Algebra & Number Theory

On the discrete logarithm problem in elliptic curves II

Claus Diem

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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).

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11Y16: Algorithms; complexity [See also 68Q25]
Secondary: 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx] 11G20: Curves over finite and local fields [See also 14H25]

elliptic curves discrete logarithm problem


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.

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