An Additively Homomorphic Encryption over Large Message Space

Hu Chen, Yupu Hu, Zhizhu Lian, Huiwen Jia and Xu An Wang
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Hu Chen: State Key Laboratory of Integrated Service Networks, Xidian University, Shanxi, Xi'an, China
Yupu Hu: State Key Laboratory of Integrated Service Networks, Xidian University, Shanxi, Xi'an, China
Zhizhu Lian: State Key Laboratory of Integrated Service Networks, Xidian University, Shanxi, Xi'an, China
Huiwen Jia: State Key Laboratory of Integrated Service Networks, Xidian University, Shanxi, Xi'an, China
Xu An Wang: State Key Laboratory of Integrated Service Networks, Xidian University, Shanxi, Xi'an, China

International Journal of Information Technology and Web Engineering (IJITWE), 2015, vol. 10, issue 3, 82-102

Abstract: Fully homomorphic encryption schemes available are not efficient enough to be practical, and a number of real-world applications require only that a homomorphic encryption scheme is somewhat homomorphic, even additively homomorphic and has much larger message space for efficiency. An additively homomorphic encryption scheme based heavily on Smart-Vercauteren encryption scheme (SV10 scheme, PKC 2010) is put forward, where both schemes each work with two ideals I and J. As a contribution of independent interest, a two-element representation of the ideal I is given and proven by factoring prime numbers in a number field. This two-element representation serves as the public key. The authors' scheme allows working over much larger message space than that of SV10 scheme by selecting the ideal I with larger decryption radius to generate public/private key pair, instead of choosing the ideal J as done in the SV10 scheme. The correctness and security of the scheme are shown, followed by setting parameters and computational results. The results indicate that this construction has much larger message space than SV10 scheme.

Date: 2015
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