  Most modern block ciphers are built using components whose cryptographic
strength is evaluated in terms of their resistance to attacks on the whole
cipher. In particular, differential properties of vectorial Boolean functions
are studied for the S-Boxes to thwart differential cryptanalysis. Little is
known on similar properties to avoid trapdoors in the design of the block
cipher. In this paper we present a form of trapdoors coming from alternative
vector space structures, which we call hidden sums, and give a characterization
on the Boolean function S-Box to avoid any such hidden sum. We also study some
properties of this new class of vectorial Boolean functions, which we call
anti-crooked, and provide a toy cipher with a hidden sum trapdoor.
