✦ LIBER ✦
Computing the order of points on an elliptic curve modulo N is as difficult as factoring N
✍ Scribed by S. Martín; P. Morillo; J.L. Villar
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 292 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
Communicated by J. Lagarias
Abstract--Given a square-free integer N, the group of points on an elliptic curve over the ring ZN is defined in the natural way. We prove that computing the order of points on elliptic curves over ZN is as difficult as factoring N, in the sense of randomly polynomial time reduction. Therefore, cryptosystems based on the difficulty of computing the order of points on elliptic curves over the ring ZN will be at least as robust as those based on the difficulty of factoring N. (~) 2001 Elsevier Science Ltd. All rights reserved.