  We analyze the point decomposition problem (PDP) in binary elliptic curves.
It is known that PDP in an elliptic curve group can be reduced to solving a
particular system of multivariate non-linear system of equations derived from
the so called Semaev summation polynomials. We modify the underlying system of
equations by introducing some auxiliary variables. We argue that the trade-off
between lowering the degree of Semaev polynomials and increasing the number of
variables is worth.
