Elliptic Curve Cryptography + Python

• Elliptic Curve Cryptography with Python

  public version (demo only) | members-only version (demo, write, and test run)

  • find all points that satisfy elliptic curve equation

  • show cyclic behavior of a generator point in a small group

  • use double and add algorithm for fast point hopping

  • quick intro to elliptic curves

  • singular versus nonsingular elliptic curves

  • why use elliptic curve in cryptography

  • equations for elliptic curve point addition and doubling

  • what is a field

  • elliptic curve group operations

  • associativity proof for elliptic curve point addition

  • elliptic curve over prime fields

  • implement checking if curve to be instantiated is singular

  • implement point addition and doubling

  • imlement finding all points that satisfy elliptic curve equation

  • implement checking if 2 points are inverse of each other

  • explain elliptic curve order, subgroup size n, and cofactor h

  • implement double and add algorithm

  • what does 'Points on elliptic curve + O have cyclic subgroups' mean

  • when do all points on an elliptic curve form a cyclic group