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Nowadays, many applications are focused on Elliptic Curves which is a plane algebraic curve, non-singular and has no cusps or self-intersections.

To apply for key agreement, cryptographic applications, integer factorization, digital signatures, pseudo-random generators and other related tasks, you must study Elliptic Curves. This introductory [course_title] will help you understand these more effectively to some advanced material with the proof of Fermat’s Last Theorem.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

Module: 01
Introduction to Elliptic Curves 01:00:00
The Group Law, Weierstrass and Edwards Equations 00:30:00
Finite Fields and Integer Arithmetic 01:15:00
Finite Field Arithmetic 01:00:00
Isogenies 00:45:00
Isogeny Kernels and Division Polynomials 01:30:00
Endomorphism Rings 00:45:00
Hasse’s Theorem, Point Counting 01:00:00
Module: 02
Schoof’s Algorithm 00:45:00
Generic Algorithms for Discrete Logarithms 01:15:00
Index Calculus, Smooth Numbers, Factoring Integers 01:30:00
Elliptic Curve Primality Proving (ECPP) 00:45:00
Endomorphism Algebras 01:00:00
Ordinary and Supersingular Curves 00:45:00
Elliptic Curves over C (Part 1) 01:30:00
Elliptic Curves over C (Part 2) 00:45:00
Module: 03
Complex Multiplication 00:45:00
The CM Torsor 00:45:00
Riemann Surfaces and Modular Curves 00:45:00
The Modular Equation 00:45:00
The Hilbert Class Polynomial 00:45:00
Ring Class Fields and the CM Method 01:00:00
Isogeny Volcanoes 00:45:00
The Weil Pairing 01:30:00
Modular Forms and L-series 01:30:00
Fermat’s Last Theorem 01:00:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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