A noiseless key-homomorphic PRF: Application on distributed storage systems

Abstract

Key-homomorphic pseudo random functions (KH-PRF) have many practical applications including proxy re-encryption, distributed credential protection systems and updatable encryption.We present a key-homomorphic pseudo random function that is homomorphic with respect to a significant part of the secret key and analyse its security. Previous constructions rely on the learning with errors problem which adds some small error to the homomorphic operations due to the noisy outputs. Our construction, based on elliptic curves, removes the need of adding this noise at the cost of adding a few bits to the secret key for which homomorphism does not follow. The main advantage of our construction is that homomorphism can be applied several times without incurring into errors. In particular, we show how our KH-PRF can be used to provide key updatable encryption to distributed storage networks. Also, by relaxing the security assumptions, our PRF can be modified to be homomorphic with respect to the entire key.