Adding Points on an Elliptic Curve

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Elliptic curves are the solutions sets of nonsingular cubic polynomials of degree three. It is possible to define an addition law for these points so that they form an abelian algebraic group. In order to add distinct points, construct the line between them and determine the third point of intersection with the curve. The sum of the two points is then the reflection of the third point about the axis of symmetry, which is the axis for the case illustrated here. In order to add a point to itself, use the tangent line to the curve at that point.

Contributed by: John McGee (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

For an introduction to the mathematics and applications of elliptic curves, see L. C. Washington, Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications) [online], Boca Raton, FL: Chapman & Hall/CRC, 2003. http://www.math.umd.edu/~lcw/ec.html.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send