| 摘要: |
| 构造高效、安全的全同态加密方案目前仍然是一个公开问题.通过扩展近似GCD到近似理想格的方法,首先构造一个基于整数上部分近似理想格问题(PAILP)的有点同态加密方案,并使用Gentry的引导技术将其转换到全同态加密方案.归约有点同态加密方案的安全性到求解部分近似理想格问题;其次,构造基于PAILP的批全同态加密方案和基于近似理想格(AILP)的全同态加密方案;最后,实现基于PAILP/AILP的全同态加密方案,并通过计算实验,其结果表明,所提方案比已有方案性能更好. |
| 关键词: 全同态加密 近似理想格问题 近似GCD 整数分解 稀疏子集和 |
| DOI：10.13328/j.cnki.jos.004808 |
| 分类号: |
| 基金项目:教育部人文社会科学研究规划基金(14YJAZH023);江苏省"青蓝工程"项目(KYQ14004);常州市应用基础研究项目(CJ20140040);江苏省前瞻性联合研究项目(BY2014038-03);中国科学院信息工程研究所信息安全国家重点实验室开放课题(2015-MSB-10) |
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| Fully Homomorphic Encryption from Approximate Ideal Lattices |
|
GU Chun-Sheng1,2,3
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1.School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China;2.School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, China;3.State Key Laboratory of Information Security, Institute of Information Engineering, The Chinese Academy of Sciences, Beijing 100093, China
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| Abstract: |
| Constructing efficient and secured fully homomorphic encryption is still an open problem. By generalizing approximate GCD to approximate ideal lattice, a somewhat homomorphic encryption scheme is first presented based on partial approximate ideal lattice problem (PAILP) over the integers. The scheme is then converted it into a fully homomorphic encryption scheme (FHE) by applying Gentry's bootstrappable techniques. Next, the security of the somewhat homomorphic encryption scheme is reduced to solving a partial approximate ideal lattice problem. Furthermore, a PAILP-based batch FHE and an AILP-based FHE are constructed. Finally, the PAILP/AILP-based FHE is implemented, and the performance of the proposed scheme is demonstrated to be better than that of previous schemes by computational experimental. |
| Key words: fully homomorphic encryption approximate ideal lattice problem approximate GCD integer factoring SSSP (sparse subset sum problem) |
