基于LWE的高效身份基分级加密方案
发布时间：2018-08-18 14:07
【摘要】：格上可固定维数陷门派生的身份基分级加密(hierarchical identity-based encryption,HIBE)体制,因其具有在陷门派生前后格的维数保持不变的特性而受到广泛关注,但这种体制普遍存在陷门派生复杂度过高的问题.针对这一问题,分别给出随机预言模型和标准模型下的改进方案.首先利用MP12陷门函数的特性提出一种优化的Zq可逆矩阵提取算法,再基于该优化算法结合固定维数的陷门派生算法和MP12陷门函数完成方案的建立和陷门派生阶段,然后与对偶Regev算法相结合完成随机预言模型下HIBE方案的构造.并且利用二进制树加密系统将该方案改进为标准模型下的HIBE方案.两方案安全性均可归约至LWE问题的难解性,其中随机预言模型下的方案满足适应性安全,而标准模型下的方案满足选择性安全,并给出严格的安全性证明.对比分析表明:在相同的安全性下,随机预言模型下的方案较同类方案在陷门派生复杂度方面显著降低,而标准模型下的方案是同类最优方案的1/6,且格的维数、陷门尺寸和密文扩展率等参数均有所降低,计算效率明显优化.
[Abstract]:The hierarchical identity-based encryption hierarchical encryption (HIBE) system with fixed dimension on the lattice has been widely concerned because of its invariable dimension before and after the trapping school students. However, the complexity of the trapping school students is generally too high in this system. In order to solve this problem, the improved schemes under stochastic prophecy model and standard model are given respectively. Based on the MP12 trapdoor function, an optimized Zq reversible matrix extraction algorithm is proposed. Based on this algorithm, the trapdoor generation algorithm with fixed dimension and the MP12 trapdoor function are used to complete the scheme and the trapping gate generation stage. Then combined with dual Regev algorithm, the construction of HIBE scheme under stochastic prediction model is completed. And the binary tree encryption system is used to improve this scheme to HIBE scheme under the standard model. The security of the two schemes can be reduced to the insolvability of the LWE problem, in which the scheme under the stochastic prediction model satisfies the adaptive security, while the scheme under the standard model satisfies the selective security, and the strict security proof is given. The comparative analysis shows that under the same security, the scheme under the stochastic prediction model is significantly lower than the similar scheme in terms of the complexity of the trapping scheme, while the scheme under the standard model is 1 / 6 of the optimal scheme of the same kind and the dimension of the lattice. The trapdoor size and ciphertext expansion rate are reduced, and the computational efficiency is optimized.
【作者单位】： 河南理工大学计算机科学与技术学院;
【基金】：国家自然科学基金项目(61300216) 河南省科技厅基础与前沿技术研究计划项目(142300410147) 河南省教育厅自然科学研究项目(12A520021);河南省教育厅高等学校重点科研项目(16A520013)~~
【分类号】：TP309.7
[Abstract]:The hierarchical identity-based encryption hierarchical encryption (HIBE) system with fixed dimension on the lattice has been widely concerned because of its invariable dimension before and after the trapping school students. However, the complexity of the trapping school students is generally too high in this system. In order to solve this problem, the improved schemes under stochastic prophecy model and standard model are given respectively. Based on the MP12 trapdoor function, an optimized Zq reversible matrix extraction algorithm is proposed. Based on this algorithm, the trapdoor generation algorithm with fixed dimension and the MP12 trapdoor function are used to complete the scheme and the trapping gate generation stage. Then combined with dual Regev algorithm, the construction of HIBE scheme under stochastic prediction model is completed. And the binary tree encryption system is used to improve this scheme to HIBE scheme under the standard model. The security of the two schemes can be reduced to the insolvability of the LWE problem, in which the scheme under the stochastic prediction model satisfies the adaptive security, while the scheme under the standard model satisfies the selective security, and the strict security proof is given. The comparative analysis shows that under the same security, the scheme under the stochastic prediction model is significantly lower than the similar scheme in terms of the complexity of the trapping scheme, while the scheme under the standard model is 1 / 6 of the optimal scheme of the same kind and the dimension of the lattice. The trapdoor size and ciphertext expansion rate are reduced, and the computational efficiency is optimized.
【作者单位】： 河南理工大学计算机科学与技术学院;
【基金】：国家自然科学基金项目(61300216) 河南省科技厅基础与前沿技术研究计划项目(142300410147) 河南省教育厅自然科学研究项目(12A520021);河南省教育厅高等学校重点科研项目(16A520013)~~
【分类号】：TP309.7
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