Multimedia Security 2

6Processing Encrypted Multimedia Data Using Homomorphic Encryption

Sébastien CANARD¹, Sergiu CARPOV², Caroline FONTAINE³ and Renaud SIRDEY⁴

¹Orange Labs, Applied Crypto Group, Caen, France

²Inpher, Lausanne, Switzerland

³LMF, ENS Paris-Saclay, University of Paris-Saclay, CNRS, Gif-sur-Yvette, France

⁴CEA, LIST, University of Paris-Saclay, Gif-sur-Yvette, France

In this chapter, we present the state of the art in homomorphic encryption techniques, which make it possible to process encrypted data. These techniques are very costly, but impressive progress has been made in recent years; experiments have already been carried out for industrial applications, including in the multimedia field. We shall present the results of some of these experiments, along with the theoretical background needed to understand their development.

6.1. Context

This chapter concerns encryption techniques in the cryptographic sense of the term, that is, techniques designed to ensure the confidentiality of data in general, regardless of its nature. We consider the data to be protected as bits, bit vectors or numbers. These data are first encoded in an alphabet or a suitable mathematical structure, depending on the chosen encryption technique.

Encryption techniques have been used since ancient times; their general development will not be discussed here. In this chapter, we shall focus on homomorphic techniques, in which operations performed on encrypted data are also performed, indirectly, on the underlying ...