Homomorphic Encryption Enabling Computation on Encrypted Data for Secure Cloud Computing

Abstract

Homomorphic encryption enables computations on encrypted data, providing confidentiality for cloud computing applications. This chapter explains the foundations, classifications, and security definitions for homomorphic encryption schemes. Partially and somewhat homomorphic cryptosystems allow limited operations whereas fully homomorphic encryption supports arbitrary depth circuits through bootstrapping. Various homomorphic schemes are presented including RSA, Paillier, learning/ring with errors, Gentry's ideal lattices, and code-based cryptosystems. Their underlying hardness assumptions based on lattices, codes, and number theory are analyzed. Applications of fully homomorphic encryption for secure cloud analytics, machine learning, signal processing, database queries, and information retrieval are described. However, performance overhead remains a key challenge. Recent optimizations using leveled FHE, ciphertext packing, and function approximation aim to improve efficiency. Hardware acceleration via FPGAs and ASICs offers further speedups.