Augmented sets of output differences and new distinguishers for SPN ciphers.

We introduce augmented vector spaces of output differences, new generic and black-box distinguishers for Substitution Permutation Network (SPN) ciphers. Our distinguishers are based on a novel method of constructing a vector of size bits from a given vector of size n bits, where and d is a positive integer. We list all such -bit vectors into a set called the corresponding -order augmented set and define its linear span as the corresponding -order augmented vector space .