Difference between revisions of "Math 485: Mathematical Cryptography"
From MathWiki
| Line 15: | Line 15: | ||
== Desired Learning Outcomes == | == Desired Learning Outcomes == | ||
| − | This is a course in the mathematics and algorithms of modern cryptography. It complements, rather than being equivalent to, the current CS course on | + | This is a course in the mathematics and algorithms of modern cryptography. It complements, rather than being equivalent to, the current CS course on Computer Security (CS 465). |
=== Prerequisites === | === Prerequisites === | ||
| Line 23: | Line 23: | ||
=== Minimal learning outcomes === | === Minimal learning outcomes === | ||
| − | The student should gain a understanding of the following topics. In particular this includes knowing the definitions, being familiar with standard examples, and being able to solve mathematical and algorithmic problems by directly using the material taught in the course. This includes appropriate use of Maple, Mathematica | + | The student should gain a understanding of the following topics. In particular this includes knowing the definitions, being familiar with standard examples, and being able to solve mathematical and algorithmic problems by directly using the material taught in the course. This includes appropriate use of Maple, Mathematica or Matlab. |
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
| Line 39: | Line 39: | ||
#* Simple discussion of finite fields. | #* Simple discussion of finite fields. | ||
# The DES and AES encryption standards. | # The DES and AES encryption standards. | ||
| − | # RSA and its weaknesses. | + | # RSA and its strengths and weaknesses; attacks on RSA. |
| + | #* Wiener's continued fraction attack on low decryption exponent. | ||
| + | # Primality testing algorithms. | ||
| + | # Factorization techniques. | ||
| + | #* The Quadratic Sieve. | ||
# Discrete logarithms. Diffie-Hellman key exchange. ElGamal. | # Discrete logarithms. Diffie-Hellman key exchange. ElGamal. | ||
# Lattices and Lattice Algorithms. The LLL algorithm. The NTRU system. Lattice attacks on RSA. | # Lattices and Lattice Algorithms. The LLL algorithm. The NTRU system. Lattice attacks on RSA. | ||
Revision as of 16:00, 19 August 2008
Contents
Catalog Information
Title
Introduction to Cryptography.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Prerequisite
Description
A mathematical introduction to some of the high points of modern cryptography.
Desired Learning Outcomes
This is a course in the mathematics and algorithms of modern cryptography. It complements, rather than being equivalent to, the current CS course on Computer Security (CS 465).
Prerequisites
The requirement for Math 371 ensures both an appropriate level of mathematical maturity and a basic knowledge of linear algebra.
Minimal learning outcomes
The student should gain a understanding of the following topics. In particular this includes knowing the definitions, being familiar with standard examples, and being able to solve mathematical and algorithmic problems by directly using the material taught in the course. This includes appropriate use of Maple, Mathematica or Matlab.
- Classical systems, including:
- Substitution theory
- Block ciphers
- Enigma
- Elementary number theory as follows:
- Euclid's algorithm
- Modular arithmetic and the algorithm for modular exponentiation
- Chinese Remainder Theorem
- Fermat and Euler Theorems
- Primitive roots
- Elementary continued fractions
- Simple discussion of finite fields.
- The DES and AES encryption standards.
- RSA and its strengths and weaknesses; attacks on RSA.
- Wiener's continued fraction attack on low decryption exponent.
- Primality testing algorithms.
- Factorization techniques.
- The Quadratic Sieve.
- Discrete logarithms. Diffie-Hellman key exchange. ElGamal.
- Lattices and Lattice Algorithms. The LLL algorithm. The NTRU system. Lattice attacks on RSA.
Additional topics
If time allows: Elliptic curve cryptography.
Courses for which this course is prerequisite
None.
