Partially homomorphic encryption schemes over finite fields

Homomorphic encryption scheme enables computation in the encrypted domain, which is of great importance because of its wide and growing range of applications. The main issue with the known fully (or partially) homomorphic encryption schemes is the high computational complexity and large communication cost required for their execution. In this work, we study symmetric partially homomorphic encryption schemes over finite fields, establishing relationships between homomorphisms over finite fields with $q$-ary functions. Our proposed partially homomorphic encryption schemes have perfect secrecy and resist cipher-only attacks to some extent