# 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
• email: shoup@cs.nyu.edu
• Office hours: Tuesday, 3:30-4:30pm

Mailing List

• It is important that you subscribe to the class mailing list, in order to receive announcements.
• To subscribe to the list, follow these instructions.

Lectures: Wed 5:00-6:50pm, 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 in-depth 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.