Factoring bivariate sparse (lacunary) polynomials

We present a deterministic algorithm for computing all irreducible factors of degree ⩽d of a given bivariate polynomial f∈K[x,y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over of degree ⩽d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d.