IACR News item: 04 September 2013
Koh-ichi Nagao
ePrint ReportPetit et al. shows that assuming first fall degree assumption and using Gr\\\"obner basis computation, its complexity is heuristically subexponential.
On the other hands, the author shows that the decomposition problem of Jacobian of plane curve over $F_{p^n}$ also essentially reduces to solving low degree equations system over $F_p$ coming from Weil descent.
In this paper, we generalize ($p>2$ cases, Jacobian cases) and revise (precise estimation of first fall degree) the results of Petit et al. and show that the discrete logarithm problem
of elliptic curve over small characteristic field $F_{p^n}$ is subexponential of input size $n$, and the discrete logarithm problem of Jacobian of small genus curve over small characteristic field $F_{p^n}$ is also subexponential of input size $n$,
under first fall degree assumption.
Additional news items may be found on the IACR news page.