Bridges connecting Encryption Schemes

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by Gentry to produce fully homomorphic encryption schemes, we exhibit a general recipe for the construction of bridges. Our main theorem asserts that the security of a bridge reduces to the security of the first encryption scheme together with a technical additional assumption.