The Digraph of the Square Mapping on Elliptic Curves

Authors

Katrina Glaeser, University of California - Berkeley

Document Type

Article

Publication Date

9-19-2009

First Advisor

Joshua Holden

Abstract

Consider a subgroup of an elliptic curve generated by a point P of order n. It is possible to match any point Q to an integer k (mod n) such that Q = kP using a brute force method. By observing patterns in the digraph of the squaring map on the integers modulo n it is possible to perform this matching. These techniques can be applied to solving the Elliptic Curve Discrete Log Problem given a complete graph of the square mapping k P -> k^2 P for the elliptic curve points.

Comments

MSTR 09-08

Recommended Citation

Glaeser, Katrina, "The Digraph of the Square Mapping on Elliptic Curves" (2009). Mathematical Sciences Technical Reports (MSTR). 18.
https://scholar.rose-hulman.edu/math_mstr/18