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The Digraph Of The Square Mapping On Elliptic Curves, Katrina Glaeser
The Digraph Of The Square Mapping On Elliptic Curves, Katrina Glaeser
Mathematical Sciences Technical Reports (MSTR)
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.