18.783 | Fall 2025 | Undergraduate

Elliptic Curves

Course Description

This course offers a computationally focused introduction to elliptic curves, emphasizing their deep connections to number theory and cryptography. Core topics include point-counting, isogenies, pairings, and the theory of complex multiplication. Throughout the course, these concepts are applied to practical problems …
This course offers a computationally focused introduction to elliptic curves, emphasizing their deep connections to number theory and cryptography. Core topics include point-counting, isogenies, pairings, and the theory of complex multiplication. Throughout the course, these concepts are applied to practical problems such as integer factorization, primality proving, and elliptic curve cryptography.
Learning Resource Types
Lecture Notes
Open Textbooks
Problem Sets
Readings
A diagram featuring a circle with evenly spaced red dots around its perimeter and a red-dots tree for each red dot.
A 3-volcano of depth 2. (Image courtesy of Dr. Andrew Sutherland.)