Purchase Solution

Elliptic Curves

Not what you're looking for?

Let E be the elliptic curve over F5 defined by y^2 = x^3+1.
1. Write down the division polynomial (psi_3)(x) for this curve.
2. Show that the greatest common divisor of (psi_3)(x) and "x^5 -x" is "x(x-1)."
3. Use part (2) to show that the 3-torsion points in E(F5) are {Origin,(0,1),(0,-1)}."

I have also attached the problem for easier reading.

Solution Summary

In this solution we solve several number theory problems involving points on an elliptic curve over a finite field. Included is one reference.

Solution Preview

** Please see the attached file for the complete solution **
Thank you for using BrainMass.com. I hope that this helps.

We are given the elliptic curve E over (please see the attached file) defined by:

a) We wish to compute the division polynomial (please see the attached file) for E.

In general, for the elliptic curve defined by (please see the attached file) we have [1]

Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability