Pseudorandom functions revisited: the cascade construction and its concrete security

Pseudorandom function families are a powerful cryptographic primitive, yielding, in particular simple solutions for the main problems in private key cryptography. Their existence based on general assumptions (namely the existence of one-way functions) has been established. The authors investigate new ways of designing pseudorandom function families. The goal is to find constructions that are both efficient and secure, and thus eventually to bring the benefits of pseudorandom functions to practice. The basic building blocks in the design are certain limited versions of pseudorandom function families, called finite length input pseudorandom function families, for which very efficient realizations exist impractical cryptography. Thus rather than starting from one-way functions, they propose constructions of "full-fledged" pseudorandom function families from these limited ones. In particular they propose the cascade construction, and provide a concrete security analysis which relates the strength of the cascade to that of the underlying finite pseudorandom function family in a precise and quantitative way.