An Update on Known Invariants of Vectorial Boolean Functions Almost Perfect Nonlinear functions are of great practical importance for cryptography as they provide optimum resistance to differential cryptanalysis. Due to the large number of such functions, they are classified up to CCZequivalence, which leaves this resistance to differential cryptanalysis invariant. Deciding the equivalence of two given functions from the definition is computationally difficult. We summarize computational results on some properties that remain invariant under CCZequivalence for the known APN functions, including more than 8000 new CCZinequivalent functions that have previously never been considered with respect to these invariants. Knowing these invariants greatly facilitates the classification of APN functions, since different values of these invariants immediately imply that two functions are CCZinequivalent.

Functional encryption for threshold functions (or fuzzy IBE) from lattices Cryptosystems based on the hardness of lattice problems have recently acquired much importance due to their averagecase to worstcase equivalence, their conjectured resistance to quantum cryptanalysis, their ease of implementation and increasing practicality, and, lately, their promising potential as a platform for constructing advanced  :44,this work, we construct xe2x80x9cFuzzyxe2x80x9d Identity Based Encryption from the hardness of the Learning With Errors (LWE) problem. We note that for our parameters, the underlying lattice problems (such as gapSVP or SIVP) are assumed to be hard to approximate within supexponential factors for adversaries running in subexponential time. We give CPA and CCA secure variants of our construction, for small and large universes of attributes. All our constructions are secure against selectiveidentity attacks in the standard model. Our construction is made possible by observing certain special properties that secret sharing schemes need to satisfy in order to be useful for Fuzzy IBE. We also discuss some obstacles towards realizing latticebased attributebased encryption (ABE).