全同态加密函数库调试分析

Debug and Analysis on Fully Homomorphic Cryptography

本文选取了HElib库、FHE-CODE库和FHE-master基于三种不同算法的全同态加密程序,一方面,通过对程序本身的调试运行,不断更改噪声、运行时间、所占存储空间等运行参数,对程序性能进行动态比较分析.提高安全参数可以实现较高精度的加密,安全参数越高,则其对应的密文长度越长、所占存储空间越大,所以增加密文长度、重加密密文的长度等可以提高算法的安全级别.同时,减小模数、适当减小安全参数,可以减小噪声比并提高运行效率.另一方面,分析了三种软件对应的三种全同态算法:Gentry提出的理想格算法、DGHV算法和BGV算法,从安全性、有效性、实现程序以及相互联系对三种方案进行对比研究.其中,HElib库操作较为复杂,运行时间较长,但安全性较高,FHE-CODE代码的逻辑相对比较清晰,运行效率较高,FHE-master库利用文件读取操作实现了对于密文的检索功能,针对不同密钥读写操作效率参差不齐.本文一方面验证算法在理论研究的相关性质,另一方面从程序实现方面分析算法的相关属性,为全同态加密研究提供实践基础.

The studies on three FHE programs, HElib, FHE-CODE and FHE-master, which are based respectively on three different encryption algorithms, are conducted in this paper. Through debugging and parameter-modification, this paper analyzes noise, runtime and storage space, in order to verify the theoretical and practical properties of related algorithms. They can achieve high precision encryption by increasing security parameter. The longer security parameter, the longer the length of the cipher text, but the storage space occupied will be larger. As a result, increasing the length of the cipher text or encrypted cipher text can improve the security level of the algorithm. Meanwhile, reducing the modulus or reducing security parameters can reduce the noise and increase the efficiency. In addition, we analyze corresponding three kinds of algorithms: Gentry's algorithm, DGHV and BGV. We compare the three schemes from the aspects of security, efficiency, program implementation and their relations. It is concluded that HElib is more complex and secure, and the running time is longer. The logic of FHE-CODE is relatively clear, and it is more efficient. FHE-master achieves the retrieval of the cipher text by file read operation. By means of comparison, this paper is intended to provide advice for the studies of the FHE-encryption algorithms.