Cryptography:
An Introduction to Cryptology
Math 348:02 - Spring 2021
MTh 3rd period (12-1:20 PM)
Announcements
Instructor J. Tunnell, tunnell at math.rutgers.edu, OFFICE HOURS: to
be announced
General Information
This is an upper level MATH course. It is directed at
students in mathematics, electrical engineering, or computer science
who have strong interest in mathematics and want to learn about the
exciting applications of algebra and number theory to cryptography
and cryptanalysis.
course syllabus and
homework assignments
Prerequisites:
Linear Algebra (Math 250) and one of Math 300, 356, or 477, or
permission of department.
Part of the course will cover the needed background material on
number theory (see below).
Textbook
Jeffrey Hoffstein, Jill Pipher, Joseph Silverman
An Introduction to Mathematical Cryptology, 2nd edition
Springer, 2014.
The text for the course
is available in electronic form to Rutgers
Students at no charge.
The Errata
to 2nd edition is available and should be consulted.
Description
As the title indicates, this is an introduction to modern cryptography.
Topics to be covered include:
- Symmetric Cryptography:
Classical Cryptography: Simple Ciphers and Cryptograms.
Vigenère Cipher, Hill Cipher;
- Modern Cryptography: Advanced Encryption Standard (AES).
Public Key/Private Key Cryptography:
- Ciphers: Rivest-Shamir-Adleman (RSA), El Gamal, Diffie-Hellman and
trapdoors, Elliptic Curve Cryptography, Lattices and Cryptography
- Protocols: Kerberos, PGP, SSL, Digital Signatures.
Number Theory:
- Congruences and Finite fields,
- Primitive roots and discrete logarithms.
- Finding large primes, pseudoprimes and primality testing.
- Square root algorithms, factoring techniques.
- Legendre and Jacobi symbols.
Quizzes There will be various 15 minute quizzes on material
from the lectures, reading and homework to provide a check on
student's understanding the material
Exams: Exam 1 3/1/21 , Exam 2 4/5/21, Final exam: 5/6/21 8-11 AM
Grading: Quizzes: 15 % ; Homework: 15%, Midterms 30%, Final: 40 %
Last updated: January 19, 2021