Discrete logarithm based additively homomorphic encryption and secure data aggregation

At PKC 2006, Chevallier–Mames, Paillier, and Pointcheval proposed discrete logarithm based encryption schemes that are partially homomorphic, either additively or multiplicatively and announced an open problem: finding a discrete logarithm based cryptosystem that would help realize fully   additive or multiplicative homomorphism. In this study, we achieve this goal by enclosing two opposite settings on the discrete logarithm problems (DLP) simultaneously: the first setting is that DLP over Zp0Zp0 (where p0 − 1 is smooth) is used to encode messages, while the second setting is that DLP over ZpZp (where p − 1 is non-smooth, i.e., containing large prime factors) is used to encrypt plaintexts. Then, based on the proposed scheme, novel protocols for secure data aggregation in wireless sensor networks are presented. Finally, taking Paillier’s factoring-based additively homomorphic encryption schemes as the reference framework, we present detailed performance comparisons and further enhancement.