G22.3220-001 Spring 2005
Class on Feb. 9 meets from 11am-1pm in 613 WWH!!
Instructor: Victor Shoup
Phone: (212) 998-3511
Office: 511 WWH
Office hours: Tuesday, 3:30-4:30pm
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in order to receive announcements.
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Lectures: Wed 5:00-6:50pm, room 102 WWH
Grading will be based on problem sets,
taking scribe notes, and class participation.
There will be no exams.
This semester, we will focus on elliptic curve cryptography.
After a fairly in-depth study of the mathematics underlying
elliptic curves, we will study some algorithmic questions
as well as applications to cryptography.
Students should be comfortable with the basics of abstract
algebra (groups, rings, fields).
Elliptic Curves and their Application to Cryptography: An Introduction.
Charlap and Robbins: An Elementary Introduction to Elliptic Curves.
Freely availble notes -- fairly nice, but sometimes rather sketchy.
The Enge text expands and refines these notes to a large degree.
Download: postscript or
Fulton: Algebraic Curves.
A classic -- a completely elementary but thorough introduction
to the theory of algebraic curves.
Washington: Elliptic Curves -- Number Theory and Cryptography.
Another elemntary introduction to elliptic curves.
Shoup: A Computational Introduction to Number Theory and Algebra.
One resource for algebraic basics -- see the chapters Rings and More Rings.
Notes on Scribe Notes
- A digression on valuations:
this cleans up some possibly confiusing remarks I made in class
As an exercise, you should work
through the examples and prove all the assertions.