Advanced Cryptography
G22.3220001 Spring 2005
Class on Feb. 9 meets from 11am1pm in 613 WWH!!
Instructor: Victor Shoup

Phone: (212) 9983511

Office: 511 WWH

email: shoup@cs.nyu.edu

Office hours: Tuesday, 3:304:30pm
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Lectures: Wed 5:006:50pm, room 102 WWH
Grading:
Grading will be based on problem sets,
taking scribe notes, and class participation.
There will be no exams.
Course description:
This semester, we will focus on elliptic curve cryptography.
After a fairly indepth study of the mathematics underlying
elliptic curves, we will study some algorithmic questions
as well as applications to cryptography.
Prerequisites:
Students should be comfortable with the basics of abstract
algebra (groups, rings, fields).
Text:
A. Enge:
Elliptic Curves and their Application to Cryptography: An Introduction.
Other References:

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
PDF.

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.
Download here.
Notes on Scribe Notes
Problem Sets
Misc.
 A digression on valuations:
this cleans up some possibly confiusing remarks I made in class
about valuations.
As an exercise, you should work
through the examples and prove all the assertions.