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18.7831

Elliptic Curves

3-0-9 units · Graduate

Computationally focused introduction to elliptic curves, with applications to number theory and cryptography. Topics include point-counting, isogenies, pairings, and the theory of complex multiplication, with applications to integer factorization, primality proving, and elliptic curve cryptography. Includes a brief introduction to modular curves and the proof of Fermat's Last Theorem. Students in Course 18 must register for the undergraduate version, 18.783 .

Fall 2025

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.

Readings

Spring 2021

This course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. While this is an introductory course, we will (gently) work our way up to some fairly advanced material, including an overview of the proof of Fermat's last theorem.

Readings

Prerequisites & course information

Subject meets with 18.783 Prereq: 18.702 , 18.703 , or permission of instructor Acad Year 2027-2028: G (Fall) Acad Year 2028-2029: Not offered 3-0-9 units

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