Integer Based Fully Homomorphic Encryption

Integer-based Fully Homomorphic Encryption

"The concept of fully homomorphic encryption has been considered the 'holy grail' of cryptography since the discovery of secure public key cryptography in the 1970s. Fully homomorphic encryption allows arbitrary computation on encrypted data to be performed securely. Craig Gentry's new method of bootstrapping introduced in 2009 provides a technique for constructing fully homomorphic cryptosystems. In this paper we explore one such bootstrappable system based on simple integer arithmetic in a manner that someone without a high level of experience in homomorphic encryption can readily understand. Further, we present an implementation of the system as well as a lattice-based attack. We present performance results of our implementation under various parameter choices and the resistance of the system to the lattice-based attack under those parameters. Unfortunately, while the system is very interesting from a theoretical point of view, the results show that it is still not feasible for use."--Abstract.

Homomorphic Encryption and Applications

This book introduces the fundamental concepts of homomorphic encryption. From these foundations, applications are developed in the fields of private information retrieval, private searching on streaming data, privacy-preserving data mining, electronic voting and cloud computing. The content is presented in an instructional and practical style, with concrete examples to enhance the reader's understanding. This volume achieves a balance between the theoretical and the practical components of modern information security. Readers will learn key principles of homomorphic encryption as well as their application in solving real world problems.

Optimizations of Large Multipliers for Integer-based Fully Homomorphic Encryption