Bridges connecting Encryption Schemes

TL;DR

This paper introduces the concept of bridges connecting encryption schemes, analyzing their security and providing a construction method inspired by Gentry's bootstrapping for fully homomorphic encryption.

Contribution

It defines and studies the security of bridges between encryption schemes and presents a general construction approach inspired by bootstrapping techniques.

Findings

Security of a bridge reduces to the security of the initial scheme

Provides a general recipe for constructing bridges

Establishes a connection between bridges and fully homomorphic encryption

Abstract

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.