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GSW-type hierarchical identity-based fully homomorphic encryption scheme from learning with errors
DAI Xiaoming, ZHANG Wei, ZHENG Zhiheng, LI Zhenlin
Journal of Computer Applications
2016, 36 (7):
1856-1860.
DOI: 10.11772/j.issn.1001-9081.2016.07.1856
Focusing on the function defect of the traditional Identity-Based Encryption (IBE) scheme that the ciphertexts can not be calculated directly, a new IBE scheme was proposed. The homomorphism transformation mechanism proposed by Gentry was used to transform the hierarchical IBE scheme proposed by Agrawal into a homomorphic hierarchical IBE scheme. Compared with the GSW (Gentry, Sahai, Waters) scheme (GENTRY C, SAHAI A, WATERS B. Homomorphic encryption from learning with errors:conceptually-simpler, asymptotically-faster, attribute-based. CRYPTO 2013:Proceedings of the 33rd Annual Cryptology Conference on Advances in Cryptology. Berlin:Springer, 2013:75-92) and CM (Clear, Mcgoldrick) scheme (CLEAR M, MCGOLDRICK C. Bootstrappable identity-based fully homomorphic encryption. CANS 2014:Proceedings of 13th International Conference on Cryptology and Network Security. Berlin:Springer, 2014:1-19), the construction method of the proposed scheme was more natural, the level of space complexity was reduced from cubic to square with higher efficiency. In the current environment of cloud computing, the proposed scheme can contribute to the transformation from theory to practice of fully homomorphic encryption scheme based on Learning With Errors (LWE) problem. The performance analysis and the verification results under the random oracle model prove the security for Indistinguishability of the Identity-Based Encryption Scheme under Chosen-Plaintext Attack (IND-ID-CPA) of the proposed scheme.
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