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Created by:
Last updated:
December 7, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
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.
Course Curriculum
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- Introduction to Elliptic Curves (notes) Unlimited
- Introduction to Elliptic Curves (slides) Unlimited
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- The Group Law and Weierstrass and Edwards Equations (notes) Unlimited
- Finite Field Arithmetic (notes) Unlimited
- Finite Field Arithmetic (slides) Unlimited
- Isogeny Kernels and Division Polynomials (notes) Unlimited
- Isogeny Kernels and Division Polynomials (slides) Unlimited
- Hasse’s Theorem and Point Counting (notes) Unlimited
- Hasse’s Theorem and Point Counting (slides) Unlimited
- Generic Algorithms for the Discrete Logarithm Problem (notes) Unlimited
- Elliptic Curve Primality Proving (ECPP) (notes) Unlimited
- Ordinary and Supersingular Curves (notes) Unlimited
- Elliptic Curves over C (Part II) (notes) Unlimited
- The CM Torsor (notes) Unlimited
- The Modular Equation (notes) Unlimited
- Ring Class Fields and the CM Method (notes) Unlimited
- The Weil Pairing (notes) Unlimited
- Fermat’s Last Theorem (notes) Unlimited
About the instructor
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Instructor Rating
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1520
Courses
1916
Students
Massachusetts Institute of Technology
