循环安全的同态加密方案

赵秀凤; 付雨; 宋巍涛

doi:10.7544/issn1000-1239.2020.20200422

循环安全的同态加密方案

(信息工程大学密码工程学院郑州 450001) (zhao_xiu_feng@163.com)

基金项目: 国家自然科学基金项目(61601515,61702578,61902428)；河南省自然科学基金项目(162300410332)；军事类研究生资助课题(JYKT910372019307)

详细信息

中图分类号: TP391
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出版历程
- 发布日期: 2020-09-30

Circular Secure Homomorphic Encryption Scheme

(College of Cryptography Engineering, Information Engineering University, Zhengzhou 450001)

Funds: This work was supported by the National Natural Science Foundation of China (61601515, 61702578, 61902428), the Natural Science Foundation of Henan Province of China (162300410332), and the Military Graduate Project (JYKT910372019307).

摘要

摘要: 全同态加密可以对密文进行有效计算，是实现云计算、大数据以及机器学习中数据隐私安全的一项重要密码技术.利用“自举”技术可以构造全同态加密方案，但是使得运算密钥随着运算电路的深度线性增长，这是全同态加密方案实用性的一个主要瓶颈.然而，如果同态加密方案满足循环安全性，即可以对方案的私钥进行安全的加密，则可以使得运算密钥的规模独立于运算电路的深度.因此，满足循环安全性的同态加密方案是值得研究的一个问题.基于噪声淹没技术，给出了循环安全的公钥同态加密方案，并给出了安全性证明和参数设置；进一步，通过引入拒绝采样技术，给出了优化的循环安全公钥同态加密方案，在增加部分采样算法的代价下，将系统参数从超多项式级降低到多项式级，大大约减方案公钥和密文规模，从而可以有效改善密文运算的计算复杂性，提升同态加密方案的性能.
- 同态加密 /
- 循环安全 /
- 错误学习问题 /
- 噪声淹没技术 /
- 拒绝采样
Abstract: Homomorphic encryption allows evaluation on encrypted data, and it is an important encryption technique to realize data privacy security in cloud computing, big data and machine learning. Constructions of fully homomorphic encryption employ a “bootstrapping” technique, which enforces the public key of the scheme to grow linearly with the maximal depth of evaluated circuits. This is a major bottleneck with regards to the usability and the eciency of the scheme. However, the size of the public key can be made independent of the circuit depth if the somewhat homomorphic scheme can securely encrypt its own secret key. Achieving circular secure somewhat homomorphic encryption has been an interesting problem which is worth studying. This paper presents a circular secure public key homomorphic encryption scheme using noise flooding technique, and gives the security proof and parameter setting; furthermore, by introducing the refuse sampling technique, an optimized circular secure public key homomorphic encryption scheme is given, and the system parameters are reduced from the super polynomial level to the polynomial level, which greatly reduces the public key and ciphertext size. And then the computational complexity of ciphertext evaluation can be effectively improved and the performance of homomorphic encryption scheme be improved.
- homomorphic encryption /
- circular secure /
- learning with errors problem /
- noise flooding technique /
- reject sampling

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