Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 6 (2013), 1281-1323.
On the discrete logarithm problem in elliptic curves II
We continue our study on the elliptic curve discrete logarithm problem over finite extension fields. We show, among others, the following results:
For sequences of prime powers and natural numbers with and for , the discrete logarithm problem in the groups of rational points of elliptic curves over the fields can be solved in subexponential expected time .
Let , be fixed. Then the problem over fields , where is a prime power and a natural number with , can be solved in an expected time of .
Algebra Number Theory, Volume 7, Number 6 (2013), 1281-1323.
Received: 28 July 2011
Revised: 12 June 2012
Accepted: 15 July 2012
First available in Project Euclid: 20 December 2017
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Diem, Claus. On the discrete logarithm problem in elliptic curves II. Algebra Number Theory 7 (2013), no. 6, 1281--1323. doi:10.2140/ant.2013.7.1281. https://projecteuclid.org/euclid.ant/1513730029