Cryptography with Constant Input Locality

So far we studied the possibility of implementing cryptographic tasks using functions with constant output locality. In this chapter we turn to the dual question of constant input locality. In particular, we ask: Which cryptographic primitives (if any) can be realized by functions in which every bit of the input influences only a constant number of bits of the output? We prove several positive and negative results that together form the following characterization. Essentially, primitives that require some form of non-malleability (e. g., digital signatures) cannot be realized with constant input locality, while primitives that require secrecy (e.g., encryption schemes) can be implemented with constant input locality. Some of our constructions enjoy both constant input locality and constant output locality, giving rise to cryptographic hardware that has constant-depth, constant fan-in and constant fan-out.