密码学报2018，Vol.5Issue(3)：262-270,9.DOI:10.13868/j.cnki.jcr.000237
对称三进制编码的同态加密算术运算研究
Homomorphically Encrypted Arithmetic Operations over Symmetric Ternary Coding
摘要
Abstract
Fully homomorphic encryption can support the operation of any function of the ciphertext obtaining the result of the corresponding operation on the plaintext after decryption. Fully homomor- phic encryption application needs to encode the data into plaintext strings by encoding, and then homomorphic encrypts the plaintext into a ciphertext and performs the function operation on the ciphertext. Then, decrypts the ciphertext, and finally decode the decryption results into the data type in the application. Different coding schemes have a great influence on the efficiency of fully homo-morphic encryption applications. In this paper, the symmetric ternary coding method is applied to the fully homomorphic encryption application, and an integer symmetric ternary coding algorithm is designed. Meanwhile, the bitwise multiplication depth of integer addition, integer subtraction and in-teger multiplication under symmetric ternary coding is analyzed. Designed integer symmetric ternary coding arithmetic operations do not require the setting of the sign bits for the code, and the operation process is optimized according to the principle of reducing the number of bitwise multiplication depth. Finally, we use the HElib library to achieve the integer symmetric ternary encoding under the 10-bit homomorphism addition, homomorphic subtraction and homomorphism multiplication arithmetic, and the calculation period does not need Bootstrapping process. The experimental results show that the homomorphic arithmetic efficiency of integers under symmetric ternary coding is superior to binary coding.关键词
全同态加密/HElib/对称三进制编码/算术运算Key words
fully homomorphic encryption/HElib/symmetric ternary coding/arithmetic operation分类
信息技术与安全科学引用本文复制引用
傅海军,蔡斌,向宏,桑军..对称三进制编码的同态加密算术运算研究[J].密码学报,2018,5(3):262-270,9.基金项目
国家重点研发计划(2017YFB0802000) （2017YFB0802000）
国家自然科学基金(61472054) （61472054）
中央高校基本科研业务费(106112014CDJZR095501) （106112014CDJZR095501）
National Key Research and Development Program of China (2017YFB0802000) （2017YFB0802000）
National Natural Science Foundation of China (61472054) （61472054）
the Fundamental Research Funds for the Central Universities (106112014CD-JZR095501) （106112014CD-JZR095501）
