Algebra & Number Theory

On the discrete logarithm problem in elliptic curves II

Claus Diem

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Abstract

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

Source
Algebra Number Theory, Volume 7, Number 6 (2013), 1281-1323.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730029

Digital Object Identifier
doi:10.2140/ant.2013.7.1281

Mathematical Reviews number (MathSciNet)
MR3107564

Zentralblatt MATH identifier
1300.11132

Subjects
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]

Keywords
elliptic curves discrete logarithm problem

Citation

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


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References

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