Explore BrainMass
Share

Explore BrainMass

    Elliptic Curves

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:37 am ad1c9bdddf
    https://brainmass.com/math/curves/elliptic-curves-over-finite-field-511538

    Attachments

    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:
    (please see the attached file)

    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]
    (please see the attached ...

    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.

    $2.19