This article gives an introduction to Elliptic Curve Cryptography and Quantum Computing. It includes an analysis of Peter Shor’s algorithm for the quantum computer breakdown of Discrete Log Cryptosystems and an analog to Shor’s algorithm for Elliptic Curve Cryptosystems. An extended example is included which illustrates how this modified Shor’s algorithm will work.
Jodie Eicher and Yaw Opoku. Using the Quantum Computer to Break Elliptic Curve Cryptosystems. Technical paper (TR-97-02). Math and Computer Science Technical Report Series. Richmond, Virginia: Department of Mathematics and Computer Science, University of Richmond, July, 1997.