Using the Quantum Computer to Break Elliptic Curve Cryptosystems
Jodie Eicher, Yaw Opoku · 1997
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. # Thanks to Hewlett-Packard for their generous support 1 1. Introduction The goa of this study is to developa nunderstaGW]] of howa qua tum computer, when creaW5( will bea]X tobrea the present da y elliptic curve cryptosystems. Elliptic curvesa re di#cult to work witha nd very di#cult ot understaN5 According to Dr.RonaN L. Rivest, founder of RSA Da ta Security, ... the security of crypotosystemsbaos on elliptic curves is not well understood, due inla]] pa] to thea7M5MX[ naM5M of elliptic curves. Few cryptograWX)( understaW elliptic curves, so there is not the sa( widesprea understaX)( an consensus concerning the security...