Open Access
2013 On the discrete logarithm problem in elliptic curves II
Claus Diem
Algebra Number Theory 7(6): 1281-1323 (2013). DOI: 10.2140/ant.2013.7.1281


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 (qi)i and natural numbers (ni)i with ni and nilog(qi)20 for i, the discrete logarithm problem in the groups of rational points of elliptic curves over the fields Fqini can be solved in subexponential expected time (qini)o(1).

Let a, b>0 be fixed. Then the problem over fields Fqn, where q is a prime power and n a natural number with a log(q)13nb log(q), can be solved in an expected time of eO(log(qn)34).


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Claus Diem. "On the discrete logarithm problem in elliptic curves II." Algebra Number Theory 7 (6) 1281 - 1323, 2013.


Received: 28 July 2011; Revised: 12 June 2012; Accepted: 15 July 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1300.11132
MathSciNet: MR3107564
Digital Object Identifier: 10.2140/ant.2013.7.1281

Primary: 11Y16
Secondary: 11G20 , 14H52

Keywords: discrete logarithm problem , Elliptic curves

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 6 • 2013
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