A new proof is given for the correctness of the powers of two descent method
for computing discrete logarithms. The result is slightly stronger than
the original work, but more importantly we provide a unified geometric
argument, eliminating the need to analyse all possible subgroups of
. Our approach sheds
new light on the role of
,
in the hope to eventually lead to a complete proof that discrete logarithms can be
computed in quasipolynomial time in finite fields of fixed characteristic.