Homomorphic Public Key Encryption Techniques

Abstract

This chapter discusses two popular homomorphic public key encryption (PKE) techniques, i.e., Paillier PKE and Boneh-Goh-Nissim (BGN) PKE, which serve as the preliminary for building most privacy-enhancing aggregation techniques in the rest chapters of this monograph. In addition, the Java source codes of the two homomorphic PKEs are also provided for the interested readers to better understand and implement them. In order to attain privacy-preserving data aggregation in smart grid communications, we need to first understand the homomorphic public key encryption (HPKE) techniques [1, 2, 3, 4, 5, 6, 7]. Different from the general public key encryption algorithms [8, 9], HPKE further holds an additional “homomorphic” property, which makes the privacy-preserving data aggregation possible. As shown in Fig. 2.1, when we directly operate over two encrypted data E(x) and E(y) with some operation “•”, we can gain E(x ∘ y) = E(x)•E(y). In most HPKE cases, the operations “•” and “∘” are respectively referred to the common multiplication “×” and addition “+” operations. Because most of privacy-enhancing aggregation techniques illustrated in this monograph are based on Paillier public key encryption [2] and Boneh-Goh-Nissim (BGN) public key encryption [6], in this chapter, we first take a close look at these two popular homomorphic encryption techniques. Note that, both of them are randomized encryption algorithms [1], i.e., in addition to the plaintext as the input of encryption, a random number is also input for achieving semantic security.