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Discrete logarithm based additively homomorphic encryption and secure data aggregation |
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| Authors: | Licheng Wang Lihua Wang Zonghua Zhang |
| Affiliation: | a State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, 10 West Tucheng Road, Beijing 100876, PR China b National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi, Koganei-shi, Tokyo 184-8795, Japan c Communication University of China, 1 East Street of Dingfuzhuang, Beijing 100024, PR China d Institut TELECOM/TELECOM Lille1, Cité Scientifique Rue Guglielmo Marconi, BP 20145, 59653 Villeneuve d’Ascq cedex, France |
| Abstract: | 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 Zp0 (where p0 − 1 is smooth) is used to encode messages, while the second setting is that DLP over Zp (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. |
| Keywords: | Homomorphic encryption Discrete logarithm problem Wireless sensor networks Secure data aggregation |
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