Algorithmic Number Theory and Cryptography (CS 303 and CS 680)
Announcments Lectures Programs
Course Resources Assignments
and Solutions Grading Policy
- Course Description
Covers fundamental algorithms for integer arithmetic, greatest
common divisor calculation, modular arithmetic, and other number
theoretic computations. Algorithms are derived, implemented and
analyzed for primality testing and integer factorization.
Applications to cryptography are explored including symmetric and
public-key cryptosystems. A cryptosystem will be implemented and
methods of attack investigated.
- Course Goals
To be able to implement and analyze algorithms for integer
factorization and primality testing. To be able to use a system
like Maple to explore concepts and theorems from number theory.
To understand fundamental algorithms from symmetric key and public
- Course Objectives
- To understand fundamental number theoretic algorithms such as the
Euclidean algorithm, the Chinese Remainder algorithm, binary powering,
and algorithms for integer arithmetic.
- To understand fundamental algorithms for symmetric key and public
- To understand the number theoretic foundations of modern
cryptography and the principles behind their security.
- To implement and analyze cryptographic and number theoretic
- To be able to use Maple to explore mathematical concepts and
- Undergraduate computer science, computer engineering,
mathematics, and students interested in security, cryptography and
applied number theory. The course will cover both the underlying
mathematical theory and practice as algorithms will be implemented
and analyzed (the Maple computer algebra system will be used for
implementation of algorithms and exploration of concepts). For
computer science students, the course counts towards the numeric and
symbolic computing and computer and network security tracks.
- Undergraduate data structures course (CS 260)
- Courses in linear algebra (MATH 201 or equivalent), discrete
mathematics (MATH 221 or equivalent).
- Jeremy Johnson
Office: 100C University Crossings
phone: (215) 895-2669
e-mail: jjohnson AT cs DOT drexel DOT edu
office hours: R 4-6 (UC 100 and online). Additional hours by appointment.
- Gavin Harrison
Office: Univ. Crossings 147 (CS Student Resource Center)
e-mail: gmh33 AT drexel DOT edu
office hours: M 3:00-4:00 and 8:00-9:00 (online).
- Meeting Time
- TR 12:30-2:00 in Univ. Crossings 153
- Course Mailing List
- BbVista will be used for discussion and announcements
Please use the discussion groups for questions and discussions related to the
course. If you know the answer to someone's question, please feel free
to jump in, as long as well it is not an answer to a homework problem.
You should check the discussion and announcements regularly.
Please do NOT post answers to homework.
- Jeffrey Hoffstein, Jill Pipher, and Joseph Silverman,
An Introduction to Mathematical Cryptography,
- Every student must have access to Maple.
Course notes will be provided on the web page as Maple
worksheets that can not be read without Maple.
Maple is available in the CS labs as well as Drexel labs,
and is available for free to Drexel students as part of
the campus site license.
- Students will be required to read several additional
- Maple Computer Algebra System
- Integer and polynomial arithmetic
- Euclidean algorithm and continued fractions
- Modular Arithmetic, Fermat's theorem, Chinese Remainder Theorem
- Symmetric key cryptosystems (DES, AES)
- Public-key cryptosystems (RSA, El Gamel)
- Coin flipping protocols (Blum)
- Primality testing
- Algorithms for integer factorization
Assignments and exams will be returned on a regular basis to provide
feedback to students. All students must do their own work. Any
violation of this will result in a zero grade for the assignment. A
second violation will lead to an F for the course.
- Class Participation (15%)
- Three Homework assignments (45%)
- Two Quizes (40%)
Grades are based on a curve with the mean normalized to a B provided
the mean performance shows competency of the material.
- Reference Books
- Maple Getting Started Guide.
- Maple Users Manual.
- Maple Introductory Programming Guide.
- Maple Advanced Programming Guide.
- Web Pages
- Waterloo Maple
- Maple Student Center
- Maple Application Center
- SymbolicNet --
Symbolic Mathematical Computation Information Center
- The Prime Pages
- GIMPS: The Great Internet
Mersenne Prime Search
Look on BbVista for course announcements.
Look Here for Important
This list is subject to change.
- Week 1 (Chapter 1)
- April 3, 2012
(Introduction to Cryptography and Cryptanalysis)
- April 5, 2012
(Introduction to Modern Cryptography)
- Week 2 (Chapter 1 and 2 - RSA Algorithm)
- April 10, 2012
(The Euclidean Algorithm)
- April 12, 2012 (Modular Arithmetic and Fast Powering)
- Week 3 (Chapter 1 and 3)
- April 17, 2012 (RSA Public Key Encryption)
- April 19, 2012
(Linear Algebra and Hill Cyphers)
- Week 4 (Chapters 3 - Discrete Log)
- April 24, 2012
(El Gamal Public Key Encryption and Diffie-Hellman Key Exchange)
- April 26, 2012
(Collision Algorithms and the Discrete Log Problem)
- Week 5 (Chapter 3 - Primality Testing)
- May 1, 2012
(Unique Factorization, the Sieve of Eratosthenes and the Prime Number Theorem)
- May 3, 2012
(Strong Pseudoprimes and a Probabalistic Primality Test)
- Week 6 (Chapter 3 - Probabalistic Encryption)
- May 8, 2012
(Quadratic Reciprocity and the Solovay-Strassen Primality Test)
- May 10, 2012
(Blum Coin Flipping Protocol and Goldwasser-Micali Probabalistic Encryption)
- Week 7 (Chapter 3 - Integer Factorization)
- May 15, 2012
(Introduction to Integer Factorization Algorithms)
- May 17, 2012
(Introduction to Integer Factorization Algorithms)
- Week 8 (Chapter 3 - Integer Factorization)
- May 22, 2012
(How not to choose primes for RSA)
- May 24, 2012
- Week 9 (Chapter 4 - More Symmetric Key Encryption)
- May 29, 2012
- May 31, 2012
(Polyalphabetic Substitution Cyphers)
- Week 10 (Chapter 6 - Lattices and Cryptography)
- June 5, 2012
Programs and Worksheets
- Lab 1 - lab1.mw - practice Maple lab on substitution cyphers, modular arithmetic, and Hill cyphers.
Assignments and Exams
Final Exam (take home)- final.mw (20%) - Due Thur June 7 at 2:00pm (end of class).
- Assignment 1 - assign1.mw (15%) - Due Thur. April 26 at midnight.
- Midterm 1 - Studyguide for Midterm 1 (20%) - Take home exam to be completed between Thur. May 3 and Tue. May 8 (see study guide for instructions).
- Assignment 2 - assign2.mw (15%) - Due Tue. May 22 at midnight.
- Assignment 3 - assign3.mw (15%) - Due Thur May 31 at midnight.
Created: 9/26/05 (revised) by email@example.com