#### 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.

#### Recommended Citation

Glaeser, Katrina, "The Digraph of the Square Mapping on Elliptic Curves" (2009). *Mathematical Sciences Technical Reports (MSTR)*. 18.

http://scholar.rose-hulman.edu/math_mstr/18

## Comments

MSTR 09-08