Section: New Results
New results for solving the discrete logarithm problem
Recent results of R. Barbulescu, P. Gaudry, A. Joux, and E. Thomé
seem to indicate that
solving the discrete logarithm problem over finite fields of small
characteristic is easier than was precedently thought. F. Morain
and A. Guillevic, joined by R. Barbulescu and P. Gaudry, embarked on an
attempt to assess the security of the discrete logarithm problem in a
closely related context: that of finite fields with large characteristic and
small degree. Improving on the methods of A. Joux, R. Lercier and others, they
found new algorithms to select polynomials for the Number Field Sieve
– the algorithm of choice in this setting. Moreover, a clever study
of the algebraic properties of the fields used (e.g., algebraic
units), enabled them to break the world record for the case of