tl;dr: Better bounds on counting the number of hidden sums plus algorithms to search for them for attacking linear maps.
Paper: WCC 2017, extended version in Discrete Mathematics (Vol. 342) or personal pdf.
Carlo Brunetta, Marco Calderini, Massimiliano Sala
We report the recent results on hidden sums obtained in the unpublished preprints by Brunetta, Calderini, and Sala. These hidden sums could be used to exploit some particular trapdoors in block ciphers. Each hidden sum is related to an elementary abelian regular subgroup. Focusing on the subgroups of the affine general linear group, we are able to characterize the maps generating these groups. From the characterization we obtain a polynomial-time algorithm to represent the elements of a binary vector space with respect to the hidden sum. Such an algorithm can be used to exploit the trapdoor in a block cipher. Then we design an efficient algorithm to perform the necessary preprocessing on the components of a cipher for the exploitation of the trapdoor.
The paper(s) is based on my MSc thesis which can be retrieved from Trento’s University Library or this link.