Point decomposition problem in binary elliptic curves

Abstract

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 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 provides a significant speed-up.