Provable randomness over lightweight permutations

Permutations mostly in the form of sboxes are very efficient components largely present in cryptographic artifacts either hardware or software. They have been well studied as an individual component and have a large body of knowledge. Here we look at the properties of tiny transformations employing permutations and a few field operations. That gives functions with few components, which can be safely used either as PRG building blocks or as a component in lightweight ciphers. At the end, we propose a PRG implementation with those components. Lastly, we formalize a key assumption over the system functions and give a theorem for the equivalence of some system instances.