Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝-Reference-Cited by-同舟云学术

Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝

Published:1998 Issue:221 Volume:67 Page:353-356
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Semaev I.

Abstract

We show that to solve the discrete log problem in a subgroup of order p p of an elliptic curve over the finite field of characteristic p p one needs O ( ln ⁡ p ) O(\ln p) operations in this field.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1998-67-221/S0025-5718-98-00887-4/S0025-5718-98-00887-4.pdf

Reference10 articles.

1. Use of elliptic curves in cryptography;Miller, Victor S.,1986

2. Elliptic curve cryptosystems;Koblitz, Neal;Math. Comp.,1987

3. A. Menezes, S. Vanstone, and O. Tatsuaki, Reducing elliptic curve logarithms to logarithms in a finite field, Proc. 23rd ACM Sympos. Theory of Computing, 1991, pp. 80–89.

4. I. A. Semaev, Bystryĭ algoritm vyqisleniya sparivaniya A. Veĭlya na èlliptiqeskoĭ krivoĭ, International Conference “Modern Problems in Number Theory”, Russia, Tula, Sept. 20–25, 1993, Abstracts of papers.

5. A remark concerning 𝑚-divisibility and the discrete logarithm in the divisor class group of curves;Frey, Gerhard;Math. Comp.,1994

Cited by 134 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Solving modular cubic equations with Coppersmith's method;Information and Computation;2024-06

2. Diving into Alternate Elliptic Curves for Bitcoin: A Security Analysis;Proceedings of the 7th International Conference on Networking, Intelligent Systems and Security;2024-04-18

3. Design of a Three-Factor Authentication and Key Agreement Scheme Using Biometric Approach for Internet of Things;2024-04-02

4. Group structure of elliptic curves over ℤ/Nℤ;Journal of Mathematical Cryptology;2024-01-01

5. Cryptographically Strong Elliptic Curves of Prime Order;International Journal of Electronics and Telecommunications;2023-07-26