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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.

**Assessment**

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.

**Certification**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

- Add the certificate to your CV or resume and brighten up your career
- Show it to prove your success

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 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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