New Algorithms for the Discrete Logarithm Problem in Finite Fields of Small Characteristic (1/3)

Date

May 20, 2014

Time

4:40 PM - 6:10 PM

Speaker

Dr. Jens Zumbrägel

Affiliation

TU Dresden, Institut für Algebra

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. R. Schilling / Dipl.-Math J. Hollender

Description

Ein Vortrag im Rahmen der "Graduate Lectures in Mathematics" The Discrete Logarithm Problem (DLP) has been a long-studied problem in number theory. Its importance has raised in particular since the introduction of Public-Key Cryptography and the Diffie-Hellman protocol in 1976, which relies on the hardness of the DLP. After very little algorithmic progress for more than 20 years, the DLP in finite fields of small characteristic underwent a dramatic development since 2013. At the heart of the new methods is the usage of higher splitting probabilities of certain polynomials over finite fields. These improved algorithms have a strong impact, e.g., on the security assumptions of some well known identity-based cryptosystems. This lecture series provides an overview of the history and the recent developments of DLP algorithms. We will discuss the mathematics behind the new algorithms as well as implementational aspects that lead to some recent significant record computations.

Links

• Webseite der Graduate Lectures in Mathematics

Last modified: Apr 8, 2014, 5:51:22 PM