Difference between revisions of "Math 485: Mathematical Cryptography"
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=== Title === | === Title === | ||
| − | + | Mathematical Cryptography. | |
=== (Credit Hours:Lecture Hours:Lab Hours) === | === (Credit Hours:Lecture Hours:Lab Hours) === | ||
(3:3:0) | (3:3:0) | ||
| + | |||
| + | === Offered === | ||
| + | F | ||
| + | |||
| + | <!-- Inaccurate. Recently offered Fall 2009; scheduled to be offered Fall 2010. --> | ||
=== Prerequisite === | === Prerequisite === | ||
| − | [[Math 371]]. | + | [[Math 213]]. |
| + | |||
| + | === Recommended === | ||
| + | [[Math 371]]. | ||
=== Description === | === Description === | ||
| Line 15: | Line 23: | ||
== 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 Computer Security (CS 465). | + | 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) and the current Information Technology course on Encryption and Compression (IT 531). |
=== Prerequisites === | === Prerequisites === | ||
| − | The requirement for [[Math | + | The requirement for [[Math 213]] ensures both an appropriate level of mathematical maturity and a basic knowledge of linear algebra. The recommendation for [[Math 371]] encourages students to be familiar with the concepts of groups, rings, and fields. |
=== 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 or | + | 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 another appropriate computing language. |
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
| Line 36: | Line 44: | ||
#* Fermat and Euler Theorems | #* Fermat and Euler Theorems | ||
#* Primitive roots | #* Primitive roots | ||
| + | #* Legendre and Jacobi symbols | ||
#* Elementary continued fractions | #* Elementary continued fractions | ||
| − | #* 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 strengths and weaknesses; attacks on RSA | + | # RSA and its strengths and weaknesses; attacks on RSA |
| − | #* Wiener's continued fraction attack on low decryption exponent | + | #* Wiener's continued fraction attack on low decryption exponent |
| − | # Primality testing algorithms | + | # Primality testing algorithms |
| − | # Factorization techniques | + | # Factorization techniques |
| − | #* The Quadratic Sieve | + | #* The Quadratic Sieve |
| − | # Discrete logarithms | + | # Discrete logarithms |
| − | # | + | #* Diffie-Hellman key exchange |
| + | #* ElGamal | ||
</div> | </div> | ||
| + | === Textbooks === | ||
| + | |||
| + | Possible textbooks for this course include (but are not limited to): | ||
| + | |||
| + | * | ||
=== Additional topics === | === Additional topics === | ||
| − | If time allows, additional topics may include, but are not limited to: Elliptic curve cryptography, birthday attacks and probability, quantum cryptography (key distribution, Shor's algorithm), hash functions, digital signatures. | + | If time allows, additional topics may include, but are not limited to: Elliptic curve cryptography, birthday attacks and probability, quantum cryptography (key distribution, Shor's algorithm), hash functions, digital signatures, and lattices and lattice algorithms (LLL algorithm, NTRU system, lattice attacks on RSA). |
=== Courses for which this course is prerequisite === | === Courses for which this course is prerequisite === | ||
Latest revision as of 14:26, 22 August 2019
Contents
Catalog Information
Title
Mathematical Cryptography.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
Recommended
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) and the current Information Technology course on Encryption and Compression (IT 531).
Prerequisites
The requirement for Math 213 ensures both an appropriate level of mathematical maturity and a basic knowledge of linear algebra. The recommendation for Math 371 encourages students to be familiar with the concepts of groups, rings, and fields.
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 another appropriate computing language.
- 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
- Legendre and Jacobi symbols
- 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
Textbooks
Possible textbooks for this course include (but are not limited to):
Additional topics
If time allows, additional topics may include, but are not limited to: Elliptic curve cryptography, birthday attacks and probability, quantum cryptography (key distribution, Shor's algorithm), hash functions, digital signatures, and lattices and lattice algorithms (LLL algorithm, NTRU system, lattice attacks on RSA).
Courses for which this course is prerequisite
None.
