Evaluation of discrete logarithms in a group of π-torsion points of an elliptic curve in characteristic π
Open Access
- 1 January 1998
- journal article
- Published byΒ American Mathematical Society (AMS)Β inΒ Mathematics of Computation
- Vol.Β 67 Β (221) , 353-356
- https://doi.org/10.1090/s0025-5718-98-00887-4
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 β‘ p ) O(\ln p) operations in this field.Keywords
This publication has 7 references indexed in Scilit:
- Use of Elliptic Curves in CryptographyPublished by Springer Nature ,2000
- A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of CurvesMathematics of Computation, 1994
- Reducing elliptic curve logarithms to logarithms in a finite fieldPublished by Association for Computing Machinery (ACM) ,1991
- Elliptic Curve CryptosystemsMathematics of Computation, 1987
- The Arithmetic of Elliptic CurvesPublished by Springer Nature ,1986
- Monte Carlo Methods for Index Computation (mod p)Mathematics of Computation, 1978
- An improved algorithm for computing logarithms overGF(p)and its cryptographic significance (Corresp.)IEEE Transactions on Information Theory, 1978