit
their website.
Students are also reminded that all forms are now available on their website.
Intellectual Honesty
This course, as all other courses, is subject to the university's Intellectual
Honesty guidelines; please see the appropriate section in the
Undergraduate Calendar.
Other Related Mathematics Courses:
-
MATH 3070-B: Theory of Numbers.
Some of the topics from elementary number theory that are needed in
cryptography (especially modular arithmetic and factorization and primality)
are treated in greater detail, and are supplemented by related
topics. Although ideally this course should be taken before Cryptography,
those interested in classical topics of number theory will benefit
from this course also after having taken 4116.
This year the course will be taught by Dr. Richard Wood.
Solutions to assignments:
Will be posted on OWL after an assignment is due.
Other useful information
Books:
- Other textbooks covering the material of the course:
- W. Trappe and L.C. Washington
Introduction to Cryptography with Coding Theory, 2nd Ed.
Prentice Hall, 2006.
