| 摘要: |
| 全同态加密可以在不解密的条件下对密文进行有效运算,为云计算的数据隐私保护提供了一种理想的解决方案,但目前已有的全同态加密体制普遍存在公钥尺寸大、计算效率较低等问题.利用构造特征向量的思想,基于任意次数分圆环代数结构,提出全同态加密体制,并提出一种转换方法将该体制转换为基于身份的全同态加密体制.与已有体制相比,使用特征向量思想构造基于身份的体制有效地避免了计算密钥,实现了真正意义上基于身份的体制;相比次数为2的方幂特殊分圆环,使用任意次数分圆环最大会使加密体制的计算效率提升一倍,同时还可应用单指令多数据(single instruction multiple data,简称SIMD)技术进一步提升计算和存储效率. |
| 关键词: 全同态加密 特征向量 基于身份加密 任意分圆环 |
| DOI：10.13328/j.cnki.jos.004991 |
| 分类号: |
| 基金项目:河南省科技创新杰出青年基金(134100510002);河南省基础与前沿技术研究(142300410002);数学工程与先进计算国家重点实验室开放基金 |
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| Identity-Based Fully Homomorphic Encryption from Eigenvector |
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KANG Yuan-Ji1, GU Chun-Xiang1,2, ZHENG Yong-Hui1,2, GUANG Yan1
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1.Information Engineering University, Zhengzhou 450002, China;2.State Key Laboratory of Mathematical Engineering and Advanced Computing, Wuxi 214125, China
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| Abstract: |
| Fully homomorphic encryption allows valid operation on encrypted data without decrypting, providing a new solution to data confidentiality and privacy protection. However, current fully homomorphic encryption schemes are faced with challenges like large size of public key or low efficiency in calculation. To achieve an efficient fully homomorphic encryption scheme, this work provides an identity-based fully homomorphic encryption scheme employing the idea of eigenvector and arbitrary cyclotomic rings. Compared with existing scheme, this identity-based fully homomorphic encryption with eigenvector is able to successfully avoid the evaluation key, resulting a true identity-based scheme. Compared with special cyclotomic rings whose degree is power of 2, utilizing arbitrary cyclotomic rings may double the efficiency of encryption schemes and further improve the efficiency of calculation and memory using SIMD technique. |
| Key words: fully homomorphic crypto system eigenvector identity-based encryption arbitrary cyclotomic ring |
